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Interactive Notebook Foldables, Organizers and Templates

Interactive Notebook Foldables, Organizers and Templates

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Math connects course 3 notebook foldables ebook Math connects course 3 notebook foldables ebook Document Transcript

  • Contributing AuthorDinah ZikeConsultantDouglas Fisher, Ph.D.Professor of Language and Literacy EducationSan Diego State UniversitySan Diego, CA®
  • Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may bereproduced or distributed in any form or by any means, or stored in a database or retrieval system, withoutthe prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storageor transmission, or broadcast for distance learning.Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027Printed in the United States of America.ISBN: 978-0-07-890238-3 Math Connects: Concepts, Skills, and Problem Solving, Course 3MHID: 0-07-890238-X Noteables™: Interactive Study Notebook with Foldables®1 2 3 4 5 6 7 8 9 10 009 17 16 15 14 13 12 11 10 09 08
  • Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ContentsFoldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . . . 21-1 A Plan for Problem Solving. . . . . . . . . . . 41-2 Variables, Expressions, and Properties . . 61-3 Integers and Absolute Value . . . . . . . . . 91-4 Adding Integers. . . . . . . . . . . . . . . . . . . 121-5 Subtracting Integers . . . . . . . . . . . . . . . 161-6 Multiplying and Dividing Integers. . . . . 181-7 Writing Equations . . . . . . . . . . . . . . . . . 211-8 Problem-Solving Investigation:Work Backward . . . . . . . . . . . . . . . . . . . 231-9 Solving Addition and SubtractionEquations . . . . . . . . . . . . . . . . . . . . . . . 241-10 Solving Multiplication andDivision Equations. . . . . . . . . . . . . . . . . 26Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . . 332-1 Rational Numbers . . . . . . . . . . . . . . . . . 352-2 Comparing and OrderingRational Numbers . . . . . . . . . . . . . . . . . 382-3 Multiplying Positive andNegative Fractions. . . . . . . . . . . . . . . . . 402-4 Dividing Positive and NegativeFractions. . . . . . . . . . . . . . . . . . . . . . . . . 422-5 Adding and SubtractingLike Fractions. . . . . . . . . . . . . . . . . . . . . 452-6 Adding and Subtracting UnlikeFractions. . . . . . . . . . . . . . . . . . . . . . . . . 472-7 Solving Equations with RationalNumbers. . . . . . . . . . . . . . . . . . . . . . . . . 492-8 Problem-Solving Investigation:Look for a Pattern . . . . . . . . . . . . . . . . 512-9 Powers and Exponents . . . . . . . . . . . . . 522-10 Scientific Notation. . . . . . . . . . . . . . . . . 54Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . . 623-1 Square Roots . . . . . . . . . . . . . . . . . . . . . 643-2 Estimating Square Roots. . . . . . . . . . . . 663-3 Problem-Solving Investigation:Use a Venn Diagram . . . . . . . . . . . . . . . 683-4 The Real Number System . . . . . . . . . . . 693-5 The Pythagorean Theorem . . . . . . . . . . 723-6 Using the Pythagorean Theorem . . . . . 753-7 Geometry: Distance on theCoordinate Plane. . . . . . . . . . . . . . . . . . 77Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . . 854-1 Ratios and Rates . . . . . . . . . . . . . . . . . . 874-2 Proportional and NonproportionalRelationships . . . . . . . . . . . . . . . . . . . . . 894-3 Rate of Change . . . . . . . . . . . . . . . . . . . 914-4 Constant Rate of Change . . . . . . . . . . . 944-5 Solving Proportions . . . . . . . . . . . . . . . 974-6 Problem-solving Investigation:Draw a Diagram . . . . . . . . . . . . . . . . . . 994-7 Similar Polygons . . . . . . . . . . . . . . . . . 1004-8 Dilations. . . . . . . . . . . . . . . . . . . . . . . . 1034-9 Indirect Measurement. . . . . . . . . . . . . 1054-10 Scale Drawings and Models . . . . . . . . 108Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 110Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 1165-1 Ratios and Percents . . . . . . . . . . . . . . . 1185-2 Comparing Fractions, Decimals,and Percents . . . . . . . . . . . . . . . . . . . . 1205-3 Algebra: The Percent Proportion . . . . 1235-4 Finding Percents Mentally . . . . . . . . . 1255-5 Problem-Solving Investigation:Reasonable Answers . . . . . . . . . . . . . . 1275-6 Percent and Estimation. . . . . . . . . . . . 1285-7 Algebra: The Percent Equation . . . . . 1315-8 Percent of Change. . . . . . . . . . . . . . . . 1335-9 Simple Interest. . . . . . . . . . . . . . . . . . . 137Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 139Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 1446-1 Line and Angle Relationships . . . . . . . 1466-2 Problem-Solving Investigation:Use Logical Reasoning. . . . . . . . . . . . . 1496-3 Polygons and Angles. . . . . . . . . . . . . . 1506-4 Congruent Polygons . . . . . . . . . . . . . . 1526-5 Symmetry . . . . . . . . . . . . . . . . . . . . . . . 1546-6 Reflections . . . . . . . . . . . . . . . . . . . . . . 1566-7 Translations . . . . . . . . . . . . . . . . . . . . . 159Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 162Math Connects, Course 3 iii
  • Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ContentsFoldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 1677-1 Circumference and Area of Circles. . . 1697-2 Problem-Solving Investigation:Solve a Simpler Problem . . . . . . . . . . . 1717-3 Area of Composite Figures . . . . . . . . . 1727-4 Three-Dimensional Figures . . . . . . . . . 1747-5 Volume of Prisms and Cylinders . . . . . 1777-6 Volume of Pyramids and Cones . . . . . 1807-7 Surface Area of Prisms andCylinders. . . . . . . . . . . . . . . . . . . . . . . . 1827-8 Surface Area of Pyramids . . . . . . . . . . 1857-9 Similar Solids . . . . . . . . . . . . . . . . . . . . 187Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 190Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 1968-1 Simplifying Algebraic Expressions . . . 1978-2 Solving Two-Step Equations . . . . . . . . 2008-3 Writing Two-Step Equations. . . . . . . . 2038-4 Solving Equations with Variableson Each Side. . . . . . . . . . . . . . . . . . . . . 2068-5 Problem-Solving Investigation:Guess and Check . . . . . . . . . . . . . . . . . 2088-6 Inequalities . . . . . . . . . . . . . . . . . . . . . 2098-7 Solving Inequalities by Addingor Subtracting . . . . . . . . . . . . . . . . . . . 2128-8 Solving Inequalities by Multiplyingor Dividing . . . . . . . . . . . . . . . . . . . . . . 214Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 216Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 2219-1 Sequences . . . . . . . . . . . . . . . . . . . . . . 2239-2 Functions . . . . . . . . . . . . . . . . . . . . . . . 2269-3 Representing Linear Functions . . . . . . 2299-4 Slope . . . . . . . . . . . . . . . . . . . . . . . . . . 2339-5 Direct Variation . . . . . . . . . . . . . . . . . . 2369-6 Slope-Intercept Form . . . . . . . . . . . . . 2399-7 Systems of Equations . . . . . . . . . . . . . 2419-8 Problem-Solving Investigation:Use a Graph . . . . . . . . . . . . . . . . . . . . . 2449-9 Scatter Plots . . . . . . . . . . . . . . . . . . . . . 245Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 248Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 25410-1 Linear and Nonlinear Functions . . . . . 25510-2 Graphing Quadratic Functions . . . . . . 25810-3 Problem-Solving Investigation:Make a Model . . . . . . . . . . . . . . . . . . . 26010-4 Graphing Cubic Functions. . . . . . . . . . 26110-5 Multiplying Monomials. . . . . . . . . . . . 26410-6 Dividing Monomials . . . . . . . . . . . . . . 26610-7 Powers of Monomials . . . . . . . . . . . . . 26910-8 Roots of Monomials . . . . . . . . . . . . . . 271Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 273Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 27811-1 Problem-Solving Investigation:Make a Table . . . . . . . . . . . . . . . . . . . . 28011-2 Histograms. . . . . . . . . . . . . . . . . . . . . . 28111-3 Circle Graphs . . . . . . . . . . . . . . . . . . . . 28411-4 Measures of Central Tendencyand Range . . . . . . . . . . . . . . . . . . . . . . 28811-5 Measures of Variation. . . . . . . . . . . . . 29111-6 Box-and-Whisker Plots . . . . . . . . . . . . 29411-7 Stem-and-Leaf Plots . . . . . . . . . . . . . . 29711-8 Select an Appropriate Display . . . . . . 301Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 303Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 30812-1 Counting Outcomes . . . . . . . . . . . . . . 31012-2 Probability of Compound Events . . . . 31312-3 Experimental andTheoretical Probability . . . . . . . . . . . . 31612-4 Problem-Solving Investigation:Act It Out . . . . . . . . . . . . . . . . . . . . . . . 32012-5 Using Sampling to Predict. . . . . . . . . . 321Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 324iv Math Connects, Course 3
  • Math Connects, Course 3 vCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Organizing Your FoldablesHave students make this Foldable to help themorganize and store their chapter Foldables.Begin with one sheet of 11" × 17" paper.FoldFold the paper in half lengthwise. Then unfold.Fold and GlueFold the paper in half widthwise and glue all of the edges.Glue and LabelGlue the left, right, and bottom edges of the Foldableto the inside back cover of your Noteables notebook.Reading and Taking Notes As you read and study each chapter, recordnotes in your chapter Foldable. Then store your chapter Foldables insidethis Foldable organizer.
  • ®Chapter3Math Connects, Course 3 61Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R3 Real Numbers andthe Pythagorean TheoremUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with two sheets of 81_2" by 11" notebookpaper.Fold one in half fromtop to bottom. Cutalong fold from edgesto margin.Fold the other sheetin half from topto bottom. Cut alongfold between margins.Insert first sheetthrough secondsheet and align folds.Label each page with Chapter 3Real Numbersand thePythagoreanTheorema lesson number and title.NOTE-TAKING TIP: When you take notes, clarifyterms, record concepts, and write examples foreach lesson. You may also want to list ways inwhich the new concepts can be used in yourdaily life.061-083_CH03_881084.indd 61 11/19/07 12:58:46 PM62 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R3BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 3.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleabscissa[ab-SIH-suh]conversecoordinate planehypotenuseirrational numberlegsordered pairordinate[OR-din-it]originperfect square061-083_CH03_881084.indd 62 11/19/07 12:58:47 PMvi Math Connects, Course 3This note-taking guide is designed to help you succeed inMath Connects, Course 3. Each chapter includes:The Chapter Openercontains instructions andillustrations on how tomake a Foldable that willhelp you to organizeyour notes.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A Note-Taking Tipprovides a helpfulhint you can usewhen taking notes.The Build Your Vocabularytable allows you to writedefinitions and examplesof important vocabularyterms together in oneconvenient place.Within each chapter,Build Your Vocabularyboxes will remind youto fill in this table.
  • Math Connects, Course 3 75Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–6 Using the Pythagorean TheoremEXAMPLE Use the Pythagorean TheoremRAMPS A ramp to a newlyconstructed building mustbe built according to theguidelines stated in theAmericans with DisabilitiesAct. If the ramp is 24.1feet long and the top ofthe ramp is 2 feet off theground, how far is the bottomof the ramp from the baseof the building?Notice the problem involves a right triangle. Use thePythagorean Theorem.24.12= a2+ 22 Replace c with 24.1 andb with 2.= a2+ Evaluate 24.12and 22.- = a2= - Subtract from each side.= a2Simplify.= a Definition of square root≈ a Simplify.The end of the ramp is about from the base ofthe building.Check Your Progress If a truck ramp is 32 feet long andthe top of the ramp is 10 feet off the ground, how far is the endof the ramp from the truck?MAIN IDEA• Solve problems usingthe PythagoreanTheorem.ORGANIZE ITOn Lesson 3-6 of yourFoldable, explain thePythagorean Theorem inyour own words and givean example of how itmight be used in areal-life situation.Chapter 3Real Numbersand thePythagoreanTheorem®061-083_CH03_881084.indd 75 11/19/07 12:58:52 PMMath Connects, Course 3 viiFPO - will bereplaced withnew page 65, ifneeded.3–1Math Connects, Course 3 65Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find each square root.a. √64b. - 25_144c. ±√2.25EXAMPLE Use an Equation to Solve a ProblemMUSIC The art work of the square picture in a compactdisc case is approximately 14,161 mm2 in area. Find thelength of each side of the square.The area is equal to the square of the length of a side.Let A = the area and let s = the length of the side A = s214,161 = s2Write the equation.= √s2Take the square root of each side.The length of a side of a compact disc case is aboutmillimeters since distance cannot be negative.Check Your Progress A piece of art is a square picture thatis approximately 11,025 square inches in area. Find the lengthof each side of the square picture.ORGANIZE ITOn Lesson 3-1 of yourFoldable, explain howto find the square rootof a number and give anexample.Chapter 3Real Numbersand thePythagoreanTheorem®HOMEWORKASSIGNMENTPage(s):Exercises:061-083_CH03_881084.indd 65 11/19/07 12:58:47 PMCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Examples parallel theexamples in your textbook.Check Your Progressexercises allow you tosolve similar exerciseson your own.Lessons cover the content ofthe lessons in your textbook.As your teacher discusses eachexample, follow along andcomplete the fill-in boxes.Take notes as appropriate.Foldables featurereminds you totake notes in yourFoldable.80 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R3STUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 3 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 3, go toglencoe.comYou can use your completedVocabulary Builder(pages 62–63) to help you solvethe puzzle.3-1Square RootsComplete each sentence.1. The principle square root is the square rootof a number.2. To solve an equation in which one side of the square is a squaredterm, you can take the of each side of theequation.Find each square root.3. √900 4. -√36_495. -√625 6. √25_1213-2Estimating Square RootsDetermine between which two consecutive whole numberseach value is located.7. √23 8. √599. √27 10. √18061-083_CH03_881084.indd 80 11/19/07 12:58:54 PMBringing It All TogetherStudy Guide reviewsthe main ideas and keyconcepts from each lesson.
  • Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.NOTE-TAKING TIPSviii Math Connects, Course 3Your notes are a reminder of what you learned in class. Taking good notes canhelp students succeed in mathematics. The following tips will help you takebetter classroom notes.• Before class, ask what your teacher will be discussing in class. Reviewmentally what you already know about the concept.• Be an active listener. Focus on what your teacher is saying. Listen forimportant concepts. Pay attention to words, examples, and/or diagramsyour teacher emphasizes.• Write your notes as clear and concise as possible. The following symbolsand abbreviations may be helpful in your note-taking.Word or PhraseSymbol orAbbreviationWord or PhraseSymbol orAbbreviationfor example e.g. not equal ≠such as i.e. approximately ≈with w/ therefore ∴without w/o versus vsand + angle ∠• Use a symbol such as a star (★) or an asterisk (*) to emphasize importantconcepts. Place a question mark (?) next to anything that you do notunderstand.• Ask questions and participate in class discussion.• Draw and label pictures or diagrams to help clarify a concept.• When working out an example, write what you are doing to solve theproblem next to each step. Be sure to use your own words.• Review your notes as soon as possible after class. During this time, organizeand summarize new concepts and clarify misunderstandings.Note-Taking Don’ts• Don’t write every word. Concentrate on the main ideas and concepts.• Don’t use someone else’s notes as they may not make sense.• Don’t doodle. It distracts you from listening actively.• Don’t lose focus or you will become lost in your note-taking.
  • ®Chapter1Math Connects, Course 3 1Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R1Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a plain piece of 11" × 17" paper.Fold the paper in sixths lengthwiseOpen and Fold a 4" tab along theshort side. Then fold the rest in half.Label Draw lines along the folds and labelas shown.NOTE-TAKING TIP: When taking notes, it may behelpful to explain each idea in words and give oneor more examples.Algebra: Integers
  • 2 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R1BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 1.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleabsolute valueadditive inversealgebraalgebraic expression[AL-juh-BRAY-ihk]conjecturecoordinatecounterexampledefine a variableequation[ih-KWAY-zhuhn]evaluateinequality
  • Math Connects, Course 3 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleinteger[IHN-tih-juhr]inverse operationsnegative numbernumerical expressionoppositesorder of operationspositive numberpowerspropertysolutionsolvevariable
  • 4 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.1–1EXAMPLES Use the Four-Step PlanHOME IMPROVEMENT The Vorhees family plans to paintthe walls in their family room. They need to cover 512square feet with two coats of paint. If a 1-gallon can ofpaint covers 220 square feet, how many 1-gallon cans ofpaint do they need?UNDERSTAND Since they will be using coats of paint,we must the area to be painted.PLAN They will be covering × squarefeet or square feet. Next, divideby to determine how manycans of paint are needed.SOLVE ÷ =CHECK Since they will purchase a whole numberof cans of paint, round to .They will need to purchase cans of paint.Check Your Progress Jocelyn plans to paint her bedroom.She needs to cover 400 square feet with three coats of paint.If a 1-gallon can of paint covers 350 square feet, how many1-gallon cans of paint does she need?Some problem solving strategies require you to make anor conjecture.BUILD YOUR VOCABULARY (pages 2–3)MAIN IDEA• Solve problems usingthe four-step plan.ORGANIZE ITSummarize the four-stepproblem-solving planin words and symbols.Include an example ofhow you have used thisplan to solve a problem.®A Plan for Problem Solving
  • 1–1Math Connects, Course 3 5Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. GEOGRAPHY Study the table. The five largest states intotal area, which includes land and water, are shown.Of the five states shown, which one has the smallestarea of water?Largest States in AreaState Land Area (mi2) Total Area (mi2)Alaska 570,374 615,230Texas 261,914 267,277California 155,973 158,869Montana 145,556 147,046New Mexico 121,364 121,598Source: U.S. Census BureauUNDERSTAND What do you know? You are given the total areaand the land area for five states. What are youtrying to find? You need to find the water area.PLAN To determine the water area,the from thefor each state.SOLVE Alaska = 615,230 - 570,374 =Texas = 267,277 - 261,914 =California = 158,869 - 155,973 =Montana = 147,046 - 145,556 =New Mexico = 121,598 - 121,364 =CHECK Compare the water area for each state todetermine which state has the least water area.has the least water area withsquare miles.Check Your Progress Refer to Example 2. How many timeslarger is the land area of Alaska than the land area of Montana?HOMEWORKASSIGNMENTPage(s):Exercises:REMEMBER ITAlways check tomake sure your answeris reasonable. You cansolve the problem againif you think your answeris not correct.
  • 6 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A variable is a , usually a letter, used torepresent a .An algebraic expression contains a , anumber, and at least one symbol.When you substitute a number for the , analgebraic expression becomes a numerical expression.To evaluate an expression means to find itsvalue.To avoid confusion, mathematicians have agreed on acalled the order of operations.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLES Evaluate Algebraic ExpressionsEvaluate each expression if q = 5, r = 6, and s = 3.4(r - s)24(r - s)2= 4( - )2Replace with 6 andwith 3.= 4( )2Perform operations in thefirst.= 4 Evaluate the .= Simplify.MAIN IDEA• Evaluate expressionsand identify properties.1–2 Variables, Expressions, and PropertiesKEY CONCEPTOrder of Operations1. Do all operationswithin groupingsymbols first; startwith the innermostgrouping symbols.2. Evaluate all powersbefore otheroperations.3. Multiply and dividein order from left toright.4. Add and subtract inorder from left toright.
  • 1–2Math Connects, Course 3 7Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Expressions such as 72and 23are called powers andrepresent repeated .BUILD YOUR VOCABULARY (pages 2–3)q2- 4r - 1q2- 4r - 1 = - 4 - 1 Replace with 5 andwith 6.Evaluate beforeother operations..Add and subtract in orderfrom left to right..= - 4(6) - 1= 25 - - 1= -=6q_5sThe fraction bar is a grouping symbol. Evaluate the expressionsin the numerator and denominator separately before dividing.6q_5s=6 (5)_5 (3)Replace with 5 and with 3.= 30_15Do all first.= .Check Your Progress Evaluate each expression.a. 2(a + b)2 if a = 3 and b = 2b. b2+ 3c - 5 if b = 4 and c = 2c. 3s_q + 4if q = 2 and s = 42
  • 1–28 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The branch of mathematics that involveswith variables is called algebra.Properties are sentences that are true forany numbers.A counterexample is an example that shows that aconjecture is .BUILD YOUR VOCABULARY (pages 2–3)REMEMBER ITCommutativePropertya + b = b + aa · b = b · aAssociative Propertya + (b + c) = (a + b) + ca · (b · c) = (a · b) · cDistributive Propertya(b + c) = ab + aca(b - c) = ab - acIdentity Propertya + 0 = aa · 1 = aEXAMPLES Identify PropertiesName the property shown by 12 · 1 = 12.Multiplying by 1 does not change the number.This is the Property of Multiplication.Check Your Progress Name the property shown by3 · 2 = 2 · 3.EXAMPLES Find a CounterexampleState whether the following conjecture is true or false.If false, provide a counter example.The sum of an odd number and an even number isalways odd.This conjecture is .Check Your Progress State whether the followingconjecture is true or false. If false, provide a counterexample.Division of whole numbers is associative.HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 9Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 1–3 Integers and Absolute ValuesA negative number is a number than zero.numbers, positive numbers, andare members of the set of integers.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Compare Two IntegersReplace the with < or > to make -2 -1 atrue sentence.The number line shows that -2 is than -1, since itlies to the of -1. So, write -2 -1.Check Your Progress Replace each with < or > tomake a true sentence.a. -2 2b. -4 -6The that corresponds to a iscalled the coordinate of that point.A sentence that two different numbersor quantities is called an inequality.BUILD YOUR VOCABULARY (pages 2–3)MAIN IDEA• Compare and orderintegers and findabsolute value.
  • 1–310 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The absolute value of a number is the distance thenumber is from on the number line.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLES Expressions with Absolute ValueEvaluate each expression.REMEMBER ITThe absolute valueof a number is not thesame as the opposite ofa number. Rememberthat the absolute valueof a number cannot benegative.⎪5⎥ - ⎪5⎥The graph of 5 is units from 0 on the number line.So, ⎪5⎥ = . Then subtract 5 units.Thus, ⎪ 5⎥ - ⎪5⎥ =⎪6⎥ - ⎪-5⎥⎪6⎥ - ⎪-5⎥ = -⎪-5⎥ The absolute value of 6 is .= 6 - ⎪-5⎥ == Simplify.Evaluate ⎪6 - 9⎥ - ⎪5 - 3⎥ .⎪6 - 9⎥ - ⎪5 - 3⎥ = ⎪ ⎥- ⎪ ⎥ Simplify the absolutevalue expressions.= - ⎪2⎥ The absolute value of-3 is .= 3 - The absolute value of2 is .= Simplify.
  • 1–3Math Connects, Course 3 11Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Evaluate ⎪x⎥ + 13 if x = -4.⎪x⎥ + 13 = ⎪ ⎥+ 13 Replace x with .= + 13 ⎪-4⎥ == Simplify.Check Your Progress Evaluate each expression.a. ⎪-3⎥ - ⎪3⎥ b. ⎪9⎥ - ⎪-6 ⎥ c. ⎪4 - 7⎥ - ⎪11 - 6⎥d. Evaluate ⎪x⎥ + 7 if x = -2.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 12 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.1–4EXAMPLE Add Integers with the Same SignAdd -8 + (-4).Use a number line.Start at zero.Move units to the left.From there, move 4 units .So, -8 + (-4) = .Check Your Progress Add using a number lineor counters.KEY CONCEPTAdding Integers withthe Same Sign To addintegers with the samesign, add their absolutevalues. Give the result thesame sign as the integers.a. -3 + (-6)b. -13 + (-12)Adding IntegersMAIN IDEA• Add integers.
  • 1–4Math Connects, Course 3 13Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Add Integers with Different SignsORGANIZE ITExplain and giveexamples of how to addintegers with the samesign and how to addintegers with a differentsigns.®Find 4 + (-6).Use a number line.Start at .Move 4 units .From there, move units left.So, 4 + (-6) = .Find -5 + 9.Use a number line.Start at .Move units .From there, move units left .So, -5 + 9 = .KEY CONCEPTSAdding Integers withDifferent Signs To addintegers with differentsigns, subtract theirabsolute values. Givethe result the same signas the integer with thegreater absolute value.Find -33 + 16.-33 + 16 = To find -33 + 16, subtract⎪16⎥ from ⎪-33⎥.The sum isbecause ⎪-33⎥ > ⎪16⎥.
  • 1–414 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Add.a. 3 + (-5)b. -6 + 8c. 25 + (-15)Two numbers with the same butdifferent signs are called opposites.An integer and its are also calledadditive inverses.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Add Three or More IntegersFind 2 + (-5) + (-3).2 + (-5) + (-3) = 2 + [ + (-3)] Associative Property= 2 + Order of operations= Simplify.
  • 1–4Math Connects, Course 3 15Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find each sum.a. 3 + (-6) + (-2) b. -10 + 5 + 10 + 7EXAMPLE Add Three or More IntegersSTOCKS An investor owns 50 shares in a video-gamemanufacturer. A broker purchases 30 shares more forthe client on Tuesday. On Friday, the investor asks thebroker to sell 65 shares. How many shares of this stockwill the client own after these trades are completed?Selling a stock decreases the number of shares, so the integerfor selling is .Purchasing new stock increases the number of shares, so theinteger for buying is .Add these integers to the starting number of shares to find thenew number of shares.50 + + ( )= (50 + )+ ( ) Associative Property= + (-65) 50 + == Simplify.Check Your Progress MONEY Jaime gets an allowanceof $5. She spends $2 on video games and $1 on lunch. Her bestfriend repays a $2 loan and she buys a $3 pair of socks. Howmuch money does Jaime have left?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 16 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.1–5 Subtracting IntegersEXAMPLES Subtract a Positive IntegerFind 2 - 6.2 - 6 = 2 + (-6) To subtract 6, add .= Add.Find -7 - 5.-7 - 5 = 7 (-5) To subtract , add -5.= -12 Add.KEY CONCEPTSubtracting IntegersTo subtract an integer,add its opposite oradditive inverse.EXAMPLES Subtract a Negative IntegerFind 11 - (-8).11 - (-8) = + 8 To subtract -8, add .= Add.WEATHER The overnight temperature at a researchstation in Antarctica was -13°C, but the temperaturerose to 2°C during the day, what was the differencebetween the temperatures?2 - (-13) = 2 To subtract -13, .= 15 Add.The difference between the temperatures was .Check Your Progress Subtract.ORGANIZE ITRecord in your Foldablehow to subtract integers.Be sure to includeexamples.®a. 3 - 7 b. -6 - 2c. 15 - (-3) d. -7 - (-11)MAIN IDEA• Subtract integers.
  • 1–5Math Connects, Course 3 17Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Evaluate Algebraic ExpressionsEvaluate each expression if p = 6, q = -3, and r = -7.12 - r12 - r = 12 - Replace r with .= 12 + To subtract add .= Add.q - p2q - p = -3 - (6)2 Replace q with andp with .= -3 + To subtract , add .= Add.Check Your Progress Evaluate each expression ifa = 3, b = -6, and c = 2.a. 10 - c b. b - aWRITE ITExplain why -b does notnecessarily mean that thevalue of -b is negative.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 18 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Multiplying and Dividing IntegersEXAMPLE Multiply Integers with Different SignsFind 8(-4).8(-4) =The factors have signs. The product is.EXAMPLE Multiply Integers with the Same SignFind -12(-12).-12(-12) =The factors have the sign. The productis .EXAMPLE Multiply More Than Two IntegersFind 6(-2)(-4).6(-2)(-4) = [6(-2)] Property= -12 6(-2) == -12(-4) =Check Your Progress Multiply.a. 6(-3) b. -2(6)c. -8(-8) d. 5(-3)(-2)1–6MAIN IDEA• Multiply and divideintegers.KEY CONCEPTSMultiplying Two IntegersThe product of twointegers with differentsigns is negative.The product of twointegers with the samesign is positive.Dividing Integers Thequotient of two integerswith different signs isnegative.The quotient of twointegers with the samesign is positive.REMEMBER ITDecide on the signof the product beforemultiplying. If thenumber of negativesis even the product ispositive. If the numberof negatives is odd theproduct is negative.
  • 1–6Math Connects, Course 3 19Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Divide IntegersFind 30 ÷ (-5).30 ÷ -5 =The dividend and the divisor have signs.The quotient is .Check Your Progress Divide.a. 36 ÷ (-6) b. -30_-5EXAMPLE Evaluate Algebraic ExpressionsEvaluate -3x - (-4y) if x = -10 and y = -4.3x - (-4y)= 3( )- [-4( )] Replace x withand y with .= - 3(-10) =-4(-4) == -30 + To subtract , add.= Add.Check Your Progress Evaluate 2a - (-3b) if a = -6 andb = -4.ORGANIZE ITDescribe why theproduct or quotient oftwo integers with thesame sign is positiveand the product orquotient of two integerswith different signs isnegative.®
  • 1–620 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find the Mean of a Set of IntegersGOLF Justin scored the following points for a roundof nine holes of golf. Find Justin’s average score forthe round.Hole 1 2 3 4 5 6 7 8 9Score +4 +3 0 -1 +2 -1 +2 +1 -1To find the mean of a set of numbers, find the sum of thenumbers. Then divide the result by how many numbers thereare in the set.4 + 3 + 0 + (-1) + 2 + (-1) + 2 + 1 + (-1)________9= __9= 1Justin’s average score was .Check Your Progress Average Low TemperaturesMonth Temp. (°C)Jan. -20Feb. -15March -5April 10May 25June 31July 41Aug. 38Sept. 34Oct. 19Nov. 3Dec. -15The table shows a set of recordlow temperatures. Find themean (average) of all12 temperatures.HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 21Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 1–7 Writing EquationsA mathematical sentence that contains ansign (=) is called an equation. When you choosea variable and an unknown quantity for the variable torepresent, this is called defining the variable.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Write an Algebraic EquationCONSUMER ISSUES The cost of a book purchased onlineplus $5 shipping and handling comes to a total of $29.Write an equation to model this situation.Words The price of a book plus $5 shipping is $29.Variable Let b represent the price of the book.The priceof a book plus $5 shipping is $29.Equation + = 29The equation is .Check Your Progress Write the price of a toy plus $6shipping is $35 as an algebraic equation.EXAMPLE Write an Equation to Solve a ProblemNUTRITION A box of oatmeal contains 10 individualpackages. If the box contains 30 grams of fiber, writean equation to find the amount of fiber in one packageof oatmeal.Words Ten packages of oatmeal contain 30 grams of fiber.Variable Let f represent the grams of fiber per package.Ten packages 30 gramsof oatmeal contain of fiber.Equation = 30The equation is .MAIN IDEA• Write algebraicequations from verbalsentences and problemsituations.REMEMBER ITIt is often helpful toselect letters that caneasily be connectedto the quantity theyrepresent. For example,age = a.
  • 1–722 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress A particular box of cookies contains10 servings. If the box contains 1,200 Calories, write anequation to find the number of Calories in one serving ofcookies.EXAMPLETEST EXAMPLE The eighth grade has $35 less inits treasury than the seventh grade has. Given s, thenumber of dollars in the seventh-grade treasury, whichequation can be used to find e, the number of dollars inthe eighth-grade treasury?A e = 35 - sB e = s - 35C e = s ÷ 35D e = 35sRead the ItemThe phrase $35 less . . . than the seventh grade indicates.Solve the ItemThe amount of moneyin the eighth-gradetreasury isthe amount of money inthe seventh-gradetreasury less $35.e = s - 35The solution is .Check Your Progress MULTIPLE CHOICE Helena andher friends ordered 3 bags of popcorn and 4 drinks from thesnack stand. Which equation could be used to find c, the totalcost if p represents the cost of a bag of popcorn and d representsthe cost of a drink?F c = 7(p + d) H c = 3p + 4dG c = 7(p - d) J c = 7p + 7dExplain why it isimportant to read a wordproblem more than oncebefore attempting tosolve it.REVIEW ITHOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 23Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 1–8 Problem-Solving Investigation:Work BackwardEXAMPLESCHEDULING Wendie is meeting some friends for amovie and a dinner. She needs to be finished with dinnerby 7:30 P.M. to make it home by 8:00 P.M. The movie runsfor 90 minutes, and she wants to have at least 1 hour fordinner. If it takes 20 minutes to get from the theater tothe restaurant, what is the latest starting time she canchoose for the movie she wants to see?UNDERSTAND You know what time Wendie needs tohead home. You know the time it takesfor each event. You need to determinePLAN Start with the and workbackward.SOLVE Finish dinner 7:30 P.M.Go back 1 hour for dinner.Go back for travel. 6:10 P.M.Go back 90 minutes for the movie.CHECK Assume the movie starts at Workfoward, adding the time for each event.The latest starting time for the movie isCheck Your Progress SHOPPING Mia spent $9.50 ata fruit stand, then spent three times that amount at thegrocery store. She had $7.80 left. How much money did shehave initially?MAIN IDEA• Solve problems byworking backward.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 24 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.1–9 Solving Addition and Subtraction EquationsWhen you solve an equation, you are trying to find thevalues of the variable that makes the equation .A solution is the value of the variable that makes thevariable .BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Solve an Addition EquationKEY CONCEPTSSubtraction Property ofEquality If you subtractthe same number fromeach side of an equation,the two sides remainequal.Addition Property ofEquality If you add thesame number to eachside of an equation, thetwo sides remain equal.Solve 7 = 15 + c.METHOD 1 Vertical Method7 = 15 + c Write the equation.7 = 15 + c Subtract from each side._______-15 = -15= c 7 - 15 = ; 15 - 15 =METHOD 2 Horizontal Method7 = 15 + c Write the equation.7 - = 15 + c - Subtract from each side.= c 7 - 15 = ; and- 15 = 0Check Your Progress Solve 6 = 11 + a.MAIN IDEA• Solve equations usingthe Subtraction andAddition Properties ofEquality.
  • 1–9Math Connects, Course 3 25Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Addition and subtraction are called inverse operationsbecause they “undo” each other.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Solve an Addition EquationOCEANOGRAPHY At high tide, the top of a coralformation is 2 feet above the surface of the water.This represents a change of -6 feet from the height ofthe coral at low tide. Write and solve an equation todetermine h, the height of the coral at low tide.WordsVariableEquationThe height at low tide plus the change is theheight at high tide.Let h represent the height at low tide.h + (-6) = 2h + -6 = 2 Write the equation.h + (-6) - = 2 - Subtract from eachside.h = Simplify.The height of the coral at low tide is 8 feet.EXAMPLE Solve a Subtraction EquationSolve -5 = z - 16.Use the horizontal method.-5 = z - 16 Write the equation.-5 + = z - 16 + Add to each side.= z -16 + 16 = and+ 16 = 11.Check Your Progress Solve -6 = x - 12.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITCompare how to solvean equation involvingwhole numbers andan equation involvingintegers.®
  • 26 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Solve a Multiplication EquationSolve 7z = -49.7z = -49 Write the equation.7z__= -49__ each side by .z = 7 ÷ 7 = , -49 ÷ 7 == Identity Property; 1z =EXAMPLE Solve a Division EquationSolve c_9= -6.c_9= -6 Write the equation.c_9= -6 Multiply each side by .c = -6 =EXAMPLE Use an Equation to Solve a ProblemSURVEYING English mathematician Edmund Gunterlived around 1600. He invented the chain, which wasused as a unit of measure for land and deeds. One chainequals 66 feet. If the south side of a property measures330 feet, how many chains long is it?WordsVariableEquationOne chain equals 66 feet.Let c = the number of chains in feet.Measurement 66 times theof property is number of chains330 =1–10 Solving Multiplication and Division EquationsMAIN IDEA• Solve equations byusing the Divisionand MultiplicationProperties of Equality.KEY CONCEPTSDivision Property ofEquality If you divideeach side of an equationby the same nonzeronumber, the two sidesremain equal.Multiplication Propertyof Equality If youmultiply each side of anequation by the samenumber, the two sidesremain equal.
  • 1–10Math Connects, Course 3 27Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Solve the equation.330 = 66c Write the equation.330__ = 66c__ Divide each side by .= 330 ÷ =The number of chains in 330 feet is .Check Your Progressa. Solve 8a = -64. b. Solve x_5= -10.c. Most horses are measured in hands. One hand equals4 inches. If a horse measures 60 inches, how manyhands is it?ORGANIZE ITOn your Foldable table,explain how to solvemultiplication equationsusing the multiplicationproperties of equality.®HOMEWORKASSIGNMENTPage(s):Exercises:
  • 28 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R1STUDY GUIDE® VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 1 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 1, go to:glencoe.comYou can use your completedVocabulary Builder(pages 2–3) to help you solvethe puzzle.1-1A Plan for Problem SolvingUse the four step plan to solve the problem.1. Lisa plans to redecorate her bedroom. Each wall is 120 squarefeet. Three walls need a single coat of paint and the fourth wallneeds a double coat. If each can of paint will cover 200 square feet,how many gallons of paint does Lisa need?1-2Variables, Expressions, and Properties2. Number the operations in the correct order for simplifying2 + 4 (9 - 6 ÷ 3).addition subtractionmultiplication division3. Describe how the expressions 2 + 5 and 5 + 2 are different.Then determine whether the two expressions are equal to eachother. If the expressions are equal, name the property that saysthey are equal.
  • Math Connects, Course 3 29Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 BRINGING IT ALL TOGETHER1-3Integers and Absolute ValuesComplete each sentence with either left or right to make a truesentence. Then write a statement comparing the two numberswith either <, or >.4. -45 lies to the of 0 on a number line.5. 72 lies to the of 0 on a number line.6. -3 lies to the of -95 on a number line.7. 6 lies to the of -7 on a number line.1-4Adding IntegersDetermine whether you add or subtract the absolute values ofthe numbers to find the sum. Give reasons for your answers.8. 4 + 89. -3 + 510. 9 + (-12)11. -23 + (-16)1-5Subtracting IntegersRewrite each difference as a sum. Then find the sum.12. 2 - 913. -3 - 814. 10 - (-12)15. -5 - (-16)
  • 30 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 BRINGING IT ALL TOGETHER1-6Multiplying and Dividing IntegersFind each product or quotient.16. 9(-2) 17. -6(-7)18. 12 ÷ (-4) 19. -35 ÷ (-7)1-7Writing EquationsDetermine whether each situation requires addition,subtraction, multiplication or division.20. Find the difference in the cost of a gallon of premium gasoline andthe cost of a gallon of regular gasoline.21. Find the flight time after the time has been increased by 15minutes.1-8Problem Solving Investigation: Work Backward22. LOANS Alonso bought supplies for a camping trip. He has about$2 left. He spent $15.98 at the grocery store, then spent $21.91 atthe sporting goods store. He also spent a third of his money for adeposit on the campsite. About how much money did Alonso haveoriginally?1-9Solving Addition and Subtraction EquationsSolve each equation.23. x + 6 = 9 24. s - 5 = 14 25. 11 + m = 331-10Solving Multiplication and Division EquationsSolve each equation.26. 8r = 32 27. 3 = x_728. -9 = -9g
  • Math Connects, Course 3 31Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ChecklistC H A P T E R1Student Signature Parent/Guardian SignatureTeacher SignatureARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without using mynotes or asking for help.• You are probably ready for the Chapter Test.• You may want take the Chapter 1 Practice Test onpage 79 of your textbook as a final check.I used my Foldable or Study Notebook to complete the review ofall or most lessons.• You should complete the Chapter 1 Study Guide and Review onpages 74–78 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 1 Practice Test onpage 79 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 1 Foldable.• Then complete the Chapter 1 Study Guide and Review onpages 74–78 of your textbook.• If you are unsure of any concepts or skills, refer back to the specificlesson(s).• You may also want to take the Chapter 1 Practice Test onpage 79 of your textbook.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 1.
  • ®32 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R2Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with five sheets of 81_2" × 11" paper.Place 5 sheets of paper3_4inch apart.Roll up bottom edges.All tabs should be thesame size.Staple along the fold.Label the tabs with the2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numberslesson numbers.NOTE-TAKING TIP: As you study a lesson, writedown questions you have, comments andreactions, short summaries of the lesson, and keypoints that are highlighted and underlined.Algebra: Rational Numbers
  • Chapter2Math Connects, Course 3 33Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R2BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 2.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplebar notationbasedimensional analysisexponentlike fractionsmultiplicative inverses(continued on the next page)
  • 34 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplepowerrational numberreciprocalsrepeating decimalscientific notationterminating decimalunlike fractions
  • Math Connects, Course 3 35Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 2–1 Rational NumbersA rational number is any number that can be expressed inthe form a_bwhere a and b are and b ≠ 0.A decimal like 0.0625 is a terminating decimal becausethe division ends, or terminates, when theis 0.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLE Write a Fraction as a DecimalKEY CONCEPTRational NumbersA rational number isany number that can beexpressed in the forma_b, where a and b areintegers and b ≠ 0.Write 3_16as a decimal.3_16means 3 16.0.187516 3.0000 Divide 3 by 16.__16140__128120__11280__80 Division ends when the is 0.0You can also use a calculator.The fraction 3_16can be written as .Check Your Progress Write 1_16as a decimal.MAIN IDEA• Express rationalnumbers as decimalsand decimals asfractions.
  • 2–136 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A like 1.6666 . . . is called a repeating decimal.Since it is not possible to show all of the , youcan use bar notation to show that the 6 .BUILD YOUR VOCABULARY (pages 33–34)EXAMPLE Write a Mixed Number as a DecimalWRITE ITExplain how you decidewhere the bar is placedwhen you use barnotation for a repeatingdecimal.Write -3 2_11as a decimal.You can write -3 2_11as -35_11or 35_-11. To change -3 2_11to adecimal, find or .-11 35.0000__-3320__-1190__-8820__-1190__-882 The remainder after each step is 2 or 9.The mixed number -3 2_11can be written as.Check Your Progress Write 51_9as a decimal.ORGANIZE ITUnder the tab forLesson 2–1, explain inyour own words how toexpress rational numbersas decimals and decimalsas fractions.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
  • 2–1Math Connects, Course 3 37Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Write a Terminating Decimal as a FractionWrite 0.32 as a fraction.0.32 = 32__ 0.32 is 32 .= Simplify. Divide by the greatestcommon factor of 32 and 100, .The decimal 0.32 can be written as .Check Your Progress Write 0.16 as a fraction.EXAMPLE Write a Repeating Decimal as a FractionALGEBRA Write 2.−7 as a mixed number.Let N = 2.−7 or 2.777 . . . . Then 10N = .Multiply N by because 1 digit repeats.Subtract N = 2.777 . . . to eliminate the part,0.777 . . . .10N = 27.777 . . .________-1N = 2.777 . . . N = 1N= 25 10N - 1N == Divide each side by .N = Simplify.Check Your Progress Write 1.−7 as a mixed number.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 38 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Compare Positive Rational NumbersReplace with <, >, or = to make 3_78_13atrue sentence.Write as fractions with the same denominator.For 3_7and 8_13, the least common denominator is 91.3_7=3 ·__7 ·= _918_13=8 ·__13 ·= _91Since _91< _91, 3_78_13.EXAMPLE Compare Using DecimalsReplace with <, >, or = to make 0.7 7_11atrue sentence.0.7 7_11Express 7_11as a decimal.In the tenths place, 7 > 6.So, 0.7 7_11.Check Your Progress Replace each with <, >, or = tomake a true sentence.a. 2_33_5b. 4_90.5Comparing and Ordering Rational Numbers2–2MAIN IDEACompare and orderrational numbers.ORGANIZE ITUnder the tab forLesson 2–2, explain howyou can compare twonumbers by expressingthem as decimals andcomparing the decimals.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
  • 2–2Math Connects, Course 3 39Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Order Rational NumbersCHEMISTRY The values forSubstanceDensity(g/cm3)aluminum 2.7beryllium 1.87brick 14_5crown glass 21_4fused silica 2.−2marble 23_5nylon 1.1pyrex glass 2.32rubber neoprene 1.−3Source: CRC Handbook of Chemistryand Physicsthe approximate densitiesof various substances areshown in the table. Orderthe densities from leastto greatest.Write each fraction asa decimal.14_5=21_4=23_5=From the least to the greatest, the densities are1.1, 1.−3, 14_5, 1.87, 2.−2, 21_4, 2.32, 23_5, and 2.7. So, the isthe least dense, and is the most dense.Check Your Progress CoasterRide Time(min)Big Dipper 13_4Double Loop 1.5Mind Eraser 1.8Serial Thriller 2 1_12X-Flight 2.−3The ride times for fiveamusement parkattractions are shown inthe table. Order the lengthsfrom least to greatest.HOMEWORKASSIGNMENTPage(s):Exercises:REMEMBER ITOn a number line,a number to the leftis always less than anumber to the right.
  • 40 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.MAIN IDEA• Multiply positive andnegative fractions.Multiplying Positive and Negative Fractions2–3Dimensional analysis is the process of including units ofwhen you .BUILD YOUR VOCABULARY (pages 33–34)EXAMPLE Multiply FractionsKEY CONCEPTMultiply FractionsTo multiply fractions,multiply the numeratorsand multiply thedenominators.Find 3_7· 8_9. Write in simplest form.3_7· 8_9= 31_7· 8_93Divide 3 and 9 by their GCF, .= ___Multiply the numerators.Multiply the denominators.= 8_21Simplify.EXAMPLE Multiply Negative FractionsFind -3_4· 7_12. Write in simplest form.-3_4· 7_12= -31_4· 7_124Divide -3 and 12 by their GCF, .= ___Multiply the numerators.Multiply the denominators.= -_ The factors have different signs,so the product is negative.EXAMPLE Multiply Mixed NumbersFind 31_5· 13_4. Write in simplest form.31_5· 13_4= · 31_5= , 13_4=
  • 2–3Math Connects, Course 3 41Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.= 164_5· 7_41Divide 16 and 4 by theirGCF, .= ___5 · 1Multiply the numerators.Multiply the denominators.= , or 5 Simplify.Check Your Progress Multiply. Write in simplest form.a. - 2_15· 5_9b. 32_5· 22_9EXAMPLEVOLUNTEER WORK Last summer the 7th gradersperformed a total of 250 hours of community service.If the 8th graders spent 11_5this much time volunteering,how many hours of community service did the 8thgraders perform?The 8 graders spent 11_5times the amount of time as the7th graders on community service.6_5· 250 = ·=1,500_5orThe 8th graders did of community servicelast summer.Check Your Progress VOLUNTEER WORK Lastsummer the 5th graders performed a total of 150 hoursof community service. If the 6th graders spent 11_3thismuch time volunteering, how many hours of communityservice did the 6th graders perform?HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITUnder the tab forLesson 2–3, explain inyour own words howto multiply rationalnumbers.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
  • 42 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Two numbers whose product is one are multiplicativeinverses.The numbers 4 and 1_4areor reciprocals of each other.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLE Find a Multiplicative InverseKEY CONCEPTSInverse Property ofMultiplication Theproduct of a rationalnumber and itsmultiplicative inverse is 1.Dividing FractionsTo divide by a fraction,multiply by itsmultiplicative inverse.Write the multiplicative inverse of -24_7.-24_7= Write -24_7as an improper fraction.Since -18_7 (- 7_18)= , the multiplicative inverseof -24_7is .Check Your Progressa. Write the multiplicative inverse of -15_6.EXAMPLE Divide Negative FractionsFind 2_7÷ -8_9. Write in simplest form.2_7÷ -8_9= 2_7· Multiply by the multiplicativeinverse of -8_9which is .= 21_7· 9_84Divide 2 and 8 by their GCF, .= The fractions have different signs,so the quotient is negative.MAIN IDEA• Divide positive andnegative fractions.Dividing Positive and Negative Fractions2–4ORGANIZE ITOn the tab for Lesson2–4, explain in your ownwords how to dividerational numbers.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
  • 2–4Math Connects, Course 3 43Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Divide Mixed NumbersFind 31_4÷ (-21_8). Write in simplest form.31_4÷ (-21_8)= ÷ ( ) 31_4= ,-21_8== · (- 8_17) The multiplicativeinverse of is - 8_17.= 13_41· (- 82_17) Divide 4 and 8 by theirGCF, .= -26_17or Simplify.Check Your Progress Find each quotient. Write insimplest form.a. -3_5÷ 9_10b. 21_3÷ (-11_9)WRITE ITExplain how you woulddivide a fraction by awhole number.
  • 2–444 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLEPAINTING It took the five members of the Johnson family101_2days to paint the 7 rooms in their house. At thisrate, how long will it take the four members of the Reyesfamily to complete a similar task in their house?If persons of the Johnson family each workeddays, the project required 5 × 101_2person-days of work. Dividethis number by persons to find the number of days it willtake the Reyes family to complete their task.5 101_2person-days ÷ 4=5 × 101_2person-days____1× 1__4 personsMultiply by themultiplicative inverseof 4, which is .= 52.5_4or Simplify.It will take the Reyes family days to complete asimilar painting task in their house.Check Your Progress DECORATING Six students spent31_2hours decorating the school gym for a dance. How longwould it take 8 students to decorate the gym in the same way?HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 45Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Adding and Subtracting Like FractionsFractions with like are calledlike fractions.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLE Add Like FractionsFind 3_16+ (-15_16). Write in simplest form.3_16+ (- 15_16 )=+ ( )____16Add the numerators.The denominatorsare the same.= -12_16or Simplify.EXAMPLE Subtract Like FractionsKEY CONCEPTSAdding Like FractionsTo add fractions withlike denominators, addthe numerators andwrite the sum over thedenominator.Subtracting LikeFractions To subtractfractions with likedenominators, subtractthe numerators and writethe difference over thedenominator.Find -7_10- 9_10. Write in simplest form.- 7_10- 9_10= ___10Subtract the numerators.The denominatorsare the same.= -16_10or Rename -16_10as -1 6_10or .Check Your Progress Find each difference. Write insimplest form.a. 2_9+ (-8_9) b. -7_8- 5_82–5MAIN IDEA• Add and subtractfractions with likedenominators.
  • 2–546 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Add Mixed NumbersFind 25_8+ 61_8. Write in simplest form.25_8+ 61_8= ( + )+ (5_8+ 1_8 ) Add the whole numbersand fractions separately.= +5 + 1_8Add the numerators.= or Simplify.EXAMPLE Subtract Mixed NumbersHEIGHTS In the United States, the average heightof a 9-year-old girl is 534_5inches. The average height of a16-year-old girl is 641_5inches. How much does anaverage girl grow from age 9 to age 16?641_5- 534_5= __5- __5Write the mixed numbersas improper fractions.=-____5Subtract the numerators.The denominators arethe same.= 52_5or Rename 52_5as .The average girl grows inches from age 9 to age 16.Check Your Progressa. Find 3 3_10+ 4 1_10. Write in simplest form.b. Ainsley was 421_7inches tall when she was 4 years old. Whenshe was 10 years old, she was 503_7inches tall. How much didshe grow between the ages of 4 and 10?ORGANIZE ITUnder the tab forLesson 2–5, recordmodels illustrating theaddition and subtractionof like fractions.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 47Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Adding and Subtracting Unlike Fractions2–6Fractions with denominators are calledunlike fractions.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLES Add and Subtract Unlike FractionsAdd or subtract. Write in simplest form.5_8+ (-3_4)5_8+ (-3_4)= 5_8+ (-3_4)· The LCD is 2 · 2 · 2 or 8.= + Rename the fractionsusing the LCD.= Add the numerators.= Simplify.-7_96- (-15_128)- 7_96- (- 15_128)= - 7_96· + · 3_396 = 2 · 3, 128 = 2 .The LCD is 27· 3 or .= _384+ _384Rename using the LCD.=-28 + 45__ Add the numerators.= _384Simplify.MAIN IDEA• Add and subtractfractions with unlikedenominators.KEY CONCEPTAdding and SubtractingUnlike Fractions To findthe sum or difference oftwo fractions with unlikedenominators, renamethe fractions with acommon denominator.Then add or subtract andsimplify, if necessary.
  • 2–648 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Add or subtract. Write insimplest form.a. 5_6+ (-2_3) b. - 7_12- (- 4_15)EXAMPLE Add Mixed NumbersFind -41_8+ 2 5_12. Write in simplest form.-41_8+ 2 5_12= +Write the mixed numbersas fractions.= -33_8· 3_3+ 29_12· 2_2The LCD is 2 · 2 · 2 · 3or .= +Rename each fractionusing the LCD.= ____24Add the numerators.= or -1 Simplify.Check Your Progress Find -51_6+ 35_8. Write insimplest form.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITUnder the tab forLesson 2–6, record thedifferences betweenadding and subtractinglike and unlike fractions.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
  • Math Connects, Course 3 49Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 2–7 Solving Equations with Rational NumbersEXAMPLES Solve by Using Addition or SubtractionSolve g + 2.84 = 3.62.g + = 3.62 Write the equation.g + 2.84 - = 3.62 - Subtract fromeach side.g = Simplify.Solve -4_5= s - 2_3.-4_5= s - 2_3Write the equation.-4_5+ = s - 2_3+ Add to each side.-4_5+ = s Simplify.+ 10_15= s Rename each fractionusing the LCD.= s Simplify.EXAMPLES Solve by Using Multiplication or DivisionSolve 7_11c = -21.7_11c = -21 Write the equation.( 7_11c)= (-21) Multiply each side by .c = Simplify.MAIN IDEA• Solve equationsinvolving rationalnumbers.ORGANIZE ITUnder the tab forLesson 2–7, summarizein your own words whatyou have learned aboutsolving equations withrational numbers.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
  • 2–750 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Solve 9.7t = -67.9.9.7t = -67.9 Write the equation.9.7t__ = -67.9__ Divide each side by .t = Simplify.Check Your Progress Solve each equation.a. h + 2.65 = 5.73 b. -2_5= x - 3_4.c. 3_5x = -27 d. 3.4t = -27.2EXAMPLE Write an Equation to Solve a ProblemPHYSICS You can determine the rate an object istraveling by dividing the distance it travels by the timeit takes to cover the distance (r = d_t ). If an object travelsat a rate of 14.3 meters per second for 17 seconds, howfar does it travel?r = d_t14.3 = d__ Write the equation.(14.3) = 17(d__) Multiply each side by .= d Simplify.Check Your Progress If an object travels at a rate of73 miles per hour for 5.2 hours, how far does it travel?What is a mathematicalsentence containingequals sign called?(Lesson 1–7)REVIEW ITHOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 51Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 2–8 Problem-Solving Investigation:Look for a PatternEXAMPLEINTEREST The table below shows the amount ofinterest $3,000 would earn after 7 years at variousinterest rates. How much interest would $3,000 earnat 6 percent interest?Interest Rate(%)Interest Earned($)1 $2102 $4203 $6304 $8405 $1,050UNDERSTAND You know the amount of interest earned atinterest rates of 1%, 2%, 3%, 4%, 5%, and6%. You want to know the amount of interestearned at 6%.PLAN Look for a pattern in the amounts of interestearned. Then continue the pattern to find theamount of interest earned at a rate of .SOLVE For each increase in interest rate, the amountof interest earned increases by $210. So foran interest rate of 6%, the amount of interestearned would be $1,050 + $210 = .CHECK Check your pattern to make sure the answeris correct.Check Your Progress INTEREST The table belowshows the amount of interest $5,000 would earn after 3 yearsat various interest rates. How much interest would $5,000 earnat 7 percent interest?Interest Rate(%)Interest Earned($)1 $1502 $3003 $4504 $6005 $750MAIN IDEA• Look for a pattern tosolve problems.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 52 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The base is the number that is .The exponent tells how many times the isused as a .The number that is expressed using an iscalled a power.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLES Write Expressions Using PowersWrite 1_3· 1_3· 1_3· 7 · 7 using exponents.1_3· 1_3· 1_3· 7 · 7 = · Associative Property= Definition ofexponentsWrite p · p · p · q · p · q · q using exponents.p · p · p · q · p · q · q= p · p · p · p · q · q · q Property= (p · p · p · p) · (q · q · q) Property= · Definition of exponentsCheck Your Progress Write each expressionusing exponents.a. 2 · 2 · 2 · 2 · 5 · 5 · 5 b. x · y · x · x · y · y · y2–9 Powers and ExponentsMAIN IDEA• Use powers andexponents inexpressions.KEY CONCEPTZero and NegativeExponents Any nonzeronumber to the zeropower is 1. Any nonzeronumber to the negativen power is 1 divided bythe number to the nthpower.
  • 2–9Math Connects, Course 3 53Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Evaluate PowersEvaluate (3_4)5.(3_4)5= Definition of exponents= 243_1,024Simplify.Evaluate 3-7.3-7= 1__ Definition of negative exponents= 1__ Simplify.ALGEBRA Evaluate x3· y5if x = 4 and y = 2.x3· y5=3·5Replace x with andy with .= ( )· ( )Write the powers as products.= 64 · 32 Simplify.= Simplify.Check Your Progress Evaluate each expression.a. (3_5)3b. 2-5c. Evaluate x2· y4if x = 3 and y = 4.ORGANIZE ITOn the tab forLesson 2–9, comparehow to evaluate anexpression with positiveexponents and one withnegative exponents.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®HOMEWORKASSIGNMENTPage(s):Exercises:
  • 54 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.2–10 Scientific NotationA number is expressed in scientific notation when it iswritten as a of a factor and aof 10.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLES Express Numbers in Standard Form9.62 × 105in standard form.9.62 × 105= 962000 The decimal place movesplaces to the right.=Write 2.85 × 10-6in standard form.2.85 × 10-6= 0.00000285 The decimal point moves 6places to the left.=Check Your Progress Write each number instandard form.a. 5.32 × 104b. 3.81 × 10-4MAIN IDEA• Express numbers inscientific notation.KEY CONCEPTScientific NotationA number is expressedin scientific notationwhen it is written as theproduct of a factor anda power of 10. The factormust be greater than orequal to 1 and lessthan 10.
  • 2–10Math Connects, Course 3 55Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Write Numbers in Scientific NotationWrite -931,500,000 in scientific notation.-931500000 = -9.315 × 100,000,000 The decimal point moves8 places.= The exponent is positive.Write 0.00443 in scientific notation.0.00443 = × 0.001 The decimal point movesplaces.= 4.43 × The exponent is .EXAMPLE Compare Numbers in Scientific NotationPLANETS The following Planet Radius (km)Earth 6.38 × 103Jupiter 7.14 × 104Mars 3.40 × 103Mercury 2.44 × 103Neptune 2.43 × 104Saturn 6.0 × 104Uranus 2.54 × 104Venus 6.05 × 103Source: CRC Handbook of Chemistryand Physicstable lists the averageradius at the equator forplanets in our solar system.Order the planets accordingto radius from largest tosmallest.First order the numbersaccording to their exponents.Then order the numbers withthe same exponents bycomparing the factors.STEP 1× 1046.38 × 1032.43 × 1043.40 × 1036.0 × 104> 2.44 × 1032.54 × 104× 103Jupiter, Neptune,Saturn, UranusEarth, Mars,Mercury, VenusORGANIZE ITUnder the tab forLesson 2–10, collectand record examplesof numbers youencounter in your dailylife and write them inscientific notation.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
  • 2–1056 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.STEP 27.14 × 104> 6.0 × 104> 2.54 × 104> 2.43 × 1046.38 × 103> 6.05 × 103> 3.40 × 103> 2.44 × 103The order from largest to smallest is , Saturn,Uranus, Neptune, Earth, Venus, Mars, and .Check Your Progress Write each number inscientific notation.a. 35,600,000 b. 0.000653c. The table lists the mass forPlanetMass(in tons)Mercury 3.64 × 1020Venus 5.37 × 1021Earth 6.58 × 1021Mars 7.08 × 1020Jupiter 2.09 × 1024Saturn 6.25 × 1023Uranus 9.57 × 1023Neptune 1.13 × 1023Source: NASAeach of the planets in oursolar system. Order theplanets according to massfrom largest to smallest.Jupiter Saturn Uranus NeptuneEarth Venus Mars MercuryHOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 57Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERSTUDY GUIDE® VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 2 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 2, go to:glencoe.comYou can use your completedVocabulary Builder(pages 33–34) to help you solvethe puzzle.2-1Rational NumbersWrite each fraction or mixed number as a decimal.1. -3_42. 31_63. -72_5Write each decimal as a fraction or mixed number in simplest form.4. 9.5 5. 0.6 6. 8.1252-2Comparing and Ordering Rational NumbersUse <, >, or = to make each sentence true.7. -4_5-2_38. 4.4 42_59. 2.93 2.93Graph each pair of rational numbers on a number line.10. 1_5, 1_311. -4_5, - 9_10C H A P T E R2
  • 58 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 BRINGING IT ALL TOGETHER2-3Multiplying Positive and Negative FractionsComplete each sentence.12. The greatest common factor of two numbers is thenumber that is a of both numbers.13. Numerators and denominators are by theirgreatest common factors to the fraction.Multiply. Write in simplest form.14. - 7_12· 3_415. 42_3· 51_82-4Dividing Positive and Negative FractionsWrite the multiplicative inverse for each mixed number.16. 21_517. -13_818. 34_7Complete the sentence.19. To divide by a , multiply by itsinverse.20. To a number by 21_5, multiply by 5_11.2-5Adding and Subtracting Like FractionsDetermine whether each pair of fractions are like fractions.21. 3_5, 3_722. 5_8, 7_823. 4_7, -5_724. 5_9, -2_3Add or subtract. Write in simplest form.25. 5_9- 2_926. 5_8+ 7_827. 4_7- 5_7
  • Math Connects, Course 3 59Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 BRINGING IT ALL TOGETHER2-6Adding and Subtracting Unlike FractionsAdd or subtract. Write in simplest form.28. 5_8- 7_1229. 3_5+ 3_730. -2_3+ 5_92-7Solving Equations with Rational NumbersMatch the method of solving with the appropriate equation.31. 25a = 3.75 a. Subtract 3_5from each side.b. Multiply each side by 5_3.c. Subtract 3.75 from each side.d. Add 1.25 to each side.e. Divide each side by 25.32. 3_5m = 7_1033. r - 1.25 = 4.534. 3_5+ f = 1_22-8Problem Solving Investigation: Look for a Pattern35. LIFE SCIENCE The table shows OutsideTemperature(˚C)Flashes perMinute16 820 924 1128 14about how many times a fireflyflashes at different temperatures.About how many times will afirefly flash when thetemperature is 36°C?2-9Powers and ExponentsEvaluate each expression.36. 5437. 6338. 282-10Scientific NotationWrite each number in scientific notation.39. 8,790,000 40. 0.0000125
  • Checklist60 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study are given witheach item.I completed the review of all or most lessons without using my notesor asking for help.• You are probably ready for the Chapter Test.• You may want take the Chapter 2 Practice Test onpage 139 of your textbook as a final check.I used my Foldable or Study Notebook to complete the review ofall or most lessons.• You should complete the Chapter 2 Study Guide and Review onpages 134–138 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 2 Practice Test onpage 139 of your text book.I asked for help from someone else to complete the review of all ormost lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 2 Foldable.• Then complete the Chapter 2 Study Guide and Review on pages134–138 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 2 Practice Test onpage 139 of your textbook.C H A P T E R2Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 2.Student Signature Parent/Guardian SignatureTeacher Signature
  • ®Chapter3Math Connects, Course 3 61Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R3 Real Numbers andthe Pythagorean TheoremUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with two sheets of 81_2" by 11" notebookpaper.Fold one in half fromtop to bottom. Cutalong fold from edgesto margin.Fold the other sheetin half from topto bottom. Cut alongfold between margins.Insert first sheetthrough secondsheet and align folds.Label each page with Chapter 3Real Numbersand thePythagoreanTheorema lesson number and title.NOTE-TAKING TIP: When you take notes, clarifyterms, record concepts, and write examples foreach lesson. You may also want to list ways inwhich the new concepts can be used in yourdaily life.
  • 62 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R3UILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 3.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleabscissa[ab-SIH-suh]conversecoordinate planehypotenuseirrational numberlegsordered pairordinate[OR-din-it]originperfect square
  • Math Connects, Course 3 63Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplePythagorean Theoremquadrantsradical signreal numbersquare rootx-axisx-coordinatey-axisy-coordinate
  • 64 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–1 Square RootsNumbers such as 1, 4, 9, and 25 are called perfect squaresbecause they are squares of numbers.The of squaring a number is finding asquare root.The symbol √⎯⎯ is called a radical sign and is used toindicate the positive .BUILD YOUR VOCABULARY (pages 62–63)EXAMPLES Find Square RootsKEY CONCEPTSquare Root A squareroot of a number is oneof its two equal factors.Find each square root.√81√81 indicates the square root of 81.Since = 81, √81 = .- 16_81- 16_81indicates the square root of 16_81.Since = 16_81, - 16_81= .±√1.44±√1.44 indicates bothsquare roots of 1.44.Since = 1.44 and = 1.44, ±√1.44 = ±1.2,or .MAIN IDEA• Find square roots ofperfect squares.
  • 3–1Math Connects, Course 3 65Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find each square root.a. √64b. - 25_144c. ±√2.25EXAMPLE Use an Equation to Solve a ProblemMUSIC The art work of the square picture in a compactdisc case is approximately 14,161 mm2 in area. Find thelength of each side of the square.The area is equal to the square of the length of a side.Let A = the area and let s = the length of the side A = s214,161 = s2Write the equation.= √s2Take the square root of each side.The length of a side of a compact disc case is aboutmillimeters since distance cannot be negative.Check Your Progress A piece of art is a square picture thatis approximately 11,025 square inches in area. Find the lengthof each side of the square picture.ORGANIZE ITOn Lesson 3-1 of yourFoldable, explain howto find the square rootof a number and give anexample.Chapter 3Real Numbersand thePythagoreanTheorem®HOMEWORKASSIGNMENTPage(s):Exercises:
  • 66 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Estimating Square RootsEXAMPLES Estimate Square RootsEstimate √54 to the nearest whole number.The first perfect square less than 54 is .The first perfect square greater than 54 is .49 < 54 < 64 Write an inequality.< 54 < 49 = and 64 =√72< √54 < √82Take the square root ofeach number.7 < √54 < 8 Simplify.So, √54 is between and . Since 54 is closer to 49than 64, the best whole number estimate for √54 is .Estimate √41.3 to the nearest whole number.• The first perfect square less than 41.3 is 36.• The first perfect square greater than 41.3 is 49.Plot each square rooton a number line.Then plot √41.3 .36 < 41.3 < 49 Write an inequality.< 41.3 < 36 = and 49 =√62< √41.3 < √72Find the square root of each number.< √41.3 < Simplify.So, √41.3 is between and . Since 41.3 is closer to 36than 49, the best whole number estimate for √41.3 is .MAIN IDEA• Estimate square roots.3–2
  • 3–2Math Connects, Course 3 67Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Estimate Square RootsFINANCE If you were to invest $100 in a bank account fortwo years, your investment would earn interest dailyand be worth more when you withdrew it. If you had$120 after two years, the interest rate, written as adecimal, would be found using the expression(√120 - 10)___10.Estimate the value.First estimate the value of √120.100 < 120 < 121 and areperfect squares.102< 120 < 112100 = and 121 =< √120 < Take the square root of each number.Since 120 is closer to than 100, the best wholenumber estimate for √120 is . Use this to evaluatethe expression.(√120 - 10)___10=( - 10)___10orThe approximate interest rate is 0.10 or .Check Your Progressa. Estimate √65 to the nearest whole number.b. If you were to invest $100 in a bank account for two years,your money would earn interest daily and be worth morewhen you withdrew it. If you had $250 after two years, theinterest rate, written as a decimal, would be found using theexpression(√150 - 10)___10. Estimate this value.ORGANIZE ITOn Lesson 3-2 of yourFoldable, explain how toestimate square roots.Chapter 3Real Numbersand thePythagoreanTheorem®HOMEWORKASSIGNMENTPage(s):Exercises:
  • 68 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–3 Problem-Solving Investigation:Use a Venn DiagramEXAMPLELANGUAGES Of the 40 foreign exchange studentsattending a middle school, 20 speak French, 23speak Spanish, and 22 speak Italian. Nine studentsspeak French and Spanish, but not Italian. Sixstudents speak French and Italian, but not Spanish.Ten students speak Spanish and Italian, but not French.Only 4 students speak all three languages. Use a Venndiagram to find how many exchange students do notspeak any of these languages.UNDERSTAND You know how many students speak each ofthe different languages. You want to organizethe information.PLAN Make a VennDiagram to organizethe information.SOLVE Since 4 studentsspeak all threelanguages, place athree in the sectionthat represents allthree languages.Fill in the othersections as appropriate.Add the numbers in each region of the diagram:1 + 9 + 6 + 4 + 10 + 2 =Since there are 40 exchange studentsaltogether, 40 - 32 = of them do notspeak French, Spanish, or Italian.CHECK Check each circle to see if the appropriatenumber of students is represented.Check Your Progress SPORTS Of the 30 students in Mr.Hall’s gym class, 14 play basketball, 9 play soccer, and 11 playvolleyball. Three students play basketball and soccer, but notvolleyball. One student plays soccer and volleyball, but notbasketball. Six students play basketball and volleyball, butnot soccer. Only 2 students play all three sports. Use a Venndiagram to find how many students in the class do not play anyof these sports.1 09426 10French SpanishItalianHOMEWORKASSIGNMENTPage(s):Exercises:MAIN IDEA• Use a Venn diagram tosolve problems.
  • Math Connects, Course 3 69Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 3–4 The Real Number SystemNumbers that are not are calledirrational numbers.The set of rational numbers and the set ofnumbers together make up the set of real numbers.BUILD YOUR VOCABULARY (pages 62–63)EXAMPLES Classify NumbersName all sets of numbers to which each real numberbelongs.0.090909 . . .The decimal ends in a pattern.It is a number because it is equivalent to .√25Since √25 = , it is a number, an, and a rational number.-√12Since the decimal does not repeat or , it isan number.Check Your Progress Name all sets of numbers towhich each real number belongs.a. 0.1010101010...b. √64c. √13MAIN IDEA• Identify and classifynumbers in the realnumber system.KEY CONCEPTIrrational Number Anirrational number is anumber that cannot beexpressed as a_b, wherea and b are integersand b ≠ 0.
  • 3–470 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLES Graph Real NumbersEstimate √8 and -√2 to the nearest tenth. Thengraph √8 and -√2 on a number line.Use a calculator to determine the approximate decimal values.√8 ≈-√2 ≈Locate these points on a number line.0123 1 2 3√8 ≈ and -√2 ≈ .Check Your Progress Estimate √3 and -√6 to the nearesttenth. Then graph √3 and -√6 on a number line.EXAMPLES Compare Real NumbersReplace each with <, >, or = to make a true sentence.37_8√15Write each number as a decimal.37_8= √15 =Since is greater than ,37_8= √15.ORGANIZE ITOn Lesson 3-4 of yourFoldable, summarize theproperties of the realnumber system.Chapter 3Real Numbersand thePythagoreanTheorem®REMEMBER ITAlways simplifynumbers beforeclassifying them.
  • 3–4Math Connects, Course 3 71Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 3.−2 √10.4Write √10.4 as a decimal.√10.4 ≈Since 3.−2 is than 3.224903099...,3.−2 √10.4.Check Your Progress Replace each with <, >, or = tomake a true sentence.a. 33_8√14 b. 1.−5 √2.25EXAMPLEBASEBALL The time in seconds that it takes an object tofall d feet is 0.25√d. How many seconds would it take fora baseball that is hit 250 feet straight up in the air to fallfrom its highest point to the ground?Use a calculator to approximate the time it will take for thebaseball to fall to the ground.0.25 √d = 0.25 Replace d with .≈ 3.95 or about Use a calculator.It will take about for the baseball to fall tothe ground.Check Your Progress The time in seconds that it takes anobject to fall d feet is 0.25√d. How many seconds would it takefor a baseball that is hit 450 feet straight up in the air to fallfrom its highest point to the ground?HOMEWORKASSIGNMENTPage(s):Exercises:WRITE ITExplain why you candetermine that -√2 isless than 1.2 withoutcomputation.
  • 72 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–5 The Pythagorean TheoremA right triangle is a triangle with one right angle of 90°.The sides that form the right angle are called legs.The hypotenuse is the side opposite the right angle.The Pythagorean Theorem describes the relationshipbetween the lengths of the legs and the hypotenuse forany right triangle.BUILD YOUR VOCABULARY (pages 62–63)EXAMPLES Find the Length of a SideWrite an equation you could use to find the length of themissing side of the right triangle. Then find the missinglength. Round to the nearest tenth if necessary.12 in.16 in.cc2= a2+ b2Pythagorean Theoremc2= 122+ Replace a with and b with .c2= + Evaluate 122and 162.c2= Add 144 and 256.c = ±√400 Definition of square rootc = or Simplify.The equation has two solutions, and .However, the length of a side must be positive. So, thehypotenuse is inches long.MAIN IDEA• Use the PythagoreanTheorem.KEY CONCEPTPythagorean TheoremIn a right triangle, thesquare of the length ofthe hypotenuse is equalto the sum of the squaresof the lengths of the legs.
  • 3–5Math Connects, Course 3 73Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your ProgressWrite an equation you could use to find the length of themissing side of the right triangle. Then find the missing length.Round to the nearest tenth if necessary.8 cm15 cmcEXAMPLE Find the Length of a SideThe hypotenuse of a right triangle is 33 centimeterslong and one of its legs is 28 centimeters. What is a, thelength of the other leg?c2= a2+ b2Pythagorean Theorem2= a2+2Replace the variables.1,089 = a2+ 784 Evaluate each power.- = a2+ - Subtract.= a2Simplify.± √305 = a Definition of square root= a Use a calculator.The length of the other leg is about centimeters.Check Your Progress The hypotenuse of a right triangle is26 centimeters long and one of its legs is 17 centimeters. Findthe length of the other leg.ORGANIZE ITOn Lesson 3-5 of yourFoldable, explain howto use the PythagoreanTheorem to find themissing length of a sideof a right triangle.Chapter 3Real Numbersand thePythagoreanTheorem®REMEMBER ITThe longest side of aright triangle is thehypotenuse. Therefore, crepresents the length ofthe longest side.
  • 3–574 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.If you the parts of the Pythagorean Theorem,you have formed its converse.BUILD YOUR VOCABULARY (pages 62–63)EXAMPLE Identify a Right TriangleThe measures of three sides of a triangle are 24 inches,7 inches, and 25 inches. Determine whether the triangleis a right triangle.c2= a2+ b2Pythagorean Theorem25272+ 242c = 25, a = 7, b = 24625 + 576 Evaluate 252, 72, and 242.= 625 Simplify. The triangle is a right triangle.Check Your ProgressThe measures of three sides of a triangle are 13 inches,5 inches, and 12 inches. Determine whether the triangleis a right triangle.HOMEWORKASSIGNMENTPage(s):Exercises:KEY CONCEPTConverse of thePythagorean TheoremIf the sides of a trianglehave lengths a, b, and cunits such thatc2= a2+ b2, thenthe triangle is a righttriangle.
  • Math Connects, Course 3 75Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 3–6 Using the Pythagorean TheoremEXAMPLE Use the Pythagorean TheoremRAMPS A ramp to a newlyconstructed building mustbe built according to theguidelines stated in theAmericans with DisabilitiesAct. If the ramp is 24.1feet long and the top ofthe ramp is 2 feet off theground, how far is the bottomof the ramp from the baseof the building?Notice the problem involves a right triangle. Use thePythagorean Theorem.24.12= a2+ 22 Replace c with 24.1 andb with 2.= a2+ Evaluate 24.12and 22.- = a2= - Subtract from each side.= a2Simplify.= a Definition of square root≈ a Simplify.The end of the ramp is about from the base ofthe building.Check Your Progress If a truck ramp is 32 feet long andthe top of the ramp is 10 feet off the ground, how far is the endof the ramp from the truck?MAIN IDEA• Solve problems usingthe PythagoreanTheorem.ORGANIZE ITOn Lesson 3-6 of yourFoldable, explain thePythagorean Theorem inyour own words and givean example of how itmight be used in areal-life situation.Chapter 3Real Numbersand thePythagoreanTheorem®
  • 3–676 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLETEST EXAMPLE The cross-sectionof a camping tent is shown. Find thewidth of the base of the tent.A 6 ft C 10 ftB 8 ft D 12 ftRead the ItemFrom the diagram, you know that the tent forms two congruentright triangles.Solve the ItemUse the Pythagorean Theorem.c2= a2+ b2Pythagorean Theorem= a2+ c = , b == a2+ Evaluate 102and 82.100 - 64 = a2+ 64 - 64 Subtract 64 from each side.= a2Simplify.= a Definition of square root= a SimplifyThe width of the base of the tent is a + a or + =feet. Therefore, choice is correct.Check Your Progress32 ft12 ftr rMULTIPLE CHOICE Thediagram shows the cross-section of a roof. How longis each rafter, r?F 15 ft G 18 ft H 20 ft J 22 ftHOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 77Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Geometry: Distance on the Coordinate PlaneA coordinate plane is formed by two number lines thatform right angles and intersect at their points.The point of intersection of the two number lines is theorigin.The number line is the y-axis.The number line is the x-axis.The number lines separate the coordinate plane intosections called quadrants.Any point on the coordinate plane can be graphed by usingan ordered pair of numbers.The number in the ordered pair is called thex-coordinate.The number of an ordered pair is they-coordinate.Another name for the is abscissa.Another name for the is ordinate.BUILD YOUR VOCABULARY (pages 62–63)EXAMPLE Name an Ordered PairName the ordered pair for point A.• Start at the origin.• Move right to find theof point A, which is .(continued on the next page)3–7yxAMAIN IDEAS• Graph rational numberson the coordinateplane.• Find the distancebetween points on thecoordinate plane.ORGANIZE ITOn Lesson 3-7 of yourFoldable, explain inwriting how to useordered pairs to find thedistance between twopoints.Chapter 3Real Numbersand thePythagoreanTheorem®
  • 3–778 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.• Move up to find the ,which is .So, the ordered pair for point A is .Check Your Progress Name the orderedyxApair for point A.EXAMPLES Graphing Ordered PairsGraph and label each point on the same coordinateplane.J(-3, 2.75)• Start at and moveunits to the .Then move units.• Draw a dot and label it.K(4, -11_4)• Start at and move units to the .Then move units.• Draw a dot and label it .Check Your Progress yxOGraph and label eachpoint on the samecoordinate plane.a. J(-2.5, 3.5)b. K(2, -21_2)yxK 4, 1J( 3, 2.75)14)(
  • 3–7Math Connects, Course 3 79Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Find the Distance on the Coordinate PlaneGraph the ordered pairs (0, -6)and (5, -1). Then find the distancebetween the points.Let c = distance between the two points, a = 5, and b = 5.c2= a2+ b2Pythagorean Theoremc2= + Replace a with and b with .c2= + =√c2= Definition ofc = Simplify.The points are about apart.Check Your Progress Graph the ordered pairs (0, -3) and( 2, -6). Then find the distance between the points.REMEMBER ITYou can use thePythagorean Theoremto find the distancebetween two points ona coordinate plane.xyO(5, 1)(0, 6)yxOHOMEWORKASSIGNMENTPage(s):Exercises:
  • 80 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R3STUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 3 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 3, go toglencoe.comYou can use your completedVocabulary Builder(pages 62–63) to help you solvethe puzzle.3-1Square RootsComplete each sentence.1. The principle square root is the square rootof a number.2. To solve an equation in which one side of the square is a squaredterm, you can take the of each side of theequation.Find each square root.3. √900 4. -√36_495. -√625 6. √25_1213-2Estimating Square RootsDetermine between which two consecutive whole numberseach value is located.7. √23 8. √599. √27 10. √18
  • Math Connects, Course 3 81Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 BRINGING IT ALL TOGETHER3-3Problem-Solving Investigation: Use a Venn Diagram11. NUMBER THEORY A subset is a part of a set. The symbol ⊂ means“is a subset of.” Consider the following two statements.integers ⊂ rational numbersrational numbers ⊂ integersAre both statements true? Draw a Venn diagram to justifyyour answer.3-4The Real Number SystemMatch the property of real numbers with the algebraicexample.12. Commutative13. Associative14. Distributive15. Identity16. Multiplicative Inverse3-5The Pythagorean TheoremUse the Pythagorean Theorem to determine whether each ofthe following measures of the sides of a triangle are the sidesof a right triangle.17. 4, 5, 6 18. 9, 12, 1519. 10, 24, 26 20. 5, 7, 9a. (x + y) + z = x + (y + z)b. pq = qpc. h + 0 = hd. c + (-c) = 0e. x(y + z) = xy + xzf . a_b· b_a= 1
  • 82 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 BRINGING IT ALL TOGETHER3-6Using the Pythagorean Theorem21. The triple 8-15-17 is a Pythagorean Triple. Complete the table tofind more Pythagorean triples.a b c Check: c2= a2+ b2original 8 15 17 289 = 64 + 225× 2× 3× 5× 10Determine whether each of the following is a Pythagoreantriple.22. 13-84-85 23. 11-60-6124. 21-23-29 25. 12-25-373-7Geometry: Distance on the Coordinate PlaneMatch each term of the coordinate plane with its description.26. ordinate a. one of four sections of thecoordinate plane27. y-axis b. x-coordinate28. origin c. y-coordinate29. abscissa d. vertical number line30. x-axis e. horizontal number linef . point where number lines meet
  • Math Connects, Course 3 83Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ChecklistARE YOU READY FORTHE CHAPTER TEST?C H A P T E R3Check the one that applies. Suggestions to help you study are givenwith each item.I completed the review of all or most lessons without using mynotes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 3 Practice Test onpage 183 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 3 Study Guide and Reviewon pages 179–182 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 3 Practice Test onpage 183 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 3 Foldable.• Then complete the Chapter 3 Study Guide and Review onpages 179–182 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 3 Practice Test onpage 183 of your textbook.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 3.Student Signature Parent/Guardian SignatureTeacher Signature
  • ®84 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R4 Proportions and SimilarityUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a plain sheet of 11" by 17" paper.Fold in thirds widthwise.Open and fold the bottomto form a pocket.Glue edges.Label each pocket. Placeindex cards in each pocket.NOTE-TAKING TIP: When you take notes, definenew vocabulary words, describe new ideas, andwrite examples that help you remember themeanings of the words and ideas.
  • Chapter4Math Connects, Course 3 85Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R4YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 4.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecongruentconstant of proportionalitycorresponding partscross productsequivalent ratiosnonproportionalpolygonproportion(continued on the next page)
  • 86 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 4 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleproportionalraterate of changeratioscalescale drawingscale factorscale modelsimilarunit rateunit ratio
  • Math Connects, Course 3 87Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 4–1A ratio is a comparison of two numbers by .A rate is a special kind of . It is a comparisonof two quantities with different types of units.When a rate is so it has a denominator of, it is called a unit rate.BUILD YOUR VOCABULARY (pages 85–86)EXAMPLE Write Ratios in Simplest FormExpress 12 blue marbles out of 18 marbles insimplest form.12 marbles__18 marbles= _Divide the numerator and denominatorby the greatest common factor, .Divide out common units.The ratio of blue marbles to total marbles is orout of .EXAMPLE Find a Unit RateREADING Yi-Mei reads 141 pages in 3 hours. How manypages does she read per hour?Write the rate that expresses the comparison of pages to hours.Then find the unit rate.141 pages__3 hours= _Yi-Mei reads an average of pages per .Ratios and RatesMAIN IDEA• Express ratios asfractions in simplestform and determineunit rates.pages Divide the numerator and denominatorhour by to get a denominator of 1.
  • 4–188 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Express each ratio insimplest form.a. 5 blue marbles out of 20 marblesb. 14 inches to 2 feetc. On a trip from Columbus, Ohio, to Myrtle Beach, SouthCarolina, Lee drove 864 miles in 14 hours. What was Lee’saverage speed in miles per hour?EXAMPLE Compare Unit RatesSHOPPING Alex spends $12.50 for 2 pounds of almondsand $23.85 for 5 pounds of jellybeans. Which item costsless per pound? By how much?For each item, write a rate that compares the cost to theamount. Then find the unit rates.Almonds:$12.50__2 pounds= __1 poundJellybeans:$23.85__5 pounds= __1 poundThe almonds cost per pound and the jellybeanscost per pound. So, the jellybeans cost -or per pound less than the almonds.Check Your Progress Cameron spends $22.50 for 2 poundsof macadamia nuts and $31.05 for 3 pounds of cashews. Whichitem costs less per pound? By how much?ORGANIZE ITWrite the definitions ofrate and unit rate on anindex card. Then on theother side of the card,write examples of howto find and compare unitrates. Include these cardsin your Foldable.®HOMEWORKASSIGNMENTPage(s):Exercises:What is the greatestcommon factor of two ormore numbers? How canyou find it?(Prerequisite Skill)REVIEW IT
  • Math Connects, Course 3 89Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.If two quantities are proportional, then they have aratio.For ratios in which this ratio is , the twoquantities are said to be nonproportional.BUILD YOUR VOCABULARY (pages 85–86)EXAMPLES Identify Proportional RelationshipsHOUSE CLEANING A house-cleaning service charges$45 for the first hour and $30 per hour for eachadditional hour. The service works for 4 hours. Is the feeproportional to the number of hours worked? Make atable of values to explain your reasoning.Find the cost for 1, 2, 3, and 4 hours and make a table todisplay numbers and cost.Hours Worked 1 2 3 4Cost ($)For each number of hours, write the relationship of the cost andnumber of hours as a ratio in simplest form.cost___hours worked45_1or 75_2or 105_3or 135_4orSince the ratios of the two quantities are ,the cost is to the number of hoursworked. The relationship is .4–2 Proportional and Nonproportional RelationshipsMAIN IDEA• Identify proportionaland nonproportionalrelationships.KEY CONCEPTSProportional A statementof equality of two ratioswith a constant ratio.Nonproportional Arelationship in which twoquantities do not have acommon ratio.
  • 4–290 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BAKING A recipe for jelly frosting calls for 1_3cup of jellyand 1 egg white. Is the number of egg whites usedproportional to the cups of jelly used? Make a table ofvalues to explain your reasoning.Find the amount of jelly and egg whites needed for differentnumbers of servings and make a table to show these measures.Cups of JellyEgg whites 1 2 3 4For each number of cups of jelly, write the relationship of theto the as aratio in simplest form.1_3_1or2_3_2or11_3_4orSince the ratios between the two quantities are all equalto , the amount of jelly used is to thenumber of egg whites used.Check Your Progressa. PLUMBING A plumbing company charges $50 for the firsthour and $40 for each additional hour. Suppose a service callis estimated to last 4 hours. Is the fee proportional to thenumber of hours worked?b. COOKING Among other ingredients, a chocolate chipcookie recipe calls for 2.5 cups of flour for every 1 cupof sugar and every 2 eggs. Is the amount of flour usedproportional to the number of eggs used?HOMEWORKASSIGNMENTPage(s):Exercises:
  • Rate of ChangeMath Connects, Course 3 91Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 4–3MAIN IDEA• Find rates of change.REMEMBER ITRate of change isalways expressed as aunit rate.A rate of change is a rate that describes how one quantityin to another.BUILD YOUR VOCABULARY (pages 85–86)EXAMPLE Find a Rate of ChangeDOGS The table below shows the weight of a dog inpounds between 4 and 12 months old. Find the rateof change in the dog’s weight between 8 and 12 monthsof age.Age (mo) 4 8 12Weight (lb) 15 28 43change in weight___change in age=(43 - )pounds____( - 8)monthsThe dog grew from28 to 43 pounds fromages 8 to 12 months.=pounds___monthsSubtract to find thechange in weightsand ages.=pounds____monthExpress this rate asa .The dog grew an average of pounds per .Check Your Progress The table below shows Julia’s heightin inches between the ages of 6 and 11. Find the rate of changein her height between ages 6 and 9.Age (yr) 6 9 11Weight (in.) 52 58 60
  • 4–392 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find a Negative Rate of ChangeSCHOOLS The graph showsthe number of students inthe seventh grade between2000 and 2004. Find therate of change between2002 and 2004.Use the data to write a rate comparing the change in studentsto the change in time.change in students____change in time=-____-The number ofstudents changedfrom 485 to 459 from2002 to 2004.= __ Simplify.= __ Express as a unit rate.The rate of change is students per .Check Your Progress The graph below shows the numberof students in the 6th grade between 1999 and 2005. Find therate of change between 2003 and 2005.KEY CONCEPTRate of Change To findthe rate of change,divide the difference inthe y-coordinate by thedifference in thex-coordinate.®Record thisconcept on one side ofan index card. Write anexample on the otherside of the card.REMEMBER ITAlways read graphsfrom left to right.
  • 4–3Math Connects, Course 3 93Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Compare Rates of ChangeTEMPERATURE the graphshows the temperaturemeasured on each hourfrom 10 A.M. to 3 P.M.During which 1-hour periodwas the rate of change intemperature the greatest?Find the rates of change for each1-hour period. Use the ratiochange in temperature____change in time.10 A.M. to 11 A.M. 55° - 54°___11 A.M. - 10 A.M.=11 A.M. to 12 P.M. 59° - 55°___12 P.M. - 11 A.M.=12 P.M. to 1 P.M. 60° - 59°___2 P.M. - 12 P.M.=1 P.M. to 2 P.M. 60° - 60°___2 P.M. - 1 P.M.=2 P.M. to 3 P.M. 62° - 60°___3 P.M. - 2 P.M.=The greatest rate of change in temperature isbetweenCheck Your ProgressThe graph shows thetemperature measuredeach hour from 10 a.m.to 4 p.m. Find the 1-hourtime period in whichthe rate of change intemperature was thegreatest.HOMEWORKASSIGNMENTPage(s):Exercises:
  • MAIN IDEA• Identify proportionaland nonproportionalrelationships by findinga constant rate ofchange.94 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Constant Rate of Change4–4A relationship that has a is called alinear relationship. A has aconstant rate of change.BUILD YOUR VOCABULARY (pages 85–86)EXAMPLE Identify linear RelationshipsBABYSITTING The amountNumber ofHoursAmountEarned1 $102 $183 $264 $34a babysitter charges isshown. Is the relationshipbetween the number ofhours and the amountcharged linear? If so,find the constant rateof change. If not, explainyour reasoning.Examine the change in the number of hours worked and in theamount earned.+1+1+1Number ofHoursAmountEarned1 $102 $183 $264 $34+8+8+8Since the rate of change , this is. Theis 8_1or . This means that the babysitter earns.
  • 4–4Math Connects, Course 3 95Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your ProgressBABYSITTING The amountNumberof HoursAmountEarned1 $122 $193 $264 $33a babysitter charges is shown.Is the relationship betweenthe number of hours and theamount charged linear? If so,find the constant rate ofchange.EXAMPLE Find a Constant Rate of ChangeTRAVEL Find the constantyxMiles18024030042Hours6 8601200Miles and Hours Traveledrate of change for the hourstraveled and miles traveled.Interpret its meaning.Choose any two points on theline and find the rate of changebetween them.(2, 60)(4, 120)change in miles___change in time=The amount of milesfrom 60 to 120between hours 2and 4.= Subtract.= Express as a unit rate.The rate of speed is .Check Your ProgressTRAVEL Find the constant rateof change for the hours traveledand miles traveled. Interpretits meaning.
  • 4–496 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLETAXIS Use the graph to5 10 15 200$4$8$12$16$20$24ChargeMilesCost of a Taxidetermine if there is aproportional linearrelationship between themiles driven and thecharge for a ride.Explain your reasoning.Since the graph of the dataforms a line, the relationshipbetween the two scales is linear.This can also be seen in the table of values created using thepoints on the graph.+4 +4 +4 +4 Constant Rate of ChangeCharge ($) 4 8 12 16 20Miles 0 5 10 15 20change in charge___change in miles=+5 +5 +5 +5To determine if the two scales are proportional, express therelationship between the charges for several miles as a ratio.charge__miles8_5= 12_10= 16_15≈Since the ratios are , the total chargeis to the number of miles driven.Check Your ProgressMOVIES Use the graphto determine if there is aproportional linear relationshipbetween the number of moviesrented and the total cost.Explain your reasoning.HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 97Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 4–5In a proportion, two are .Equivalent ratios simplify to the same .In a proportion, the cross products are .BUILD YOUR VOCABULARY (pages 85–86)EXAMPLE Write and Solve a Proportion.COOKING A recipe serves 10 people and calls for 3 cupsof flour. If you want to make the recipe for 15 people,how many cups of flour should you use?cups of flourtotal people served3_10= n_15cups of flourtotal people served= Find the crossproducts.45 = 10n Multiply.45_ = 10n_ Divide eachside by .= n Simplify.You will need cups of flour to make the recipe for15 people.Check Your Progress COOKING A recipe serves 12people and calls for 5 cups of sugar. If you want to make therecipe for 18 people, how many cups of sugar should you use?Solving ProportionsMAIN IDEA• Use proportions tosolve problems.KEY CONCEPTSProportion A proportionis an equation statingthat two ratios areequivalent.Property of ProportionsThe cross products of aproportion are equal.Be sure toinclude this definitionand property in yourFoldable.
  • 4–5You can use the constant of proportionality to write aninvolving two quantities.BUILD YOUR VOCABULARY (pages 85–86)EXAMPLEFOOD Haley bought 4 pounds of tomatoes for $11.96.Write an equation relating the cost to the number ofpounds of tomatoes. How much would Haley pay for6 pounds at this same rate? for 10 pounds?Find the constant of proportionality between cost and pounds.cost in dollars____pounds of tomatoes= 11.96_4or 2.99 The cost is $2.99 perpound.WordsVariablesEquationThe cost is $2.99 times the number of pounds.Let c represent the cost.Let p represent the number of pounds.c = 2.99 · pUse this same equation to find the cost for 6 and 10 pounds oftomatoes sold at the same rate.c = 2.99p Write the equation. c = 2.99pc = 2.99 Replace p with thenumber of pounds.c = 2.99c = Multiply. c =The cost for 6 pounds of tomatoes is and for10 pounds is .Check Your Progress FOOD Cameron bought 3 poundsof apples for $11.37. Write an equation relating the cost to thenumber of pounds of apples. How much would Cameron pay for5 pounds at this same rate?HOMEWORKASSIGNMENTPage(s):Exercises:98 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.
  • 4–6Math Connects, Course 3 99Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Problem-Solving Investigation:Draw a DiagramEXAMPLEVOLUME A bathtub is being filled with water. After4 minutes, 1_5of the bathtub is filled. How much longerwill it take to completely fill the bathtub assuming thewater rate is constant?UNDERSTAND After 4 minutes, the bathtub is 1_5of the wayfilled. How many more minutes will it take tofill the bathtub?PLAN Draw a diagram showing the water level afterevery 4 minutes.SOLVE The bathtub will be filled after4-minute periods. This is a total of 5 × 4or .CHECK The question asks how much longer will ittake to completely fill the bathtub afterthe initial 4 minutes. Since the total timeneeded is 20 minutes, it will takeor to completely fillthe bathtub.Check Your Progress VOLUME A swimming pool is beingfilled with water. After 3 hours, 1_4of the pool is filled. Howmuch longer will it take to completely fill the swimming poolassuming the water rate is constant?HOMEWORKASSIGNMENTPage(s):Exercises:MAIN IDEA• Solve problems bydrawing a diagram.
  • 4–7100 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A polygon is a simple closed figure in a plane formedby line segments.Polygons that have the shape are called similarpolygons.The parts of figures that “match” are calledcorresponding parts.Congruent means to have the measure.BUILD YOUR VOCABULARY (pages 85–86)EXAMPLE Identify Similar PolygonsDetermine whether triangle DEF is similar to triangleHJK. Explain your reasoning.4 53.755 6.253ED FJH KFirst, check to see if corresponding angles are congruent.∠D ∠H, <E ∠J, and ∠F ∠K.Next, check to see if corresponding sides are proportional.DE_HJ= = 0.8 EF_JK= = 0.8DF_HK= = 0.8Since the corresponding angles are congruent and4_5= 5_6.25= 3_3.75, triangle DEF is to triangle HJK.Similar PolygonsMAIN IDEA• Identify similarpolygons and findmissing measures ofsimilar polygons.KEY CONCEPTSimilar Polygons If twopolygons are similar, then• their correspondingangles are congruent,or have the samemeasure, and• their correspondingsides are proportional.
  • 4–7Math Connects, Course 3 101Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your ProgressA345C BT4.567.5I RDetermine whethertriangle ABC is similar totriangle TRI. Explainyour reasoning.The of the lengths of twosides of two similar polygons is called the scale factor.BUILD YOUR VOCABULARY (pages 85–86)EXAMPLE Finding Missing MeasuresGiven that rectangleLMNO ∼ rectangle GHIJ,find the missing measure.METHOD 1 Write a proportion.The missing measure n is the length of−−−NO. Write a proportioninvolving NO that relates corresponding sides of the tworectangles.=2_3= 4_n GJ = , LO = , IJ = , and NO =· n = · 4 Find the cross products.= Multiply.= Divide each side by 2.METHOD 2 Use the scale factor to write an equation.Find the scale factor from rectangle GHIJ to rectangle LMNOby finding the ratio of corresponding sides with known lengths.scale factor: GJ_LO= The scale factor is the constant ofproportionality.rectangle GHIJrectangle LMNOrectangle GHIJrectangle LMNOORGANIZE ITMake vocabularycards for each term inthis lesson. Be sure toplace the cards in yourFoldable.®(continued on the next page)
  • 4–7WordsVariablesEquation4 = 2_3n Write the equation.4 · = · 2_3n Multiply each side by .= Simplify.Check Your Progress Given that rectangle ABCD ∼rectangle WXYZ, write a proportion to find the measure of−−ZY.Then solve.HOMEWORKASSIGNMENTPage(s):Exercises:A length on rectangle GHIJ is times as longas a corresponding length on rectangle .Let represent the measure of .102 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.
  • Math Connects, Course 3 103Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 4–8 DilationsThe image produced by or reducing afigure is called a dilation. The center of a dilation is a fixed. A scale factor greater than producesan enlargement. A scale factor between andproduces a reduction.BUILD YOUR VOCABULARY (pages 85–86)EXAMPLE Graph a DilationGraph MNO with vertices M(3, -1), N(2, -2), andO(0, 4). Then graph its image MNO after a dilationwith a scale factor of 3_2.To find the vertices of the dilation, multiply each coordinatein the ordered pairs by 3_2. Then graph both images on thesame axes.M(3, -1) M (9_2, -3_2)N(2, -2) (2 · 3_2, -2 · 3_2) NO(0, 4) OyxOMAIN IDEA• Graph dilations on acoordinate plane.4–8
  • 4–8104 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your ProgressGraph JKL with vertices J(2, 4),K(4, -6), and L(0, -4). Then graphyxOits image JKL after a dilationwith a scale factor of 1_2.EXAMPLE Find and Classify a Scale FactorIn the figure, segment X Y is a yxOXXYYdilation of segment XY. Find thescale factor of the dilation, andclassify it as an enlargement oras a reduction.Write a ratio of the x- or y-coordinate of one vertex of thedilation to the x- or y-coordinate of the corresponding vertexof the original figure. Use the y-coordinates of X(-4, 2) andX(-2, 1).y-coordinate of X___y-coordinate of X=The scale factor is . Since the image is smaller than theoriginal figure, the dilation is a .Check Your Progress In the figure, segment AB is adilation of segment AB. Find the scale factor of the dilation,and classify it as an enlargement or as a reduction.yxOAABBHOMEWORKASSIGNMENTPage(s):Exercises:REMEMBER ITIf the scale factor isequal to 1, the dilationis the same size as theoriginal figure.
  • Math Connects, Course 3 105Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 4–9Indirect measurement uses the properties ofpolygons and to measure distance oflengths that are too to measure directly.BUILD YOUR VOCABULARY (pages 85–86)EXAMPLE Use Shadow ReckoningTREES A tree in front of Marcel’sh ft12 ft3 ft5.5 fthouse has a shadow 12 feet long.At the same time, Marcel has ashadow 3 feet long. If Marcel is5.5 feet tall, how tall is the tree?tree’s shadowMarcel’s shadowtree’s heightMarcel’s height12_3= h_5.5=Find the crossproducts.= Multiply.__ = __Divide each side.by .= h Simplify.The tree is feet tall.Indirect MeasurementMAIN IDEA• Solve problemsinvolving similartriangles.WRITE ITWhich property of similarpolygons is used to setup the proportion for theshadow and height ofMarcel and the tree?
  • 4–9106 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Jayson casts a shadow that is10 feet. At the same time, a flagpole casts a shadow that is40 feet. If the flagpole is 20 feet tall, how tall is Jayson?x ft10 ft20 ft40 ftEXAMPLE Use Indirect MeasurementSURVEYING The two triangles48 m20 m60 md mAB C DEshown in the figure aresimilar. Find the distance dacross the stream.In this figure ABC ∼ EDC.So,−−AB corresponds to−−−ED, and−−−BC corresponds to .AB_EB= BC_DCWrite a .= AB = 48, ED = d, BC = 60, and DC = 20= Find the cross products.= Multiply. Then divide each side by .= d Simplify.The distance across the stream is .ORGANIZE ITInclude a definition ofindirect measurement.Also include anexplanation ofhow to use indirectmeasurement with yourown words or sketch.®
  • 4–9Math Connects, Course 3 107Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress The two triangles shown in thefigure are similar. Find the distance d across the river.5 ft20 ft28 ftd ftTSRQPHOMEWORKASSIGNMENTPage(s):Exercises:
  • 108 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.4–10 Scale Drawings and ModelsA scale drawing or a scale model is used to represent anobject that is too or too to be drawnor built at actual size.The scale is determined by the of given lengthon a to the corresponding actuallength of the object.BUILD YOUR VOCABULARY (pages 85–86)EXAMPLE Find a Missing MeasurementRECREATION Use the map to find the actual distancefrom Bingston to Alanton.DolifAlantonBingstonTribunetScale: 1 in. = 5 miUse an inch ruler to measure the map distance.The map distance is about 1.5 inches.METHOD 1 Write and solve a proportion.1 in._5 mi== Find the cross products.x = Simplify.METHOD 2 Write and solve an equation.Write the scale as which meansper inch.mapactualMAIN IDEA• Solve problemsinvolving scaledrawings.REMEMBER ITScales and scalefactors are usuallywritten so that thedrawing length comesfirst in the ratio.
  • 4–10Math Connects, Course 3 109Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.WordsVariablesEquationThe actual distance is per inch ofmap distance.Let a represent the actual distance in miles.Let m represent the map distance in inches.a = Write the equation.a = 5 Replace m with .a = Multiply.The actual distance from Bingston to Alanton is .EXAMPLE Find the ScaleSCALE DRAWINGS A wall in a room is 15 feet long. On ascale drawing it is shown as 6 inches. What is the scaleof the drawing?Write and solve a proportion to find the scale of the drawing.6 in._15 ft= 1 in._x ft=Find the crossproducts. Multiply.Then divide eachside by 6.x = Simplify.So, the scale is 1 inch = .Check Your Progress The length of a garage is 24 feet. Ona scale drawing the length of the garage is 10 inches. What isthe scale of the drawing?HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITWrite definitions of scale,scale drawing, and scalemodel on cards and giveyour own examples. Besure to explain how tocreate a scale for a scaledrawing or model.®Length of Roomscale drawing lengthactual lengthScale Drawingscale drawing lengthactual length
  • 110 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R4STUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 4 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 4, go to:glencoe.comYou can use your completedVocabulary Builder(pages 85–86) to help you solvethe puzzle.4-1Ratios and RatesMatch each phrase with the term they describe.1. a comparison of two numbers2. a comparison of two quantitieswith different types of units3. a rate that is simplified so ithas a denominator of 14. Express 12 wins to 14 losses as a ratio in simplest form.5. Express 6 inches of rain in 4 hours as a unit rate.4-2Proportional and Nonproportional RelationshipsDetermine whether each relationship is proportional.6. Side length (ft) 1 2 3 4 5Perimeter (ft) 4 8 12 16 207. Time (hr) 1 2 3 4 5Rental Fee ($) 10.00 12.50 15.00 17.50 20.00a. unit rateb. numeratorc. ratiod. rate
  • Math Connects, Course 3 111Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 4 BRINGING IT ALL TOGETHER4-3Rate of ChangeUse the table shown to answer each question.8. Find the rate of change in the numberof bicycles sold between weeks 2 and 4.9. Between which weeks is the rate ofchange negative?4-4Constant Rate of ChangeFind the constant rate of change for each graph and interpretits meaning.10.11. yxScoops42068102 4 6 8 10ServingsWeek Bicycles Sold2 24 146 148 12
  • 112 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 4 BRINGING IT ALL TOGETHER4-5Solving Proportions12. Do the ratios a_band c_dalways form a proportion? Why or why not?Solve each proportion.13. 7_b= 35_514. a_16= 3_815. 4_13= 3_c4-6Problem-Solving Investigation: Draw a Diagram16. FAMILY At Willow’s family reunion, 4_5of the people are 18 yearsof age or older. Half of the remaining people are under 12 yearsold. If 20 children are under 12 years old, how many people areat the reunion?4-7Similar Polygons17. If two polygons have corresponding angles that are congruent,does that mean that the polygons are similar? Why or why not?18. Rectangle ABCD has side lengths of 30 and 5. Rectangle EFGHhas side lengths of 15 and 3. Determine whether the rectanglesare similar.
  • Math Connects, Course 3 113Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 4 BRINGING IT ALL TOGETHER4-8Dilations19. If you are given the coordinates of a figure and the scale factor ofa dilation of that figure, how can you find the coordinates of thenew figure?20. Complete the table.If the scale factor is Then the dilation isbetween 0 and 1greater than 1equal to 14-9Indirect Measurement21. When you solve a problem using shadow reckoning, the objectsbeing compared and their shadows form two sides oftriangles.22. STATUE If a statue casts a 6-foot shadow and a 5-foot mailboxcasts a 4-foot shadow, how tall is the statue?4-10Scale Drawings and Models23. The scale on a map is 1 inch = 20 miles.Find the actual distance for the map distance of 5_8inch.24. What is the scale factor for a model if part of the model that is4 inches corresponds to a real-life object that is 16 inches?
  • Checklist114 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R4Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 4 Practice Test onpage 247 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 4 Study Guide and Reviewon pages 242–246 of your textbook.• If you are unsure of any concepts or skills, refer to the specificlesson(s).• You may also want to take the Chapter 4 Practice Test onpage 247.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in yourStudy Notebook and Chapter 4 Foldable.• Then complete the Chapter 4 Study Guide and Review onpages 242–246 of your textbook.• If you are unsure of any concepts or skills, refer to thespecific lesson(s).• You may also want to take the Chapter 4 Practice Test onpage 247.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 4.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher Signature
  • ®Chapter5Math Connects, Course 3 115Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R5 PercentUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with 4 sheets of 81_2" × 11" paper.Draw a large circle onone of the sheetsof paper.Stack the sheets of paper.Place the one with thecircle on top. Cut all foursheets in the shape ofa circle.Staple the circles on thePercentleft side. Write the chaptertitle and the first four lessonnumbers on each circle.Turn the circles to the backLesson5-6side so that the staples arestill on the left. Write thelast four lesson titles onthe front and right pagesof the journal.NOTE-TAKING TIP: When you take notes, it mayhelp to create a visual representation, such as adrawing or a chart, to organize the informationyou learn. When you use a visual, be sure toclearly label it.
  • 116 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R5UILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 5.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecompatible numberscompound interestdiscountinterestmarkuppercent
  • Math Connects, Course 3 117Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 5 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplepercent equationpercent of changepercent of decreasepercent of increasepercent proportionprincipalselling price
  • 118 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.5–1such as 27 out of 100 or 8 out of 25 can bewritten as percents.BUILD YOUR VOCABULARY (pages 116–117)EXAMPLES Write Ratios as PercentsPOPULATION According to a recent census, 13 out ofevery 100 people living in Delaware were 65 or older.Write this ratio as a percent.13 out of every = 13%BASEBALL Through 2005, Manny Ramirez has gottenon base 40.9 times for every 100 times at bat. Write thisratio as a percent.40.9 out of = 40.9%Check Your Progress Write each ratio as a percent.a. 59 out of 100 b. 68 out of 100EXAMPLES Write Ratios and Fractions as PercentsTRANSPORTATION About 4 out of 5 commuters in theUnited States drive or carpool to work. Write this ratioas a percent.4_5= 80_100××So, out of equals .MAIN IDEA• Write ratios as percentsand vice versa.Ratios and PercentsKEY CONCEPTPercent A percent is aratio that compares anumber to 100.
  • 5–1Math Connects, Course 3 119Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. INTERNET In 2000, about 3_200of the population in Peruused the Internet. Write this fraction as a percent.÷3_200= 1.5_100÷So, out of equals .Check Your Progress Write each ratio or fractionas a percent.a. 3 out of 5 b. 122_200teensEXAMPLE Write Percents as FractionsSCHEDULE The circle graph shows an estimate of thepercent of his day that Peter spends on each activity.Write the percents for eating and sleeping as fractions insimplest form.Eating: 5% = or30%School35%Sleep15%Other15%TelevisionHow Peter Spends His Day5%EatSleeping: 35% = orCheck Your ProgressThe circle graph shows anestimate of the percent of hisday that Leon spends on eachactivity. Write the percents forschool and television asfractions in simplest form.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITWrite in words andsymbols what you’velearned about expressingratios as percents.Lesson5-1®
  • 120 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.5–2 Comparing Fractions, Decimals, and PercentsEXAMPLES Percents as DecimalsWrite each percent as a decimal.52%52% = 52% Divide by .= Remove the percent symbol.245%245% = 245% Divide by .= Remove the percent symbol.Check Your Progress Write each percent as a decimal.a. 28% b. 135%EXAMPLES Decimals as PercentsWrite each decimal as a percent.0.30.3 = 0.30 Multiply by .= Add the percent symbol.0.710.71 = 0.71 Multiply by .= Add the percent symbol.Check Your Progress Write each decimal as a percent.a. 0.91 b. 1.65MAIN IDEA• Write percents asfractions and decimalsand vice versa.KEY CONCEPTSDecimals and PercentsTo write a percent as adecimal, divide by 100and remove the percentsymbol.To write a decimal asa percent, multiply by100 and add the percentsymbol.
  • 5–2Math Connects, Course 3 121Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Fractions as PercentsWrite 3_4as a percent.METHOD 1Use a proportion.3_4= x_1003 · 100 =300 === xSo, 3_4can be written as .METHOD 2First write as a decimal.Then write as a percent.3_4= 0.75 0.754 3.00_2820_200=Write 1_6as a percent.METHOD 1Use a proportion.1_6= x_100= 6 · x= 6x== xMETHOD 2First write as a decimal.Then write as a percent.1_6= 0.16−6 0.166...6 1.0000_640_3640_364=So, 1_6can be written as .Check Your Progress Write each fraction as a percent.a. 1_4b. 1_9Show an example ofhow to write fractions asdecimals. (Lesson 2-1)REVIEW IT
  • 5–2122 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Compare NumbersPOLITICS In Sun City, 0.45 of voters are Democrats. InMoon Town, 48% of voters are Democrats. In which townis there a greater portion of Democrats?Write 0.45 as a percent.0.45 = and addthe symbol.Since is less than , there areDemocrats in Moon Town.Check Your Progress In Star City, 3_20of voters areRepublicans. In Meteorville, 13% of voters are Republicans.In which town is there a greater proportion of Republicans?EXAMPLE Order NumbersOrder 70%, 7_100, 19_25, and 0.77 from least to greatest.7_100= 19_25= __100or 0.77 =From least to greatest, the numbers are7_100, , 19_25, and .Check Your Progress Order 18%, 1_5, 3_10, and 0.21 fromleast to greatest.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITWrite in words andsymbols what you havelearned about therelationship betweenpercents, decimals, andfractions.Lesson5-2®
  • Math Connects, Course 3 123Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.In a percent proportion, of the numbers, calledthe part, is being compared to the quantity,also called the base. The other ratio is the percent, writtenas a fraction, whose base is .BUILD YOUR VOCABULARY (pages 116–117)EXAMPLE Find the Percent34 is what percent of 136?Since 34 is being compared to 136, is part and isthe whole. You need to find the percent. Let n represent thepercent.partwhole34_136= n_100Write the percent proportion.· = · n Find the cross products.= Multiply.= Divide each side by .= Simplify.So, 34 is of 136.Check Your Progress 63 is what percent of 210?5–3 Algebra: The Percent ProportionMAIN IDEA• Solving problems usingthe percent proportion.KEY CONCEPTPercent Proportionpart_whole=percent__100
  • 5–3124 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find the PartWhat number is 70% of 600?The percent is 70, and the whole is 600. You need to find thepart. Let n represent the part.partwholen_600= 70_100Write the percent proportion.n · 100 = 600 · 70 Find the cross products.100n = Multiply.100n_100=42,000__100Divide each side by .n = Simplify.So, is 70% of 600.Check Your Progress What number is 40% of 400?EXAMPLE Find the BaseBASEBALL From 1999 to 2001, Derek Jeter had 11 hitswith the bases loaded. This was about 30% of his atbats with the bases loaded. How many times was he atbat with the bases loaded?The percent is 30, and the part is 11 hits. You need to find thewhole number of hits.partwhole11_n = 30_100percentWrite the percentproportion.11 · = n · Find the cross products.= Multiply.≈ n Divide each side by 30.He had about at bats with the bases loaded.Check Your Progress BASEBALL In 2005, AlexRodriguez had 194 hits. This was about 32% of his at bats.How many times was he at bat?ORGANIZE ITBe sure to explain howto find the percent, thepart, and the base of apercent proportion. Youalso may want to showthe ideas in a chart likethe Concept Summary inyour text.Lesson5-3®HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 125Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLES Use Fractions to Compute MentallyCompute mentally.40% of 8040% of 80 = of 80 or Use the fraction form of40%, which is .662_3% of 75662_3% of 75 = of 75 or . Use the fraction form of662_3%, which is .EXAMPLES Use Decimals to Compute MentallyCompute mentally.10% of 6510% of 65 = of 65 or1% of 3041% of 304 = of 304 orCheck Your Progress Compute mentally.a. 20% of 60 b. 662_3% of 300c. 10% of 13 d. 1% of 244Finding Percents Mentally5–4MAIN IDEA• Compute mentally withpercents.WRITE ITExplain how you canmove the decimal pointto mentally multiply 0.1by 1.1.
  • 5–4126 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Use Mental Math to Solve a ProblemTECHNOLOGY A company produces 2,500 of aparticular printer. They later discover that 25% ofthe printers have defects. How many printers fromthis group have defects?METHOD 1 Use a fraction.25% of 2,500 = of 2,500THINK 1_4of 2,000 is and 1_4of 500 is .So, of 2,500 is + or .METHOD 2 Use a decimal.25% of 2,500 = of 2,500THINK 0.5 of 2,500 is .So, 0.25 of 2,500 is · or .There were printers that had defects.Check Your Progress A company produces 1,400 ofa particular monitor. They later discover that 20% of themonitors have defects. How many monitors from this grouphave defects?HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITIn your Foldable, be sureto include examples thatshow how to estimatepercents of numbers.Lesson5-4®
  • Math Connects, Course 3 127Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLESHOPPING Cara sees an advertisement for a pair ofshoes. One pair costs $34.99 plus 5 percent tax. Shewants to buy a black pair and a brown pair. Cara has$75 saved in her clothing budget. Can she afford bothpairs of shoes?UNDERSTAND You know the cost of the shoes and the salestax rate. You want to know if two pairs ofshoes plus sales tax will be orthan .PLAN Use to determine areasonable answer.SOLVE THINK $34.99 × 2 ≈10% of $70 = $7, so 5% of $70 =The total cost will be about $70 + $3.50 =. Since Cara has $75, she will haveenough to buy .CHECK Find the of the two pairsof shoes. Then compute the sales tax andcompare the sumto $75.Check Your Progress SHOPPING David wants to buy aCD for $11.99 and a pack of batteries for $3.99. The sales taxrate is 5 percent. If David has $17 in his wallet, will he haveenough to buy the CD and batteries?5–5 Problem-Solving Investigation:Reasonable AnswersMAIN IDEA• Determine areasonable answer.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 128 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Compatible numbers are two numbers that are easy to add,subtract, multiply, or divide mentally.BUILD YOUR VOCABULARY (pages 116–117)EXAMPLES Estimate Percents of NumbersEstimate.48% of 7048% is about or . and 70 arecompatible numbers.of 70 is .So, 48% of 70 is about .12% of 8112% is about 12.5% or , and areand 81 is about .compatible numbers.of is .So, 12% of 81 is about .23% of 8223% is about 1_4, and 82 is about . 1_4and arecompatible numbers.1_4of is .So, 23% of 82 is about .Percent and Estimation5–6MAIN IDEA• Estimate by usingequivalent fractionsand percents.
  • 5–6Math Connects, Course 3 129Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Estimate.a. 51% of 60 b. 34% of 59 c. 25% of 33EXAMPLEPOPULATION About 9% of the population of Texas lives inthe city of Houston. If there are about 22 million peoplein the state of Texas, estimate the population of Houston.9% of 22 million ≈ or of 22 million 9% is about.= × 22 =So, the population of Houston is about .Check Your Progress LEFT-HANDEDNESS About 11%of the population is left-handed. If there are about 17 millionpeople in Florida, about how many Florida residents areleft-handed?EXAMPLES Estimate PercentsEstimate each percent.12 out of 4712_47≈ or 1_447 is about .1_4= %So, 12 out of 47 is about .ORGANIZE ITInclude the meaning ofthe symbol “≈.” Youmay wish to include anexample of estimatinga percent in which thesymbol ≈ is used.Lesson5-6®
  • 5–6130 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.41 out of 20041_200≈ or 1_541 is about .1_5=So, 41 out of 200 is about .58 out of 7158_71≈ or 5_658 is about , and 71 is about .5_6= %So, 58 out of 71 is about .Check Your Progress Estimate each percent.a. 15 out of 76b. 58 out of 121c. 14 out of 47HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 131Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The percent equation is an equivalent form of the percentproportion in which the is written as a.BUILD YOUR VOCABULARY (pages 116–117)EXAMPLE Find the PartFind 30% of 450.Estimate 10% of 450 is 45. So, 30% of 450 is 3 · 45 or 135.The percent is . The whole is . You need to find thepart. Let n represent the part.part = percent · wholen = · Write the percent equation.n = Multiply.So, 30% of 450 is .EXAMPLE Find the Percent102 is what percent of 150?Estimate 102_150≈ 100_150or 662_3%The part is . The whole is . You need to find thepercent. Let n represent the percent.part = percent · whole= n · Write the percent equation.102_150= 150n_150Divide each side by 150.= n Simplify.Since = %, 102 is % of 150.Algebra: The Percent Equation5–7MAIN IDEA• Solve problems usingthe percent equation.Explain how to write adecimal as a percent.(Lesson 5-2)REVIEW IT
  • 5–7132 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find the Base144 is 45% of what number?Estimate 144 is 50% of 288.The part is . The percent is . You need to find thewhole. Let n represent the whole.part = percent · whole= · n Write the percent equation.144_0.45= 0.45n_0.45Divide each side by 0.45.= n Simplify.So, 144 is 45% of .Check Your Progress Find the part, percent, or base.a. Find 20% of 315. b. 135 is what percent of 250?c. 186 is 30% of what number?EXAMPLE Solve a Real-Life ProblemSALES TAX The price of a sweater is $75. The sales tax is53_4%. What is the total price of the sweater?You need to find what amount is 53_4% of $75.Let t = the amount of tax.t = · Write the equation.t = Simplify.The amount of tax is . The total cost of the sweateris $75 + or .Check Your Progress The price of a pair of shoes is $60.The sales tax is 5 percent. What is the total price of the shoes?ORGANIZE ITWrite the percentequation in words andsymbols. Explain whythe rate in a percentequation is usuallywritten as a decimal.Lesson5-7®HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 133Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Percent of Change5–8A percent of change is a that compares thechange in quantity to the original amount. When the newamount is than the original, the percent ofchange is called a percent of increase.When the new amount is than the original, thepercent of change is called a percent of decrease.BUILD YOUR VOCABULARY (pages 116–117)EXAMPLE Find the Percent of IncreaseHOMES The Neitos bought a house several years agofor $120,000. This year, they sold it for $150,000. Findthe percent of change. State whether the change is anincrease or decrease.Step 1 The amount of change is 150,000 - 120,000 =Step 2 Percent of change =amount of change____original amountDefinition ofpercent ofchange= ___= 0.25 Divide.Step 3 The decimal 0.25 written as a percent is . So, thepercent of change is .The new amount is than the original. The percentof is 25%.Check Your Progress CLUBS Last year Cedar Park SwimClub had 340 members. This year they have 391 members.Find the percent increase.MAIN IDEA• Find and use thepercent of increase ordecrease.KEY CONCEPTPercent of Change Apercent of change is aratio that compares thechange in quantity to theoriginal amount.
  • 5–8134 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find the Percent of ChangeSCHOOLS Johnson Middle School had 240 students lastyear. This year, there are 192 students. Find the percentof change. State whether the percent of change is anincrease or a decrease.Step 1 The amount of change is 240 - 192 = .Step 2 Percent of change =amount of change____original amount= __= 0.20 Divide.Step 3 The decimal 0.20 written as a percent is .The percent of change is . Since the new amount isthan the original, it is a percent of .Check Your Progress CARS Meagan bought a new carseveral years ago for $14,000. This year she sold the car for$9,100. Find the percent of change. State whether the percentof change is an increase or a decrease.The markup is the amount the price of an item isabove the price the storefor the item.The selling price is the amount the pays.The amount by which a isis called the discount.BUILD YOUR VOCABULARY (pages 116–117)ORGANIZE ITBe sure to includean explanation andexamples showing thedifference betweenpercent of increase andpercent of decrease.Lesson5-8®
  • 5–8Math Connects, Course 3 135Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Find the Selling PriceMARKUP Shirts bought by a sporting goods store costthem $20 per shirt. They want to mark them up 40%.What will be the selling price?METHOD 1 Find the amount of the markup first.The whole is . The percent is . You need to find theamount of the markup, or the part. Let m represent the amountof the markup.part = percent · wholem = · Write the equation.m = Multiply.Add the markup to the cost of each shirt to find the sellingprice. + =METHOD 2 Find the total percent first.The customer will pay 100% of the store’s cost plus an extra40% of the cost. Find 100% + 40% or 140% of the store’s cost.Let p represent the price.part = percent · wholep = · Write the equation.p = Multiply.The selling price of the shirts for the customer is .Check Your Progress Silk flowers bought by a craft storecost them $10 per box. They want to mark them up 35 percent.What will be the selling price?REMEMBER ITThere may be morethan one way to solve aproblem. See pages 286and 287 of your textbookfor other methods youcan use to solve Examples3 and 4.
  • 5–8136 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find the Sale PriceSHOPPING A computer usually sells for $1,200. Thisweek, it is on sale for 30% off. What is the sale price?METHOD 1 Find the amount of the discount first.The percent is , and the whole is . We need tofind the amount of the discount, or the part. Let d represent theamount of discount.part = percent · wholed = · Write the equation.d = Multiply.Subtract the amount of the discount from the original price tofind the sale price.- =METHOD 2 Find the percent paid first.If the amount of the discount is 30%, the percent paid is100% - 30% or 70%. Find 70% of $1,200. Let s representthe sale price.part = percent · wholes = · Write the equation.s = Multiply.The sale price of the computer is .Check Your Progress A DVD sells for $28. This week it ison sale for 20% off. What is the sale price?HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 137Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 5–9 Simple InterestInterest is the amount of money paid or for theuse of money.Principal is the amount of money or borrowed.BUILD YOUR VOCABULARY (pages 116–117)EXAMPLE Find Simple InterestFind the simple interest for $2,000 invested at 5.5%for 4 years.I = prt Write the simple interest formula.I = · · Replace p with , rwith , and t with .I = The simple interest is .EXAMPLE Find the Total AmountTEST EXAMPLE Find the total dollar amount in anaccount where $80 is invested at a simple annualinterest rate of 6% for 6 months.A $41.20 B $82.40 C $84.80 D $108.80Read the ItemYou need to find the total amount in an account. The time isgiven in months. Six months is 6_12or year.Solve the ItemI = prtI = · ·I =The amount in the account is $80 + or .The correct answer is choice .MAIN IDEA• Solve problemsinvolving simpleinterest.REMEMBER ITThe t in the simpleinterest formularepresents time inyears. If time is givenin months, weeks, ordays, the time must bechanged to time in years.
  • 5–9138 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progressa. Find the simple interest for $1,500 invested at 5% for3 years.b. Find the total amount of money in an account where $60 isinvested at 8% for 3 months.EXAMPLE Find the Interest RateLOANS Gerardo borrowed $4,500 from his bank for homeimprovements. He will repay the loan by paying $120a month for the next four years. Find the simple interestrate of the loan.Use the formula I = prt. To find I, first find the total amount ofmoney Gerardo will pay.$120 · 48 = .He will pay - $4,500 or in interest.So I = 1,260.The principle is $4,500. So, p = 4,500. The loan will be for48 months or 4 years. So, t = 4.I = p · r · t= · r ·= Simplify.= Divide each side by 18,000.= r Simplify.The simple interest rate is .Check Your Progress Jocelyn borrowed $3,600 from herbank for home improvements. She will repay the loan by paying$90 a month for the next 5 years. Find the simple interest rateof the loan.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITExplain what you havelearned about computingsimple interest. Be sureto include the simpleinterest formula.Lesson5-9®
  • Math Connects, Course 3 139Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R5STUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 5 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 5, go to:glencoe.comYou can use your completedVocabulary Builder(pages 116–117) to help yousolve the puzzle.5-1Ratios and PercentsWrite each ratio or fraction as a percent.1. 21 out of 100 2. 4:10 3. 9_25Write each percent as a fraction in simplest form.4. 27% 5. 50% 6. 80%5-2Comparing Fractions, Decimals, and PercentsWrite each percent as a decimal.7. 29% 8. 376% 9. 5%Write each decimal or fraction as a percent.10. 3.9 11. 7_812. 1_3
  • 140 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 5 BRINGING IT ALL TOGETHER5-3Algebra: The Percent ProportionSolve.13. What percent of 48 is 6? 14. 14 is 20% of what number?5-4Finding Percents MentallyComplete each statement.15. 40% of 25 = of 25 or 16. of 36 = 1_4of 36 or17. 662_3% of 48 = of 48 or 18. of 89 = 0.1 of 89 or5-5Problem-Solving Investigation: Reasonable Answers19. AGRICULTURE An orange grower harvested 1,260 pounds oforanges from one grove, 874 pounds from another, and 602 poundsfrom a third. What is a reasonable number of crates to have onhand if each crate holds 14 pounds of oranges?5-6Percent and Estimation20. Are 1_8and 56 compatible numbers? Explain.21. Describe how to estimate 65% of 64 using compatible numbers.
  • Math Connects, Course 3 141Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 5 BRINGING IT ALL TOGETHER5-7Algebra: The Percent EquationWrite each percent proportion as a percent equation.22. 16_64= 25_10023. a_14= 2_10024. 96_b= 48_10025. 13_100=p_6755-8Percent of ChangeFind the percent of change. Round to the nearest tenth ifnecessary. State whether the change is an increase or decrease.29. Original: 29 30. Original: 51New: 64 New: 4231. Find the selling price for the sweater.Cost to store: $15Mark up: 35%5-9Simple InterestWrite interest or principal to complete each sentence.32. is the amount of money paid or earned for the useof money.33. equals times rate times time.34. Find the total amount in the account where $560 is invested at5.6% for 6 months.First, find the earned. Then, add the earnedand the to find the total amount in the account. Whatis the total amount for $560 at 5.6% for 6 months?
  • Checklist142 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R5Check the one that applies. Suggestions to help you study are givenwith each item.I completed the review of all or most lessons without using mynotes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 5 Practice Test onpage 299 of your textbook as a final check.I used my Foldable or Study Notebook to complete the review ofall or most lessons.• You should complete the Chapter 5 Study Guide and Reviewon pages 295–298 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 5 Practice Test on page 299.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 5 Foldable.• Then complete the Chapter 5 Study Guide and Review onpages 295–298 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 5 Practice Test onpage 299.Visit glencoe.com to accessyour text book, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 5.
  • ®Chapter6Math Connects, Course 3 143Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with 7 sheets of 81_2" × 11" paper.Fold a sheet ofpaper in halflengthwise. Cut a1" tab along the leftedge through onethickness.Glue the 1" tab down.Write the lesson titleon the front tab.Repeat Steps 1–2 for theremaining sheets of paper.Staple together to form abooklet.NOTE-TAKING TIP: When you read and learnnew concepts, help yourself remember theseconcepts by taking notes, writing definitions andexplanations, and draw models as needed.Geometry and Spatial ReasoningC H A P T E R6
  • 144 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.UILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 6.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplealternate exterioranglesalternate interioranglescomplementary anglescongruent polygonequiangularequilateralequilateral triangleexterior anglesinterior anglesline of reflectionline of symmetryC H A P T E R6
  • Math Connects, Course 3 145Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 6 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleline symmetryobtuse triangleparallel linesperpendicular linesreflectionregular polygonsupplementary anglestransformationtranslationtransversalvertical angles
  • 146 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.6–1 Line and Angle RelationshipsMAIN IDEA• Identify specialpairs of angles andrelationships ofangles formed by twoparallel lines cut by atransversal.Vertical angles are angles formed byintersecting lines. Vertical angles are .The sum of the measures of supplementary anglesis .The sum of the measures of complementary anglesis .BUILD YOUR VOCABULARY (pages 144–145)EXAMPLE Finding a Missing Angle MeasureThe two angles below are supplementary. Find thevalue of x.x˚155˚155 + x = 180 Write an equation.= Subtract from each side.x = 25 Simplify.EXAMPLE Find a Missing Angle MeasureFind the value of x in the figure.Use the two vertical angles to solve68ЊxЊfor x.+ x = Write an equation.___________–68 –68 Subtract 68 from each side.x = Simplify.KEY CONCEPTSAcute angles havemeasures less than 90°.Right angles havemeasures equal to 90º.Obtuse angles havemeasures between 90°and 180°.Straight angles havemeasures equal to 180°.
  • 6–1Math Connects, Course 3 147Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find the value of x in each figure.a. b.70˚x˚Lines that intersect at angles are calledperpendicular lines.Two lines in a plane that never or cross arecalled parallel lines.A transversal is a line that two or more lines.Interior angles lie the two lines and exteriorangles lie the two lines.Alternate interior angles are angles that lieon opposite sides of the transversal.Alternate exterior angles are exterior angles that lie onsides of the transversal.Corresponding angles are those angles that are in the sameon the two lines in relation to the transversal.BUILD YOUR VOCABULARY (pages 144–145)
  • 6–1148 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Find an Angle MeasureBRIDGES The sketch below shows a simple bridgedesign. The top beam and the floor of the bridgeare parallel. If ∠2 ∠3 and m∠3 = 55°, classify therelationship between ∠1 and ∠5. Then find m∠1and m∠5.Since ∠3 and ∠5 are angles, they arecongruent. Also, since ∠1 and ∠2 are ,∠1 and ∠3 are , and ∠1 and ∠5 aresupplementary.Since m∠3 = 55° and ∠2 ∠3, m∠2 = .Since ∠3 and ∠5 are alternate interior angles, m∠5 = .Since ∠1 and ∠2 are supplementary, the sum of their measuresis 180°.Therefore, m∠1 = 180° − 55° or .Check Your Progress BRIDGES The sketch below showsa simple bridge design. The top beam and floor of the bridge areparallel. If m∠1 = 45° and m∠3 = 40°, find m∠4.1423ORGANIZE ITUse sketches and wordsto define the lines andangles discussed in thislesson. Try to showrelationships amongdifferent lines andangles. Write this in yourFoldable.®
  • Math Connects, Course 3 149Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.MAIN IDEA• Solve problems byusing the logicalreasoning strategy.EXAMPLE Use Logical ReasoningFOOD Mona, Sharon, Pat, and Dena each have a favoritefood. One likes pizza, another fish and chips, anotherchicken, and another hamburgers. From the given clues,give each person’s favorite food.• Pat does not like pizza, hamburgers, or fish and chips.• Neither Mona nor Dena likes hamburgers.• Mona does not like to eat fried food.UNDERSTAND You know that each of the four students hasa particular favorite food. Use the clues givenand logical reasoning to determine the favoritefood of each student.PLAN Read each clue and deduce what you knowabout the favorite foods of the students.SOLVE According to the first clue, Pat does not like pizza,hamburgers, or fish and chips. The only otheroption is , so Pat likes .Since neither Mona nor Dena likeshamburgers, that means that mustlike hamburgers.Finally, there are two students left, Mona andDena, and two food choices left, pizza and fishand chips. Since Mona does not like, she must like . Denalikes .CHECK Read each clue again and make sure theanswers seem reasonable.Check Your Progress SPORTS Craig, Amy, Julia, andRonaldo each have a favorite sport. One likes soccer, anotherbasketball, another tennis, and another skateboarding. Fromthe given clues, give each person’s favorite sport.• Amy does not like soccer, basketball, or skateboarding.• Neither Craig nor Ronaldo likes playing soccer.• Craig prefers team sports as opposed to individual sports.6–2 Problem-Solving Investigation:Use Logical ReasoningHOMEWORKASSIGNMENTPage(s):Exercises:
  • 150 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.An interior angle lies a polygon.BUILD YOUR VOCABULARY (pages 144–145)EXAMPLE Find the Sum of Interior Angle MeasuresFind the sum of the measures of the interior anglesof a hexagon.A hexagon has sides.S = (n - 2)180 Write an equation.S = ( - 2)180 Replace n with .S = (4)180 or Simplify.The sum of the measures of the interior angles of a hexagonis .Check Your Progress Find the sum of the measures of theinterior angles of a heptagon (7-sided figure).A polygon that is equilateral (all congruent)and equiangular (all congruent) is called aregular polygon.BUILD YOUR VOCABULARY (pages 144–145)6–3 Polygons and AnglesMAIN IDEA• Find the sum of anglemeasures of a polygonand the measure ofan interior angle of apolygon.KEY CONCEPTInterior Angle Sum of aPolygonThe sum of the measuresof the interior angles ofa polygon is (n - 2)180,where n is the numberof interior angles in thepolygon.
  • 6–3Math Connects, Course 3 151Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Find the Measure of an Interior AngleDESIGN A designer is creating a new logo for a bank.The logo consists of a regular pentagon surrounded byisosceles triangles. Find the measure of an interior angleof a pentagon.A pentagon has sides.Step 1 Find the sum of the measures of the angles.S = (n - 2)180 Write an equation.S = ( - 2)180 Replace n with .S = (3)180 or Simplify.The sum of the measures of the interior angles ofa regular pentagon is .Step 2 Divide 540 by , the number of interior angles, tofind the measure of one interior angle. So, themeasure of one interior angle of a regular pentagon is÷ or .Check Your Progress DESIGN Michelle is designing anew logo for the math club. She wants to use a regular nonagonas part of the logo. Find the measure of an interior angle of anonagon.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 152 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.6–4 Congruent PolygonsMAIN IDEA• Identify congruentpolygons.Polygons that have the same and arecalled congruent polygons.BUILD YOUR VOCABULARY (pages 144–145)EXAMPLE Identify Congruent PolygonsDetermine whether the trapezoids shown are congruent.If so, name the corresponding parts and write acongruence statement.2 cm4 cm8 cm6 cmRSTQ 2 cm 4 cm8 cm6 cmHEFGThe arcs indicate that ∠S ∠G, ∠T ∠H, ∠Q ∠E, and. The side measures indicate that−−ST−−−GH,−−−TQ−−−HE,−−−QR−−EF, and .Since pairs of corresponding angles and sides are, the two trapezoids are .One congruence statement istrapezoid EFGH trapezoid .Check Your Progress35355555ACBF EDDetermine whether thetriangles shown arecongruent. If so, namethe corresponding partsand write a congruencestatement.
  • 6–4Math Connects, Course 3 153Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Find Missing MeasuresIn the figures, FGH QRS.GHF 6 cm9 cm25˚35˚SQRFind m∠S.According to the congruence statement, ∠H and ∠S arecorresponding angles. So, .Since m∠H = , m∠S = .Find QR.−−−FG corresponds to . So, .Since FG = centimeters, QR = centimeters.Check Your Progress In the figure, ABC LMN.75555 in.3 in.50B LNA CMa. Find m∠ N. b. Find LN.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 154 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.6–5 SymmetryA figure has line symmetry if it can be folded over a lineso that one half of the figure the other half.The line is called the line of symmetry.BUILD YOUR VOCABULARY (pages 144–145)EXAMPLES Identify Line SymmetryDetermine whether the figure has line symmetry. If itdoes, draw all lines of symmetry. If not, write none.This figure has line of symmetry.Check Your ProgressDetermine whether theleaf has line symmetry.If it does, draw all lines ofsymmetry. If not, write none.A figure has rotational symmetry if it can be rotated aboutits . The measure of the angleis the angle of rotation.BUILD YOUR VOCABULARY (pages 144–145)MAIN IDEA• Identify line symmetryand rotationalsymmetry.ORGANIZE ITUse sketches andwords to show linesof symmetry and linesymmetry. Write this inyour Foldable.®
  • 6–5Math Connects, Course 3 155Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Identify Rotational SymmetryFLOWERS Determine whether the flower design hasrotational symmetry. Write yes or no. If yes, name itsangle(s) of rotation.Yes, this figure hassymmetry. It will match itself after beingrotated 90°, 180°, and .0˚270˚90˚180˚Check Your Progress Determine whether each flowerdesign has rotational symmetry. Write yes or no. If yes,name its angle(s) of rotation.a. b.WRITE ITHow many degrees doesone complete turn of afigure measure? Why is itthis number of degrees?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 156 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.6–6 ReflectionsMAIN IDEA• Graph reflections on acoordinate plane.KEY CONCEPTProperties of Reflections1. Every point on areflection is the samedistance from the lineof reflection as thecorresponding pointon the original figure.2. The image is congruentto the original figure,but the orientation ofthe image is differentfrom that of theoriginal figure.A reflection (sometimes called a flip) is a transformation inwhich a image is produced bya figure over a line. The line is called a line of reflection.BUILD YOUR VOCABULARY (pages 144–145)EXAMPLE Draw a ReflectionDraw the image of trapezoid STUV after a reflectionover the given line.Step 1 Count the number of unitsVUTSUTSVbetween each vertex andthe line of .Step 2 Plot a point for each vertexthe distanceaway from the line on theother side.Step 3 Connect the new to form theimage of trapezoid STUV, trapezoid STUV.Check Your Progress Draw the image of trapezoid TRAPafter a reflection over the given line.TPRA
  • 6–6Math Connects, Course 3 157Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Reflect a Figure over the x-axisGraph quadrilateral EFGH with verticles E(-4, 4),F(3, 3), G(4, 2), and H(-2, 1). Then graph the image ofEFGH after a reflection over the x-axis and write thecoordinates of its vertices.yxOFEHGHEFGThe coordinates of the verticles of the image are E ,F , G and H .oppositessameE(-4, 4) E(-4, -4)F(3, 3) F(3, -3)G(4, 2)H(-2, 1)Notice that the y-coordinate of a point reflected over the x-axisis the of the y-coordinate of the original point.Check Your Progress Graph quadrilateral QUAD withvertices Q(2, 4), U(4, 1), A(-1, 1), and D(-3, 3). Then graphthe image of QUAD after a reflection over the x-axis, and writethe coordinates of its vertices.xOyORGANIZE ITDraw a triangle or simplequadrilateral on graphpaper. Reflect your figureover the x-axis. Add yourwork to your Foldable.®
  • 6–6158 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Reflect a Figure over the y-axisGraph trapezoid ABCD with vertices A(1, 3), B(4, 0),C(3, -4), and D(1, -2). Then graph the image of ABCDafter a reflection over the y-axis, and write thecoordinates of its vertices.yxODCBADABCThe coordinates of the vertices of the image are A ,B , C , and D .oppositessameA(1, 3) A(-1, 3)B(4, 0) B(-4, 0)C(3, -4)D(1, -2)Notice that the x-coordinate of a point reflected over the y-axisis the opposite of the x-coordinate of the point.Check Your Progress Graph quadrilateral ABCD withvertices A(2, 2), B(5, 0), C(4, -2), and D(2, -1). Then graphthe image of ABCD after a reflection over the y-axis, and writethe coordinates of its vertices.xOyHOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 159Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 6–7 TranslationsA translation (sometimes called a slide) is theof a figure from one position to anotherturning it.BUILD YOUR VOCABULARY (pages 144–145)EXAMPLE Draw a TranslationDraw the image of EFG after a translation of 3 unitsright and 2 units up.GEFFEGStep 1 Move each vertex of the triangle units rightand units up.Step 2 Connect the new vertices to form the .Check Your Progress Draw the image of ABC after atranslation of 2 units right and 4 units down.BACMAIN IDEA• Graph translations on acoordinate plane.KEY CONCEPTProperties of Translations1. Every point on theoriginal figure ismoved the samedistance and in thesame direction.2. The image is congruentto the original figure,and the orientation ofthe image is the sameas that of the originalfigure.
  • 6–7160 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Translation in the Coordinate PlaneGraph ABC with vertices A(-2, 2), B(3, 4), andC(4, 1). Then graph the image of ABC after atranslation of 2 units left and 5 units down. Write thecoordinates of its vertices.xOyThe coordinates of the vertices of the image areA , B , and C . Notice thatthese vertices can also be found by adding to thex-coordinates and to the y-coordinates, or (-2, -5).Original Add (-2, -5) ImageA(-2, 2) (-2 + (-2), 2 + (-5))B(3, 4) (3 + (-2), 4 + (-5))C(4, 1) (4 + (-2), 1 + (-5))Check Your Progress Graph PQR with vertices P(-1, 3),Q(2, 4), and R(3, 2). Then graph the image of PQR aftera translation of 2 units right and 3 units down. Write thecoordinates of its vertices.xOyORGANIZE ITDraw a triangle or simplequadrilateral on graphpaper. Then draw atranslation. Show howyou determined thepoints needed to graphthe translated figure.Put your work in yourFoldable.®
  • 6–7Math Connects, Course 3 161Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLETEST EXAMPLE If triangle RSTis translated 4 units right andyxORTS3 units up, what are thecoordinates of point T ?A (0, 3) C (2, 1)B (1, 2) D (1, 1)Read the ItemYou are asked to find the coordinates of point T after theoriginal figure has been translated 4 units right and 3 units up.Solve the ItemYou can answer this question without translating the entiretriangle.The coordinates of point T are.Original figureThe x-coordinate of T is, so the samex-coordinate of T is + 4or .Translating 4 units right isthe as to thex-coordinate.The y-coordinate of T is ,so the y-coordinate of T is+ 3 or .Translating 3 units up is thesame as adding to they-coordinate.The coordinates of T are .The answer is .Check Your ProgressyxOLMNMULTIPLE CHOICE If triangle LMNis translated 4 units left and 2 units up,what are the coordinates of point L ?F (0, -1) H (-1, -4)G (-3, 2) J (-2, 3)HOMEWORKASSIGNMENTPage(s):Exercises:
  • 162 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERSTUDY GUIDEC H A P T E R6® VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 6 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 6, go to:glencoe.comYou can use your completedVocabulary Builder(pages 144–145) to help yousolve the puzzle.6-1Line and Angle RelationshipsFor Questions 1–4, use the figure at the right.1. Classify the relationship1 23 45 67 8acbbetween ∠5 and ∠6.2. Classify the relationshipbetween ∠5 and ∠8.3. Find m∠3 if m∠2 = 60°.4. Find m∠4 if m∠2 = 60°.6-2Problem-Solving Investigation: Use Logical Reasoning5. BASKETBALL Juan, Dallas, and Scott play guard, forward, andcenter on a team, but not necessarily in that order. Juan and thecenter drove Scott to practice on Saturday. Juan does not playguard. Who is the guard?
  • Math Connects, Course 3 163Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 6 BRINGING IT ALL TOGETHER6-3Polygons and AnglesFind the sum of the measures of the interior angles of eachpolygon.6. heptagon 7. nonagon 8. 15-gonFind the measure of one interior angle in each regularpolygon.9. hexagon 10. decagon 11. 18-gon6-4Congruent Polygons12. Complete the sentence. Two polygons are congruent if theirsides are congruent and the correspondingangles are .ABC EDF. m∠A = 40° and m∠B = 50°.∠E ∠A and ∠F ∠C.13. What is m∠C? 14. What is m∠D?6-5SymmetryWrite whether each sentence is true or false. If false, replacethe underlined words to make a true sentence.15. A figure has line symmetryif it can be folded over a lineso that one half of the figurematches the other half.16. To rotate a figure meansto turn the figure from itscenter.17. A figure has rotationalsymmetry if it first matchesitself after being rotatedexactly 360°.
  • 164 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 6 BRINGING IT ALL TOGETHER6-6Reflections18. Complete. A reflection is a image of a figureproduced by flipping the figure over a line.19. If you graphed quadrilateral HIJK yxOIJH Kreflected over the y-axis, what wouldbe the coordinates of these vertices:H ( ) J ( )6-7Translations20. Complete. A translation is the movement of a figure from oneposition to another turning it.21. If you graphed the image of yxODGEFquadrilateral DEFG aftera translation 3 units right and4 units down, what would bethe coordinates of these vertices?D ( ) F ( )
  • Math Connects, Course 3 165Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureCheck the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without using mynotes or asking for help.• You are probably ready for the Chapter Test.• You may want take the Chapter 6 Practice Test onpage 347 of your textbook as a final check.I used my Foldable or Study Notebook to complete the review ofall or most lessons.• You should complete the Chapter 6 Study Guide and Review onpages 342–346 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 6 Practice Test onpage 347.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 6 Foldable.• Then complete the Chapter 6 Study Guide and Review on pages342–346 of your textbook.• If you are unsure of any concepts or skills, refer back to the specificlesson(s).• You may also want to take the Chapter 6 Practice Test onpage 347.C H A P T E R6Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 6.Checklist
  • ®166 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R7Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a plain sheet of 81_2" × 11" paper.Fold in half widthwise.Open and fold thebottom to form a pocket.Glue edges.Label each pocket.Place several indexcards in each pocket.NOTE-TAKING TIP: As you read and learn a newconcept, such as how to measure area or volume,write examples and explanations showing themain ideas of the concept.Measurement: Area and Volume
  • Chapter7Math Connects, Course 3 167Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R7This is an alphabetical list of new vocabulary terms you will learn in Chapter 7.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplebasecentercircumferencechordcomplex figureconecylinderdiameteredgefacelateral facelateral surface area(continued on the next page)
  • 168 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 7Vocabulary TermFoundon PageDefinitionDescription orExamplenetpiplaneprismpyramidradiusregular pyramidsimilar solidsslant heighttotal surface areavertexvolume
  • Math Connects, Course 3 169Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 7–1The radius of a circle is the from the centerto any point the circle. A is any segment withendpoints on the circle.The diameter of a circle is the thecircle through the center.The circumference of a circle is the thecircle. Pi is the of the circumference to thediameter of a circle.YOUR VOCABULARY (pages 167–168)EXAMPLES Find the Circumferences of CirclesFind the circumference of each circle. Round to thenearest tenth.5 ftC = Circumference of a circleC = · Replace d with .C ≈ Use a calculator.The circumference is about .3.8 mC = Circumference of a circleC = 2 · π · Replace r with .C ≈ Use a calculator.The circumference is about .Circumference and Area of CirclesMAIN IDEA• Find the circumferenceand the area of circles.KEY CONCEPTSCircumference of a CircleThe circumference C ofa circle is equal to itsdiameter d times π, or 2times its radius r times π.Area of a Circle The areaA of a circle is equal to πtimes the square of theradius r.
  • 7–1170 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find the circumference of eachcircle. Round to the nearest tenth.a. b.EXAMPLES Find the Areas of CirclesFind the area of each circle. Round to the nearest tenth.A = Area of a circleA = π ·2Replace r with .A = π · Evaluate 32.A ≈ Use a calculator.The area is about .A = πr2Area of a circleA = π ·2r = 1_2of 10A = π · Evaluate 52.A ≈ Use a calculator.The area is about .Check Your Progress Find the area of each circle.Round to the nearest tenth.a. b.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITOn index cards, write theformulas for finding thecircumference and areaof a circle. Sketch a circleand label its parts. Placeyour cards in the “Area”pocket of your Foldable.®
  • Math Connects, Course 3 171Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLEGARDENS A series of gardens framed by tiles is arrangedsuch that each successive garden is one tile longer thanthe previous garden. The width of the gardens is fourtiles. The first three gardens are shown below. Howmany tiles surround Garden 10?UNDERSTAND You know how many tiles surround the firstthree gardens. Use this information to predicthow many tiles will surround Garden 10.PLAN It would take a long time to draw each ofthe gardens 1 through 10. Instead, find thenumber of tiles surrounding the smallergardens and look for a pattern.SOLVE Garden 1 2 3 4Surrounding Tiles 10 12 14 16+2 +2 +2For each successive garden, additional tilesare needed to surround it. The 10th garden willhave 16 + 2 + 2 + 2 + 2 + 2 + 2 or tiles.CHECK Check your answer by drawing Garden 10.Check Your Progress GAMES The figures below showthe number of tiles on a game board after the first 4 roundsof the game. Each round, the same number of tiles are addedto the board. How many tiles will be on the board after the12th round?7–2 Problem-Solving Investigation:Solve a Simpler ProblemMAIN IDEA• Solve a simplerproblem.
  • 172 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.7–3 Area of Composite FiguresA composite figure is made up of shapes.BUILD YOUR VOCABULARY (pages 167–168)EXAMPLES Find the Areas of a Composite FigureFind the area of the composite figure. Round to thenearest tenth if necessary.The figure can be separated into two anda .Area of one semicircle Area of triangleA = 1_2πr2A = wA = A =A = A =The area of the garden is 14.1 + + or100.3 square centimeters.Check Your Progress Find the area of the compositefigure. Round to the nearest tenth if necessary.MAIN IDEA• Find the area ofcomposite figures.
  • 7–3Math Connects, Course 3 173Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. GARDENING The dimensions of a flower garden areshown. What is the area of the garden?7 ft11 ft5 ft2 ftThe garden can be separated into a and twocongruent .Area of rectangle Area of one triangleA = w A = 1_2bhA = A =A = A =The area of the garden is + + orsquare feet.Check Your Progress GARDENING The dimensionsof a flower garden are shown. What is the area ofthe garden?7 ft4 ft 16 ft6 ftHOMEWORKASSIGNMENTPage(s):Exercises:
  • 174 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.7–4 Three-Dimensional FiguresCoplanar lines lie in the same . Parallel lines never. Three-dimensional figures are calledsolids. A polyhedron is a solid with surfaces thatare .An edge is where two planes in a line.A face is a surface.A vertex is where three or more planes ata point.A diagonal is a line segment whose endpoints are verticesthat are neither nor on the same .Lines that do not intersect and are not areskew lines.BUILD YOUR VOCABULARY (pages 167–168)EXAMPLES Identify RelationshipsUse the figure at the right toGH JNKPLMidentify the following.a plane that is parallel to plane GKJPlane is parallel to plane GKJ.a segment that is skew to−−JN−−JN and are skew because they do not andare not coplanar.two sets of points between which a diagonal can be drawnLines drawn between points G and and points and Jwould form diagonals.MAIN IDEA• Identify and drawthree-dimensionalfigures.KEY CONCEPTCommon Polyhedronstriangular prismrectangular prismtriangular pyramidrectangular pyramid
  • 7–4Math Connects, Course 3 175Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Use thefigure at the right to identifythe following.a. a plane that is parallelto plane QUXTb. a segment that is skew to−−−XWc. two sets of points between which a diagonal can be drawnA prism is a polyhedron with twofaces, or bases.A pyramid is a polyhedron with one base that is aand faces that are .BUILD YOUR VOCABULARY (pages 167–168)EXAMPLES Identify Prisms and PyramidsIdentify the solid. Name the number and shapes of thefaces. Then name the number of edges and vertices.The figure has two parallelbases that are, so it is anprism. The other faces are rectangles.It has a total of faces, edges, and vertices.
  • 7–4176 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Identify the solid. Name thenumber and shapes of the faces. Then name the numberof edges and vertices.EXAMPLES Analyze Real-Life DrawingsARCHITECTURE The plansfor a hotel fireplace areshown at the right.Draw and label the top,front, and side views.view view viewCheck Your ProgressThe plans for a buildingare shown to the right.Draw and label the top,front, and side views.HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 177Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Volume of Prisms and Cylinders7–5Volume is the measure of the occupied by asolid. Volume is measured in cubic units.BUILD YOUR VOCABULARY (pages 167–168)EXAMPLE Find the Volume of a Rectangular PrismFind the volume of the rectangular prism.V = Bh Volume of a prism7 in.5 in.11 in.V = ( )h The base is a rectangle,so B = .V = (5 · 7)11 = 5, w = 7, h = 11V = Simplify.The volume is 385 inches.EXAMPLE Find the Volume of a Triangular PrismFind the volume of the triangular prism.V = Bh Volume of a prism49 ft15 ftV = (1_2· 9 · 15)h The base is a, soB = 1_2· 9 · 15.V = (1_2· 9 · 15)4 The height of the prism is .V = Simplify.The volume is cubic inches.MAIN IDEA• Find the volumes ofprisms and cylinders.KEY CONCEPTVolume of a Prism Thevolume V of a prism isthe area of the base Btimes the height h.
  • 7–5178 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find the volume of each prism.a. b.A cylinder is a solid whose bases are congruent, parallel,, connected with a side.BUILD YOUR VOCABULARY (pages 167–168)EXAMPLE Find the Volumes of CylindersFind the volume of the cylinder. Round to the nearesttenth if necessary.3 cm12 cmV = πr2h Volume of a cylinderV = π ·2· r = , h =V ≈ Simplify.The volume is about 339.3 centimeters.Check Your Progress Find the volume of the cylinder.Round to the nearest tenth if necessary.KEY CONCEPTVolume of a Cylinder Thevolume V of a cylinderwith radius r is the areaof the base B times theheight h.ORGANIZE ITOn index cards, write theformula for the volumeof a rectangular prism,a triangular prism, anda cylinder. Sketch eachfigure and label its parts.Place your cards in the“Volume” pocket of yourFoldable.®
  • 7–5Math Connects, Course 3 179Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Objects that are made up of more than one type ofare called composite solids.BUILD YOUR VOCABULARY (pages 167–168)EXAMPLE Find the Volume of a Composite SolidTOYS A wooden block has a1 cm4 cm3 cm6 cmsingle hole drilled entirelythough it. What is the volumeof the block? Round to thenearest hundredth.The block is a rectangular prism with a cylindrical hole.To find the volume of the block, the volumeof the from the volume of the .Rectangular Prism CylinderV = V =V = (6 · 3)4 or 72 V = π(1)2(3) or 9.42The volume of the box is about - orcubic centimeters.Check Your ProgressA small wooden cube hasbeen glued to a larger woodenblock for a whittling project.What is the volume of thewood to be whittled?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 180 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Volume of Pyramids and ConesEXAMPLE Find the Volume of the Pyramid.Find the volume of the pyramid.V = 1_3Bh Volume of a pyramid20 cm3 cm7 cmV = 1_3( · ) B = · ,h =V = 140 Simplify.The volume is .Check Your ProgressFind the volume of the pyramid.EXAMPLE Use Volume to Solve a ProblemSOUVENIRS A novelty souvenir company wants to makesnow “globes” shaped like pyramids. It decides that themost cost-effective maximum volume of water for thepyramids is 12 cubic inches. If a pyramid globe measures4 inches in height, find the area of its base.V = 1_3Bh Volume of a pyramid= 1_3· B · 4 Replace V with and h with .12 = 4_3· B Simplify.· 12 = · 4_3· B Multiply each side by .= BThe area of the base of the snow globe is .7–6MAIN IDEA• Find the volumes ofpyramids and cones.KEY CONCEPTVolume of a PyramidThe volume V of apyramid is one-third thearea of the base B timesthe height h.
  • 7–6Math Connects, Course 3 181Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress A company is designing pyramidshaped building blocks with a square base. They want thevolume of the blocks to be 18 cubic inches. If the length ofthe side of the base is 3 inches, what should be the heightof the blocks?A cone is a three-dimensional figure with onebase. A curved surface connects the base and the .BUILD YOUR VOCABULARY (pages 167–168)EXAMPLE Find the Volume of a ConeFind the volume of the cone. Round to the nearest tenth.V = 1_3πr2h Volume of a cone3 m8 mV = 1_3· π ·2· Replace r withand h with .V ≈ Simplify.The volume is .Check Your Progress Find the volume of the cone. Roundto the nearest tenth.ORGANIZE ITOn index cards, write theformula for the volumeof a pyramid and a cone.Sketch each figure andlabel its parts. Place yourcards in the “Volume”pocket of your Foldable.®KEY CONCEPTVolume of a ConeThe volume V of a conewith radius r is one-thirdthe area of the base Btimes the height h.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 182 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.MAIN IDEA• Find the lateral andtotal surface areas ofprisms and cylinders.7–7 Surface Area of Prisms and CylindersA lateral face of a solid is any surface that is not a.The lateral surface area is the of the areas of itslateral .The total surface area is the sum of the of all itssurfaces.BUILD YOUR VOCABULARY (pages 167–168)EXAMPLE Surface Area of a Rectangular PrismFind the lateral and7 mm15 mm 9 mmtotal surface area ofthe rectangular prism.Perimeter of Base Area of BaseP = 2 + 2w B = wP = 2 + 2 or B = · orUse this information to find the lateral and total surface area.Lateral Surface Area Total Surface AreaL = Ph S = L + 2BL = 48 or S = + 2 · orThe lateral surface area is , andthe total surface area is .KEY CONCEPTSurface Area of aRectangular Prism Thesurface area S of arectangular prism withlength , width w, andheight h is the sum of theareas of the faces.
  • 7–7Math Connects, Course 3 183Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find the lateral and total surfacearea of the rectangular prism.EXAMPLE Surface Area of a Triangular PrismCAMPING A family wants to reinforce the fabric of theirtent with a waterproofing treatment. Find the totalsurface area, including the floor, of the tent below.6.3 ft5.8 ft5.8 ft5 ftA triangular prism consists of twocongruent faces andthree faces.Draw and label a net of this prism. Find the area of each face.bottom · = 29left side · = 36.54right side · = 36.54two bases 2(1_2· 5 · )= 29The surface area of the tentis 29 + 36.54 + 36.54 + 29,or about .What is the formulafor finding the area ofa triangle? How doesthis relate to findingthe surface area of atriangular prism?(Lesson 7-1)REVIEW IT
  • 7–7184 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Julia is painting triangularprisms to use as decoration in her garden. Find the surfacearea of the prism.EXAMPLE Surface Area of a CylinderFind the lateral area and5 m2 mthe surface area of thecylinder. Round to thenearest tenth.Lateral Surface Area Total Surface AreaL = 2πrh S = L + 2πr2L = 2π S ≈ + 2πL = S ≈The lateral surface area is about ,and the total surface area is about .Check Your Progress Find the lateral and total surfacearea of the cylinder. Round to the nearest tenth.KEY CONCEPTSurface Area of aCylinder The surfacearea S of a cylinder withheight h and radius ris the area of the twobases plus the area of thecurved surface.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITOn index cards, writethese formulas forfinding surface area.Then sketch and labeleach figure. Place thecards in the “Area”pocket of your Foldable.®
  • Math Connects, Course 3 185Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A regular pyramid is a pyramid with a thatis a regular .The altitude or of each iscalled the slant height.BUILD YOUR VOCABULARY (pages 167–168)EXAMPLE Surface Area of a PyramidFind the lateral and total surface5 in. 5 in.A = 10.8 in25 in.8 in.areas of the triangular pyramid.Find the lateral area and the areaof the base.Area of each lateral faceA = Area of a triangleA = 1_2( )( )or Replace b with andh with .There are 3 faces, so the lateral area is 3( )orsquare inches.Area of baseA =The total surface area of the pyramid is +or square inches.7–8 Surface Area of PyramidsORGANIZE ITOn a card, write theformula for findingthe surface area of apyramid. Then sketch apyramid and label theparts. Place the card inthe “Area” pocket ofyour Foldable.®MAIN IDEA• Find the lateral andtotal surface areas ofpyramids.
  • 7–8186 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find the total surface area of thesquare pyramid.EXAMPLETOYS A toy block has the shape ofa regular pyramid with a squarebase. The manufacturer wants topaint the lateral surface green.How many square centimeterswill be painted green?L = 1_2P Lateral surface area of a pyramidL = 1_2P = and = 8L = Simplify.The lateral surface area is .Check Your ProgressTOYS A toy block has theshape of a regular pyramidwith a triangular base. Themanufacturer wants to paintthe lateral surface green. Howmany square centimeters willbe painted green?HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 187Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 7–9 Similar SolidsSimilar solids have the same , theircorresponding linear measures are , andtheir corresponding faces are polygons.BUILD YOUR VOCABULARY (pages 167–168)EXAMPLE Find Missing Linear MeasuresThese cones are similar.What is the radius of Cone Ato the nearest tenth?Since the two cones are similar,the ratios of their correspondinglinear measures are proportional.radius cone A___radius cone Bis proportional toheight cone A___height cone B.= Write the proportion.r · 12 = Find the cross products.12r = 56 Multiply.12r_ = 56_ Divide each side by .r ≈ Simplify.The radius of cone A is about .MAIN IDEA• Find dimensions,surface area, andvolume of similarsolids.KEY CONCEPTIf the scale factor of thelinear measures of twosimilar solids is a_b, thenthe scale factor of theirsurface areas is (a_b)2andthe scale factor of theirvolumes is (a_b)3.
  • 7–9188 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your ProgressThese cones are similar. Whatis the height of Cone B to thenearest tenth?EXAMPLE Find Surface Area of a Similar SolidThese rectangular prismsare similar. Find the totalsurface area of Prism A.The ratio of the measures ofPrism A to Prism B is 12_8or 3_2.surface area of prism A____surface area of prism B= (a_b)2Write a proportion.=Substitute theknown values.= Simplify.· = · Find the cross products.=Divide each sideby .S = Simplify.The surface area of Prism A is .Check Your Progress12 cm 18 cmPyramid BPyramid AS ϭ 1,188 cm2These square pyramids aresimilar. Find the total surfacearea of Prism A.
  • 7–9Math Connects, Course 3 189Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLETEST EXAMPLE A triangularprism has a volume of 12 cubiccentimeters. Suppose thedimensions are tripled. Whatis the volume of the new prism?A 36 cm3C 324 cm3B 96 cm3D 1,728 cm3Read the ItemYou know that the prisms are similar, the ratio of the sidelengths is , and the volume of the smaller prism is12 cubic centimeters.Solve the ItemSince the volumes of similar solids have a ratio of (a_b)3anda_b= 1_3, replace a with and b with in (a_b)3.volume of smaller prism_____volume of larger prism= (a_b)3Write a proportion.= (1_3)3Substitute known values.· = · Find the cross products.= V Simplify.So, the volume of the larger prism is .The answer is .Check Your Progress MULTIPLE CHOICE A hexagonalprism has a volume of 25 cubic inches. Suppose the dimensionsare tripled. What is the volume of the new prism?F 75 in3H 200 in3G 120 in3J 675 in3HOMEWORKASSIGNMENTPage(s):Exercises:
  • 190 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 7 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 7, go to:glencoe.comYou can use your completedVocabulary Builder(pages 167–168) to help yousolve the puzzle.7-1Circumference and Area of CirclesComplete.1. The distance from the center of a circle to any point on thecircle is called the , while the distance around thecircle is called the .Find the circumference and area of each circle. Round to thenearest tenth.2. The radius is 14 miles. 3. The diameter is 17.4 in2.7-2Problem-Solving Investigation: Solve a Simpler Problem4. LANDSCAPING Laura is helpingher father make a circular walkwayaround a flower bed as shown.What is the area, in square feet,of the walkway?BRINGING IT ALL TOGETHERC H A P T E R7STUDY GUIDE
  • Math Connects, Course 3 191Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.7-3Area of Composite Figures5. What is a composite figure?6. What is the first step in finding the area of a composite figure?7. Explain how to divide up the figure shown.7-4Three-Dimensional FiguresMatch each description with the word it describes.8. a flat surface9. a polyhedron with one base that is a polygon and facesthat are triangles10. where three or more planes intersect at a point11. where two planes intersect in a line12. a polyhedron with two parallel, congruent facesa. vertexb. edgec. faced. basee. prismf. pyramidChapter 7 BRINGING IT ALL TOGETHER
  • 192 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 7 BRINGING IT ALL TOGETHER7-5Volume of Prisms and CylindersFind the volume of each solid. Round to the nearest tenthif necessary.13.31.2 m10.0 m15.1 m14.5 cm9 cm15.37 mm14 mm14 mm12.1 mm7-6Volume of Pyramids and Cones16. Fill in the table about what you know from the diagram. Thencomplete the volume of the pyramid.6 in.8 in.11 in.length of rectanglewidth of rectanglearea of baseheight of pyramidvolume of pyramid7-7Surface Area of Prisms and Cylinders17. Complete the sentence with the correct numbers. When youdraw a net of a triangular prism, there are congruenttriangular faces and rectangular faces.18. If you unroll a cylinder, what does the net look like?19. Find the surface area of the cylinder. Round the nearest tenth.
  • Math Connects, Course 3 193Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 7 BRINGING IT ALL TOGETHER7-8Surface Area of Pyramids20. Complete the steps in finding the surface area of a squarepyramid.Area of each lateral faceA = 1_2bhA = 1_2(9)(16)A = 72There are faces, so the lateral area is 4(72) =square inches.Area of baseA = s2A = 92or 81The surface area of the square pyramid is +or square inches.21. What two areas are needed to calculate the surface area of a cone?7-9Similar SolidsFind the missing measure for each pair of similar solids.Round to the nearest tenth if necessary.22. 23.
  • ChecklistCheck the one that applies. Suggestions to help you study are givenwith each item.I completed the review of all or most lessons without using mynotes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 7 Practice Test on page 409of your textbook as a final check.I used my Foldable or Study Notebook to complete the review ofall or most lessons.• You should complete the Chapter 7 Study Guide and Review onpages 405–408 of your textbook.• If you are unsure of any concepts or skills, refer to thespecific lesson(s).• You may also want to take the Chapter 7 Practice Test onpage 409.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 7 Foldable.• Then complete the Chapter 7 Study Guide and Review onpages 405–408 of your textbook.• If you are unsure of any concepts or skills, refer to thespecific lesson(s).• You may also want to take the Chapter 7 Practice Test onpage 409.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 7.194 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FOR THECHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R7
  • ®Chapter8Math Connects, Course 3 195Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R8 Algebra: More Equations and InequalitiesUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a plain sheet of 11" × 17" paper.Fold in half lengthwise.Fold again from topto bottom.Open and cutalong the secondfold to maketwo tabs.Label each tab as shown.NOTE-TAKING TIP: When you take notes, definenew terms and write about the new concepts youare learning in your own words. Write your ownexamples that use the new terms and concepts.
  • 196 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R8BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 8.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecoefficientconstantequivalent expressionslike termssimplest formsimplifying theexpressiontermtwo-step equation
  • Math Connects, Course 3 197Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Simplifying Algebraic ExpressionsEquivalent expressions are expressions that have theregardless of the value of the variable.BUILD YOUR VOCABULARY (page 196)EXAMPLE Write Equivalent ExpressionsUse the Distributive Property to rewrite 3(x + 5).3(x + 5) = 3(x) + 3(5)= 3x + Simplify.Check Your Progress Use the Distributive Property torewrite each expression.a. 2(x + 6) b. (a + 6)3EXAMPLES Write Expressions with SubtractionUse the Distributive Property to rewrite eachexpression.(q - 3)9(q - 3)9 = [q + (-3)]9 Rewrite q - 3 as q + (-3)= ( )9 +( )9 Distributive Property.= + ( ) Simplify.= - Definition of subtraction.-3(z - 7)-3(z - 7) = -3[z + (-7)] Rewrite z - 7 as z + (-7.)= -3(z) + (-3)(-7) Distributive Property= -3z + Simplify.MAIN IDEA• Use the DistributiveProperty to simplifyalgebraic expressions.What is the sign ofthe product when youmultiply two integerswith different signs?with the same sign?(Lesson 1-6)REVIEW IT8–1
  • 8–1198 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Use the Distributive Property torewrite each expression.a. (q - 2)8 b. -2(z - 4)When a plus sign separates an algebraic expression intoparts, each part is called a term.The numeric factor of a term that contains ais called the coefficient of the variable.Like terms are terms that contain the variable.A term without a is called a constant.BUILD YOUR VOCABULARY (page 196)EXAMPLE Identify Parts of an ExpressionIdentify the terms, like terms, coefficients, and constantsin 3x - 5 + 2x - x.3x - 5 + 2x - x= 3x + ( )+ 2x + ( ) Definition of Subtraction= 3x + (-5) + 2x + (-1x) Identity Property; -x = -1xThe terms are 3x, , 2x, and -x. The like terms are 3x,2x, and . The coefficients are 3, , and -1. Theconstant is .Check Your Progress Identify the terms, like terms,coefficients, and constants in 6x - 2 + x - 4x.
  • 8–1Math Connects, Course 3 199Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.An algebraic expression is in simplest form if it has noand no .When you use properties to like terms, youare simplifying the expression.BUILD YOUR VOCABULARY (page 196)EXAMPLES Simplify Algebraic ExpressionsSimplify each expression.6n - n6n and n are terms.6n - n = 6n - Identity Property; n == (6 - 1)n Distributive Property= Simplify.8z + z - 5 - 9z + 28z, z, and are like terms. 5 and are also like terms.8z + z - 5 - 9z + 2= 8z + z + ( )+ ( )+ 2 Definition of subtraction.= 8z + z + (-9z )+ (-5 )+ 2 Commutative Property= [8 + 1 + (-9)] + [(-5 )+ 2] Distributive Property= 0z + Simplify.=Check Your Progress Simplify each expression.a. 7n + nb. 6z + z - 2 - 8z + 2HOMEWORKASSIGNMENTPage(s):Exercises:
  • 200 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.8–2 Solving Two-Step EquationsA two-step equation contains .BUILD YOUR VOCABULARY (page 196)EXAMPLES Solve Two-Step EquationsSolve 5y + 1 = 26.Use the Subtraction Property of Equality.5y + 1 = 26 Write the equation.Subtract from each side.−−−−−−−−−5y = 25Use the Division Property of Equality.5y = 255y_ = 25_ Divide each side by .y = Simplify.Solve -4 = 1_3z + 2.-4 = 1_3z + 2 Write the equation.-4 - = 1_3z + 2 - Subtract from each side.= 1_3z Simplify.(-6) = · 1_3z Multiply each side by .= z Simplify.MAIN IDEA• Solve two-stepequations.REMEMBER ITTwo-step equationscan also be solved usingmodels. Refer topage 534 of yourtextbook.
  • 8–2Math Connects, Course 3 201Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ORGANIZE ITUnder the “Equations”tab, include examples ofhow to solve a two stepequation. You can useyour notes later to tellsomeone else what youlearned in this lesson.®Check Your Progress Solve each equation.a. 3x + 2 = 20b. -5 = 1_2z + 8EXAMPLE Equations with Negative CoefficientsSolve 8 - 3x = 14.8 - 3x = 14 Write the equation.8 + ( ) = 14 Definition of subtraction.8 - 8 + ( )= 14 - 8 Subtract 8 from each side.-3x = 6 Simplify.-3x__ = 6__ Divide each side by .x = -2 SimplifyCheck Your Progress Solve 5 - 2x = 11.REMEMBER ITWhen you are solvingan equation, watchfor the negativesigns. In Example 3,the coefficient of thevariable, x, is -3, not +3.So, divide each side by-3 to solve for x.
  • 8–2202 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Simplify -c + 4c.REVIEW ITEXAMPLE Combine Like Terms FirstSolve 14 = -k + 3k - 2.14 = -k + 3k - 2 Write the equation.14 = -1k + 3k - 2 Property; -k = 1k14 = - 2Combine like terms;-1k + 3k = (-1 + 3)k or 2k.14 + = 2k - 2 + Add to each side.16 = 2k Simplify.16_ = 2k_ Divide each side by .8 = k Simplify.Check Your Progress Solve 10 = -n + 4n - 5.HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 203Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 8–3 Writing Two-Step EquationsEXAMPLES Translate Sentences Into EquationsTranslate each sentence into an equation.Sentence EquationThree more than half 1_2n + = 15a number is 15.Nineteen is two more than 19 = + 2five times a number.Eight less that twice a - 8 = -35number is -35.EXAMPLE Write and Solve a Two-Step EquationTRANSPORTATION A taxi ride costs $3.50 plus $2 for eachmile traveled. If Jan pays $11.50 for the ride, how manymiles did she travel?WordsVariablesEquation$3.50 plus $2 per mile equals $11.50.Let m represent the miles driven.3.50 + 2m = 11.50+ = 11.50 Write the equation.3.50 - + 2m = 11.50 - Subtract fromeach side.2m = 8 Simplify.__ = __ Divide each side by .m = Simplify.Jan traveled miles.MAIN IDEA• Write two-stepequations thatrepresent real-lifesituations.What are at least twowords that will tell youthat a sentence can bewritten as an equation?(Lesson 1-7)REVIEW ITORGANIZE ITRecord the main ideas,definitions of vocabularywords, and other notesas you learn how to writetwo-step equations.Write your notes underthe “Equations” tab.®
  • 8–3204 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Translate each sentence intoan equation.a. Five more than one third a number is 7.b. Fifteen is three more than six times a number.c. Six less that three times a number is -22.d. A rental car costs $100 plus $0.25 for each mile traveled.If Kaya pays $162.50 for the car, how many miles didshe travel?EXAMPLEDINING You and your friend spent a total of $33 fordinner. Your dinner cost $5 less than your friend’s. Howmuch did you spend for dinner?WordsVariablesEquationYour friend’s dinner plus your dinnerequals $33.Let f represent the cost of your friend’s dinner.f + f - 5 = 33= 33 Write the equation.- 5 = 33 Combine like terms.2f - 5 + 5 = 33 + 5 Add 5 to both sides.2f = Simplify.(continued on the next page)
  • 8–3Math Connects, Course 3 205Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.= Divide each side by .f = Simplify.Your friend spent on dinner. So you spenton dinner.Check Your Progress DINING You and your friend spenta total of $48 for dinner. Your dinner cost $4 more than yourfriend’s. How much did you spend for dinner?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 206 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.8–4 Solving Equations with Variables on Each SideMAIN IDEA• Solve equations withvariables on each side.ORGANIZE ITDescribe in your ownwords the steps to followwhen you solve anequation with variableson both sides. Writean example of such anequation and solve it.®EXAMPLE Equations with Variables on Each SideSolve 7x + 4 = 9x.7x + 4 = 9x Write the equation.7x - + 4 = 9x - Subtract from each side.= Simplify by combining like terms.= Divide each side by .Check Your Progress Solve 3x + 6 = x.EXAMPLE Equations with Variables on Each SideSolve 3x - 2 = 8x + 13.3x - 2 = 8x + 13 Write the equation.3x - - 2 = 8x - + 13 Subtract from eachside.-5x - 2 = 13 Simplify.-5x - 2 + = 13 + Add to each side.= Simplify.x = Divide each side by .Check Your Progress Solve 4x - 3 = 5x + 7.
  • 8–4Math Connects, Course 3 207Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLEMEASUREMENT The measure of an angle is 8 degreesmore than its complement. If x represents the measureof the angle and 90 - x represents the measure of itscomplement, what is the measure of the angle?WordsVariablesEquation8 less than the measure of an angle equalsthe measure of its complement.Let x and 90 - x represent the measuresof the angles.x - 8 = 90 - x= Write the equation.x - 8 = 90 - x Add to each side.x = 98 - x Simplify.x + = 98 - x Add to each side.= 98 Simplify.= Divide each side by .x = Simplify.The measure of the angle is .Check Your Progress MEASUREMENT The measure ofan angle is 12 degrees less than its complement. If x representsthe measure of the angle and 90 - x represents the measure ofits complement, what is the measure of the angle?
  • 208 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.8–5EXAMPLETHEATER 120 tickets were sold for the school play. Adulttickets cost $8 each and child tickets cost $5 each. Thetotal earned from ticket sales was $840. How manytickets of each type were sold?UNDERSTAND You know the cost of each type of ticket, thetotal number of tickets sold, and the totalincome from ticket sales.PLAN Use a systematic guess and check method tofind the number of each type of ticket.SOLVE Find the combination that gives 120 totaltickets and $840 in sales. In the list, arepresents adult tickets sold, and c representschild tickets sold.a c 8a + 5c Check50 70 8(50) + 5(70) = 750 too low60 8(60) + =CHECK So adult tickets and child ticketswere sold.Check Your Progress THEATER 150 tickets were sold forthe school play. Adult tickets were sold for $7.50 each, and childtickets were sold for $4 each. The total earned from ticket saleswas $915. How many tickets of each type were sold?Problem-Solving Investigation:Guess and CheckMAIN IDEA• Guess and check tosolve problems.HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 209Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 8–6 InequalitiesEXAMPLES Write Inequalities with < or >.Write an inequality for each sentence.SPORTS Members of the little league team must beunder 14 years old.Let a = person’s age.a 14CONSTRUCTION The ladder must be over 30 feet tall toreach the top of the building.Let h = ladder’s height.h 30Check Your Progress Write an inequality for eachsentence.a. Members of the peewee b. The new building mustfootball team must be be over 300 feet tall.under 10 years old.EXAMPLES Write Inequalities with ≤ or ≥Write an equality for each sentence.POLITICS The president of the United States must be atleast 35 years old.Let a = president’s age.a 35CAPACITY A theater can hold a maximum of 300 people.Let p = theater’s capacity.p 300MAIN IDEA• Write and graphinequalities.
  • 8–6210 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Write an inequality for eachsentence.a. To vote, you must be at b. A football stadium canleast 18 years old. hold a maximum of10,000 people.EXAMPLES Determine the Truth of an InequalityFor the given value, state whether the inequality is trueor false.x - 4 < 6, x = 0x - 4 < 6 Write the inequality.- 4 6 Replace x with .< 6 Simplify.Since is less than , < is .3x ≥ 4, x = 13x ≥ 4 Write the inequality.3 4 Replace x with 1.4 Simplify.Since is not greater than or equal to 4, the sentenceis .Check Your Progress For the given value, statewhether the inequality is true or false.a. x - 5 < 8, x = 16b. 2x ≥ 9, x = 5WRITE ITWrite in words what thesymbols <, >, ≤, and ≥mean.ORGANIZE ITRecord the main ideasabout how to writeinequalities. Includeexamples to helpyou remember. Writeyour notes under the“Inequalities” tab.®
  • 8–6Math Connects, Course 3 211Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Graph an InequalityGraph each inequality on a number line.n ≤ -1Place a circle at -1. Then draw a line and anarrow to the .The closed circle means thenumber -1 is included in the graph.Ϫ3 Ϫ2 Ϫ1 0 1 2 3n > -1Place an circle at -1. Then draw a line and anarrow to the .Ϫ3 Ϫ2 Ϫ1 0 1 2 3The open circle means -1 is notincluded in the graph.Check Your Progress Graph each inequality on anumber line.a. n ≤ -3b. n > -3HOMEWORKASSIGNMENTPage(s):Exercises:
  • 212 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLES Solving InequalitiesSolve -21 ≥ d - 8.-21 ≥ d - 8 Write the inequality.-21 + ≥ d - 8 + Add to each side.≥ d or d ≤ Simplify.Solve y + 5 > 11.y + 5 > 11 Write the inequality.y + 5 - > 11 - Subtract from each side.y > Simplify.Check Your Progress Solve each inequality.a. b - 12 > 4 b. 9 ≤ g + 13EXAMPLETEST EXAMPLE Kayta took $12 to the bowling alley. Shoerental costs $3.75. What is the most he could spend ongames and snacks?Read the ItemSince we want to find the most he could spend, use less than orequal to.Solve the ItemLet x = the amount Kayta could spend on games and snacks.Estimate $12 - $4 = $8–7 Solving Inequalities by Adding or SubtractingMAIN IDEA• Solve inequalities byusing the Addition orSubtraction Propertiesof Inequality.
  • 8–7Math Connects, Course 3 213Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. shoe rental plus games andsnacksis less than orequal to$12$3.75 + d ≤ $12 Write the inequality.$3.75 - + d ≤ $12 - Subtractfrom each side.d ≤ Simplify.Kayta could spend no more than on games and snacks.Check Your Progress Monique took $20 to thebookstore. She spent $2.25 on a snack at the library café.What is the most she could spend on books?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 214 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLES Solve Inequalities by Multiplying or DividingSolve 6x < -30.6x < -30 Write the inequality.6x_ < -30_ Divide each side by .x < Simplify.Solve 1_2p ≥ 9.1_2p ≥ 9 Write the inequality.( )(1_2p)≥ ( )(9) Multiply each side by .p ≥Check Your Progress Solve each inequality.a. 4x < -24 b. 1_2p > 5EXAMPLES Multiply or Divide by a Negative NumberSolve b_-4≤ 5.b_-4≤ 5 Write the inequality.( )( b_-4) ( )(5) Multiply each side byand reverse the symbol.b ≥ Simplify.8–8 Solving Inequalities by Multiplying or DividingMAIN IDEA• Solve inequalities byusing the Multiplicationor Division Propertiesof Inequality.
  • 8–8Math Connects, Course 3 215Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Solve -4n > -60.-4n > -60 Write the inequality.-4n__ < -60__ Divide each side byand reverse symbol.n < Simplify.Check Your Progress Solve each inequality.a. x_-3≤ 7 b. -8b < -56EXAMPLEPACKAGES A box weighs 1 pound. It is filled withbooks that weigh 2 pounds each. Jesse can carry atmost 20 pounds. Assuming space is not an issue, writeand solve an inequality to find how many books he canput in the box and still carry it.The phrase at most means less than or to.WORDS 1 lb plus 2 lb per book is less than or equal to lb.VARIABLE Let p represent the number of put in the box.INEQUALITY 1 2p ≤1 + 2p ≤ 20 Write the inequality.1 - + 2p ≤ 20 - Subtract from each side.2p ≤ Simplify.2p_ ≤ 19_ Divide each side by .p ≤ Simplify.Since Jesse can not put half a book in the box, Jesse can put atmost books in the box.Check Your Progress PACKAGES A box weighs 2 pounds.It is filled with toys that weigh 1 pound each. Danielle cancarry at most 30 pounds. How many toys can she put in the boxand still carry it?HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITDescribe in your ownwords the steps to followwhen you solve aninequality by multiplyingor dividing by a negativenumber.®
  • 216 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 8 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 8, go to:glencoe.comYou can use your completedVocabulary Builder(page 196) to help yousolve the puzzle.8-1Simplifying Algebraic Expressions1. Simplify the expression 3x - 4 - 8x + 2 by writing the missinginformation:and are like terms. and are also like terms.3x - 4 - 8x + 2 = 3x + + (-8x) + 2 Definition of subtraction= 3x + + (-4) + 2 Commutative Property= x + -4 + 2 Distributive Property= Simplify.8-2Solving Two-Step Equations2. Define two-step equation.What is the first step in solving each equation?3. 3y - 2 = 16 4. 5 - 6x = -19 5. 32 = 4b + 6 - bC H A P T E R8
  • Math Connects, Course 3 217Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.8-3Writing Two-Step EquationsWrite each sentence as an algebraic equation.6. Four less than six times a number is -40.7. The quotient of a number and 9, decreased by 3 is equal to 24.8. Jennifer bought 3 CDs, each having the same price. Her total forthe purchase was $51.84, which included $3.84 in sales tax. Findthe price of each CD.Let p representEquation: Price of 3 CDs + =+ = 51.843p + 3.84 - = 51.84 -== 48_3p =8-4Solving Equations with Variables on Each SideSolve each equation.9. 3x + 2 = 2x + 5 10. 6x - 2 = 3x 11. 7x - 2 = 9x + 6Chapter 8 BRINGING IT ALL TOGETHER
  • 218 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.8-5Problem-Solving Investigation: Guess and Check12. PROMOTIONS A sports drink company is offering free mountainbikes to people who collect enough points by buying bottles of thedrink. You earn 5 points when you buy a 20-ounce bottle, and youearn 10 points when you buy a 32-ounce bottle. To get the bike,you need to have 915 points. What is the least number of bottles ofsports drink you would have to buy in order to get the bike?13. NUMBER THEORY The product of a number and its next twoconsecutive whole numbers is 60. What are the numbers?8-6InequalitiesWrite an inequality for each sentence using the symbol <, >, ≤, or ≥.14. Children under the age of 2 fly free.15. You must be at least 12 years old to go on the rocket ride.Write the solution shown by each graph.16. Ϫ3Ϫ4 Ϫ2 Ϫ1 0 1 2 3 417. Ϫ5Ϫ6 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 28-7Solving Inequalities by Adding or SubtractingSolve each inequality. Check your solution.18. 8 + x > 12 19. n - 3 ≤ -5 20. 1 < g - 68-8Solving Inequalities by Multiplying or DividingSolve each inequality. Check your solution.21. 7m ≥ 77 22. x_5> -3 23. -12b ≤ 48Chapter 8 BRINGING IT ALL TOGETHER
  • Math Connects, Course 3 219Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ChecklistARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureCheck the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 8 Practice Test onpage 459 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 8 Study Guide and Reviewon pages 454–458 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 8 Practice Test onpage 459.I asked for help from someone else to complete the reviewof all or most lessons.• You should review the examples and concepts in yourStudy Notebook and Chapter 8 Foldable.• Then complete the Chapter 8 Study Guide and Review onpages 454–458 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 8 Practice Test onpage 459.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 8.C H A P T E R8
  • ®220 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Algebra: Linear FunctionsC H A P T E R9Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with seven sheets of 81_2" × 11" paper.Fold a sheet of paperin half lengthwise. Cuta 1" tab along the leftedge through onethickness.Glue the 1" tab down.Write the title of thelesson on the front tab.Repeat Steps 1–2 forthe remaining sheetsof paper. Staple togetherto form a booklet.NOTE-TAKING TIP: When you begin studyinga chapter in a textbook, first skim through thechapter to become familiar with the topics. Asyou skim, write questions about what you don’tunderstand and what you’d like to know. Then,as you read the chapter, write answers to yourquestions.
  • Chapter9Math Connects, Course 3 221Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 9.As you complete the study notes for the chapter, you will see Build Your Vocabulary remindersto complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplearithmetic sequencecommon differenceconstant of variationdirect variationdomainfunctionfunction tableline of fitlinear functionC H A P T E R9(continued on the next page)
  • 222 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Vocabulary TermFoundon PageDefinitionDescription orExamplerangeriserunscatter plotsequenceslopeslope-intercept formsystem of equationssystem of inequalitiestermy-interceptChapter 9 BUILD YOUR VOCABULARY
  • Math Connects, Course 3 223Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 9–1 SequencesA sequence is an of numbers.Each number in a is called a term.An arithmetic sequence is a sequence in which thebetween any two consecutive terms isthe same.The difference between any twoin an sequence is called thecommon difference.BUILD YOUR VOCABULARY (pages 221–222)EXAMPLE Identify Arithmetic SequencesState whether the sequence 23, 15, 7, -1, -9, . . . isarithmetic. If it is, state the common difference. Writethe next three terms of the sequence.23, 15, 7, -1, -9 Notice that 15 - 23 = -8,7 - 15 = -8, and so on.-8 -8 -8 -8The terms have a common of -8, so the sequenceis .Continue the pattern to find the next three terms.-9, , ,-8 -8 -8The next three terms are , , and .MAIN IDEA• Write algebraicexpressions todetermine any term inan arithmetic sequence.
  • 9–1224 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress State whether the sequence 29,27, 25, 23, 21, . . . is arithmetic. If it is, state the commondifference. Write the next three terms of the sequence.EXAMPLE Describe an Arithmetic SequenceWrite an expression that can be used to find the nth termof the sequence 0.6, 1.2, 1.8, 2.4, .... Then write the nextthree terms.Use a table to example the sequence.Term Number (n) 1 2 3 4Term 0.6 1.2 1.8 2.4The terms have a common difference of 0.6. Also, each term istimes its term number.An expression that can be used to find the nth term is .The next three terms are , , and.Check Your Progress Write an expression that can be usedto find the nth term of the sequence 1.5, 3, 4.5, 6, .... Then writethe next three terms.
  • 9–1Math Connects, Course 3 225Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLETRANSPORTATION This arithmetic Miles Cost ($)1 5.252 7.003 8.754 10.50sequence shows the cost of a taxiride for 1, 2, 3, and 4 miles.What would be the cost ofa 9-mile ride?The common difference between thecosts is . This implies that theexpression for the nth mile is . Compare each cost tothe value of for each number of miles.Each cost is 3.50 more than Miles Cost ($) 1.75n1 5.25 1.752 7.00 3.503 8.75 5.254 10.50 7.00. So, the expressionis the cost of ataxi ride for n miles. To find thecost of a 9-mile ride, let crepresent the cost. Then writeand solve an equation for n = 9.c = 1.75n + 3.50 Write the equation.c = 1.75 + 3.50 Replace n with .c = + 3.50 or Simplify.It would cost for a 9-mile taxi ride.Check Your Progress TRANSPORTATION Thisarithmetic sequence shows the cost of a taxi ride for 1, 2, 3,and 4 miles. What would be the cost of a 15-mile ride?Miles Cost ($)1 6.002 7.503 9.004 10.50
  • 2–1A where one thinganother is called a function.BUILD YOUR VOCABULARY (pages 221–222)EXAMPLE Find a Function ValueFind each function value.f(4) if f(x) = x - 8f(x) = x - 8 Write the function.f( )= - 8 Substitute for x intothe function rule.= Simplify.So, f(4) = .f(-6) if f(x) = 3x + 4f(x) = 3x + 4 Write the function.f( )= 3( )+ 4 Substitute for x intothe function rule.f ( )= + 4 Multiply.= Simplify.So, f(-6) = .Check Your Progress Find each function value.a. f(2) if f(x) = x - 7 b. f(-2) if f(x) = 2x + 6MAIN IDEA• Complete functiontables.9–2ORGANIZE ITIn your Foldable, writehow you would find thevalue of a function. Youmay wish to include anexample.®226 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Functions
  • 9–2Math Connects, Course 3 227Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The set of values in a function is called thedomain.The set of values in a function is called therange.You can use a function table to organize the input,, and output.BUILD YOUR VOCABULARY (pages 221–222)EXAMPLE Make a Function TableComplete the functionInputxRule4x - 1Outputf(x)-3-2-101table for f(x) = 4x - 1.Then state the domainand the range of thefunction.Substitute each value of x, or, into the function rule.Then simplify to find the .f(x) = 4x - 1 InputxRule4x - 1Outputf(x)-3-2-101f(-3) = orf(-2) = orf(-1) = orf(0) = orf(1) = orThe domain is .The range is .
  • 9–2228 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress InputxRule3x - 2Outputf(x)-3-2-101Complete the function tablefor f(x) = 3x - 2. Then statethe domain and the rangeof the function.EXAMPLE Functions with Two VariablesPARKING FEES The price for parking at a city lot is $3.00plus $2.00 per hour. Write a function to represent theprice of parking for h hours. Then determine how muchwould it cost to park at the lot for 2 hours.Words Cost of parking equals $3.00 plus $2.00 per hour.Function p = +The function p = represents the situation.Substitute for h into the function rule.p = +p = 3 + 2 orIt will cost to park for 2 hours.Check Your Progress TAXI The price of a taxi rideis $5.00 plus $20.00 per hour. Write a function using twovariables to represent the price of riding a taxi for h hours.Then determine how much would it cost for a 3-hour taxi ride.HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 229Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLEMUSIC During a clearance sale, a music store is sellingCDs for $3 and tapes for $1. Graph the function 3x + y= 6 to find how many CDs and tapes Bill can buy with $6.First, rewrite the equation by solving for y.3x + y = 6 Write the equation.3x - + y = 6 - Subtract from each side.y = 6 - 3x Simplify.Choose values for x and substitute them to find y. Then graphthe ordered pairs.x y = 6 - 3x y (x, y)0 y = 6 - 31 y = 6 - 32 y = 6 - 3yxO1234561 2 3 4He cannot buy negative numbers of CDs or tapes, so thesolutions are CDs and tapes, CD andtapes, or CDs and tapes.Check Your Progress BAKE SALE During a bakesale, a plate of brownies is sold for $2 and a plate of cookies issold for $1. Graph the function 2x + y = 4 to find how manyplates of brownies and cookies Craig can buy with $4.9–3 Representing Linear FunctionsMAIN IDEA• Represent linearfunctions usingfunction tables andgraphs.ORGANIZE ITIn your Foldable, includea linear function and itsgraph.®
  • 9–3230 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Graph a FunctionGraph y = x - 3.Step 1 Choose some values for x. Make a function table.Include a column of ordered pairs of the form (x, y).x x - 3 y (x, y)0 - 31 - 32 - 33 - 3Step 2 Graph each ordered pair. yxODraw a line that passesthrough each point. Notethat the ordered pair forany point on this line is asolution of y = x - 3. Theline is the complete graphof the function.Check It appears from the graph that (-1, -4) is also asolution. Check this by substitution.y = x - 3 Write the function.- 3 Replace x and y.= Simplify.Check Your Progress Graph y = x - 2.yxO
  • 9–3Math Connects, Course 3 231Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A function in which the graph of solutions forms ais called a linear function.BUILD YOUR VOCABULARY (pages 221–222)EXAMPLETEST EXAMPLE Which line graphedx y0 11 32 53 7below best represents the table of values forthe ordered pairs (x, y)?A yxOC yxOB yxOD yxORead the ItemYou need to decide which of the four graphs represents the datain the table.Solve the ItemThe values in the table represent the ordered pairs ,, and . Test the ordered pairs with eachgraph. Graph is the only graph which contains all theseordered pairs. The answer is .
  • 2–19–3232 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress MULTIPLE CHOICEx y0 31 02 -33 -6Which line graphed below best represents thetable of values for the ordered pairs (x, y)?F yxOH yxOG J yxOHOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 233Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Slope is the of the rise, or change, tothe run, or change.BUILD YOUR VOCABULARY (pages 221–222)EXAMPLEACCESS RAMPS The access ramp from the sidewalk tothe door of a hotel rises 8 inches for every horizontalchange of 96 inches. What is the slope of the accessramp?slope = Definition of slope= rise = inches, run = inches= Simplify.The slope of the access ramp is .Check Your Progress ACCESS RAMPS The access rampfrom the sidewalk to the door of an office building rises14 inches for every horizontal change of 210 inches. What is theslope of the access ramp?EXAMPLE Find Slope Using a Graph yXOFind the slope of the line.Choose two points on the line. The verticalchange is -3 units while the horizontalchange is 2 units.9–4 SlopeMAIN IDEA• Find the slope of aline using the slopeformula.
  • 9–4234 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.slope = rise_run Definition of slope= rise = , run =The slope of the line is .Check Your Progress yxOϪ2Ϫ3Ϫ2Ϫ3 2123Find the slope of the line.EXAMPLE Find Slope Using a TableThe points given in the table liex -3 -1 1y -2 1 4on a line. Find the slope of theline. Then graph the line.slope =change in y__change in x=yxO=The slope is .Check Your Progress The points given in the table belowlie on a line. Find the slope of the line. Then graph the line.yxOx y2 55 78 911 11
  • 9–4Math Connects, Course 3 235Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Positive SlopeFind the slope of the line that passes through A(3, 3)and B(2, 0).m =y2 - y1__x2 - x1Definition of slopeyxOA(3, 3)B(2, 0)m = 0 - 3_2 - 3(x1, y1) = (3, 3)(x2, y2) = (2, 0)m = 3_1or 3 Simplify.EXAMPLE Negative SlopeFind the slope of the line that passes through X(-2, 3)and Y(3, 0).m =y2 - y1__x2 - x1Definition of slopem = ___ (x1, y1) = (-2, 3)(x2, y2) = (3, 0)m = -3_5or -3_5Simplify.Check Your Progress Find the slope of the line thatpasses through each pair of points.a. A(4, 3) and B(1, 0)b. X(-3, 3) and Y(1, 0)HOMEWORKASSIGNMENTPage(s):Exercises:
  • When two variable quantities have a ,their relationship is called a direct variation. The constantis called the constant variation.BUILD YOUR VOCABULARY (pages 221–222)EXAMPLE Find a Constant RatioEARNINGS The amount of moneySerena earns at her job variesdirectly as the number of hoursshe works. Determine the amountSerena earns per hour.Since the graph of the data forms aline, the rate of change .Use the graph to find .amount earned___hours workedSerena earns .Check Your ProgressyxDollarsEarned4030502010060701 2 3 4 5 6Time (hours)EARNINGS The amount of moneyElizabeth earns at her job variesdirectly as the number of hours sheworks. Determine the amountElizabeth earns per hour.MAIN IDEA• Use direct variation tosolve problems.236 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Direct Variation9–5
  • 9–5Math Connects, Course 3 237Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Solve a Direct VariationSHOPPING The total cost for cans of soup varies directlyas the number of cans purchased. If 4 cans of soup cost$5, how much would it cost to buy 8 cans?METHOD 1 Use an equation.Write an equation of direct variation. Let x represent thenumber of cans and let y represent the cost.y= kx Direct variation= k y = , x =1.25 = k Simplify.y= Substitute for .Use the equation to find y when x = 8.y = 1.25xy = 1.25 x =y = Multiply.METHOD 2 Use a proportion.canscost4_5= 8_ycanscost= Find the cross products.4y = 40 Multiply.4y_4= 40_4Divide each side by 4.y = Simplify.It would cost to buy 8 cans.Check Your Progress SHOPPING A grocery store sells6 apples for $2.70. How much would it cost to buy 10 apples?KEY CONCEPTIn a direct variation, theratio of y to x is constant.This can be stated as yvaries directly with x. Adirect variation can berepresented algebraicallyas k =y_x or y = kx wherek ≠ 0.
  • 9–5238 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLES Identify Direct VariationDetermine whether each linear function is a directvariation. If so, state the constant of variation.Days, x 2 4 6 8Hours worked, y 16 32 54 72Compare the ratios to check for a common ratio.hours_daysThe ratios are , so the function is.Hours, x 3 6 9 12Miles, y 25.5 51 76.5 102Compare the ratios to check for a common ratio.miles_hoursSince the ratios are , the function isa direct variation. The constant of variation is .Check Your Progress Determine whether the linearfunction is a direct variation. If so, state the constantof variation.a.Days, x 1 2 3 4Hours worked, y 8 16 24 32b.Hours, x 2 4 6 8Miles, y 12 25 35 45HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 239Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Slope-intercept form is when an equation is written in theform , where m is the and b isthe y-intercept.BUILD YOUR VOCABULARY (pages 221–222)EXAMPLES Find the Slopes and y-intercepts of GraphsState the slope and the y-intercept of the graph ofeach equation.y = 3_4x - 5y = 3_4x + ( ) Write the equation in the form y = mx + b.y = mx + b m = 3_4, b =The slope of the graph is , and the y-interceptis .2x + y = 82x + y = 8 Write the original equation.__________- - Subtract from each side.y = Simplify.y = Write the equation in the formy = mx + b.y = mx + b m = , b =The slope of the graph is and the y-interceptis .9–6 Slope-Intercept FormMAIN IDEA• Graph linear equationsusing the slope andy-intercept.
  • 9–6240 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.slope = 2_3y-intercept = 2HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress State the slope and they-intercept of the graph of each equation.a. y = 1_4x - 2 b. 3x + y = 5EXAMPLE Graph an EquationGraph y = 2_3x + 2 using the slope and y-intercept.Step 1 Find the slope and y-intercept.y = 2_3x + 2Step 2 Graph the y-intercept . yxOStep 3 Use the slope to locate a secondpoint on the line.change in y:up 2 unitsm = 2_3change in x:right 3 unitsStep 4 Draw a line through the two points.Check Your Progress Graph y = 1_3x + 3 using the slopeand y-intercept.yxO
  • Math Connects, Course 3 241Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Systems of Equations9–7A system of equations consists of two andtwo .BUILD YOUR VOCABULARY (pages 221–222)EXAMPLE One SolutionSolve the system y = 3x - 2 and y = x + 1 by graphing.Graph each equation on the same coordinate plane.yxO12342424 1 2 3 4The graphs appear to intersect at .Check in both equations by replacing with andwith .Checky = 3x - 2 y = x + 13 - 2 + 12.5 - 2 2.5 = 2.52.5 = 2.5The solution of the system is (1.5, 2.5).MAIN IDEA• Solve systems ofequations by graphing.
  • 9–7242 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE No SolutionSolve the system y = 2x - 1 and y = 2x + 1 by graphing.yxO1234424 1 2 3 42The graphs appear to be lines. Since there is nocoordinate point that is a solution of both questions, there isfor the system of equations.EXAMPLE Infinitely Many SolutionsSolve the system y = 3x - 2 and y - 2x = x - 2 bygraphing.Write y - 2x = x - 2 in slope-intercept form.y - 2x = x - 2 Write the equation.y - 2x + = x - 2 + Add to both sides.= - Simplify.yxO12342424 1 2 3 4The solution of the system is all pairs of theon the line y = 3x - 2.
  • 9–7Math Connects, Course 3 243Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Solve each system of equationsby graphing.a. y = x - 4 and y = 2x - 6yxOb. y = -3x - 2 and y = -3x + 4yxOc. y = 2x - 5 and y + 2 = 2x - 3yxO
  • 244 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Use a GraphThe graph shows how many boxes ofcookies were sold by five students fora school fundraiser. How many boxesdid the students sell altogether?UNDERSTAND The graph shows youhow many boxes weresold by each of fivestudents. You want toknow the total numberof boxes sold by thestudents.PLAN Use the graph to add the numbersof boxes sold.SOLVE + + + + =The students sold altogether.CHECK Look at the numbers at the top of each bar.Double check your sum.Check Your Progress PETS The graph shows how manydogs Edmond walked each day this week. How many dogs didhe walk altogether during the week?Problem-Solving Investigation: Use a Graph9–8MAIN IDEA• Solve problems byusing a graph.HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 245Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 9–9A scatter plot is a graph that shows the betweensets of data.A line of fit is a line that is very close to of the datapoints in a scatter plot.BUILD YOUR VOCABULARY (pages 221–222)EXAMPLES Identify a RelationshipExplain whether the scatter plot of the data for eachof the following shows a positive, negative, or norelationship.cups of hot chocolate sold at a concession stand and theoutside temperatureAs the temperature decreases, the number of cups of hotchocolate sold . Therefore, the scatter plot mightshow a relationship.birthday and number of sports playedThe number of sports played does not depend on your birthday.Therefore, the scatter plot shows relationship.Check Your Progress Determine whether a scatterplot of the data for the following might show a positive,negative, or no relationship.a. number of cups of lemonade sold at a concession stand andthe outside temperatureb. age and the color of your hairScatter PlotsMAIN IDEA• Construct and interpretscatter plots.
  • 9–9246 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLES Line of FitZOOS The table at the right shows the average andmaximum longevity of various animals in captivity.Make a scatter plot using the data.Longevity (years)Average Maximum12 4725 5015 408 2035 7040 7741 6120 54Source: Walker’s Mammals ofthe WorldThen draw a line that best seems torepresent the data.Animal Longevity (Years)AverageMaximum50 10 15 20 25 30 35 40 458070605040302010Write an equation for this line of fit.The line passes through points at and .Use these points to find the slope of the line.m =y2 - y1__x2 - x1Definition of slopem = (x1, y1) = , (x2, y2) =m = Simplify.The slope is , and the y-intercept is .Use the slope and the y-intercept to write the equation.y = mx + b Slope-intercept formy = x + m = , b =The equation for the line of fit is .
  • 9–9Math Connects, Course 3 247Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Use the equation to predict the maximum longevity foran animal with an average longevity of 33 years.y = 3_2x + 17.5 Equation for the line of fity = 3_2+ 17.5 orThe maximum longevity is about .Check Your ProgressThe table shows the average hourly earnings ofproduction workers since 2000.a. Make a scatter plot using Production Workers EarningsYear Since2000Average HourlyEarnings0 $11.431 $11.822 $12.283 $12.784 $13.245 $13.766 $14.32the data.b. Write an equation for thebest-fit line using points(0, 11.43) and (5, 13.76).c. Use the equation to predictthe average hourly earningsof production workersin 2009.1 2 3 4 5 6111213HourlyEarnings(dollars)14Years Since 20000Production WorkersAverage Hourly EarningsHOMEWORKASSIGNMENTPage(s):Exercises:
  • 248 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERSTUDY GUIDEC H A P T E R9®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 9 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 9, go to:glencoe.comYou can use your completedVocabulary Builder(pages 221–222) to help yousolve the puzzle.9-1SequencesState whether each sequence is arithmetic. Write yes or no. If itis, state the common difference. Write the next three terms ofthe sequence.1. 3, 7, 11, 15, 19, ... 2. 5, -15, 45, -135, 405, ...3. 5, -1, -7, -13, -19, ... 4. 41_2, 3, 11_2, 0, -11_2, ...9-2FunctionsMatch each description with the word it describes.5. an output value of a function6. the set of values of the dependent variable7. the underlined letter in f(x) = 2x + 58. Complete the function table for fx = 2x + 2.Then give the domain and range.Domain:Range:a. independent variableb. dependent variablec. domaind. rangex 2x + 2 f(x)-2013
  • Math Connects, Course 3 249Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.9-3Representing Linear Functions9. Complete the function table. Then graph y = -x + 2.x -x + 2 y (x,y)-2013yxO9-4SlopeFind the slope of the line that passes through each pair ofpoints.10. A(1, -2), B(4, 4) 11. C(1, 2), D(3, -2) 12. E(-1, 2), F(2, 2)9-5Direct VariationDetermine whether each linear function is a direct variation.If so, state the constant of variation.13. hours, x 1 2 3 4wages, y $6 $12 $18 $2414. length, x 1 3 5 7width, y 2 6 10 1415. hours, x 5 6 7 8miles, y 480 415 350 28516. minutes, x 3 6 8 12pages, y 66 132 176 264Chapter 9 BRINGING IT ALL TOGETHER
  • 250 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 9 BRINGING IT ALL TOGETHER9-6Slope-Intercept FormState the slope and the y-intercept for the graph of eachequation.17. y = -3x + 4 18. y = 2_3x - 7 19. 1_2x + y = 89-7Systems of Equations20. Solve the system y = 2x - 4 and y = -x - 1 by graphing.yxO21. Solve the system y = 4x - 4 and y = 4x + 3 by graphing.yxO
  • Math Connects, Course 3 251Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 9 BRINGING IT ALL TOGETHER9-8Problem-Solving Investigation: Use a Graph22. SHOPPING The Buy Online Company charges $1.50 perpound plus $2 for shipping and handling. The Best CatalogCompany charges $1 per pound plus $5 for shipping andhandling. Use a graph to determine the weight at which theshipping and handling will be the same for both companies.ShippingandHandlingWeight9-9Scatter Plots23. Complete. A scatter plot that shows a negative relationship willhave a pattern of data points that go .Write whether a scatter plot of the data for the following mightshow a positive, negative, or no relationship.24. favorite color and type of pet
  • Checklist252 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FOR THECHAPTER TEST?C H A P T E R9Check the one that applies. Suggestions to help you study are givenwith each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 9 Practice Test onpage 523 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 9 Study Guide and Review onpages 518–522 of your textbook.• If you are unsure of any concepts or skills, refer to the specificlesson(s).• You may also want to take the Chapter 9 Practice Test onpage 523.I asked for help from someone else to complete the reviewof all or most lessons.• You should review the examples and concepts in yourStudy Notebook and Chapter 9 Foldable.• Then complete the Chapter 9 Study Guide and Review onpages 518–522 of your textbook.• If you are unsure of any concepts or skills, refer to thespecific lesson(s).• You may also want to take the Chapter 9 Practice Test onpage 523.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 9.Student Signature Parent/Guardian SignatureTeacher Signature
  • ®Chapter10Math Connects, Course 3 253Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R10Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with eight sheets of grid paper.Cut off one section of the gridpaper along both the long andshort edges.Cut off two sections from thesecond sheet, three sectionsfrom the third sheet, and soon to the 8th sheet.Stack the sheets from narrowestto widest.Label each of the right tabs witha lesson number.NOTE-TAKING TIP: When you take notes, definenew terms and write about the new concepts youare learning in your own words. Write your ownexamples that use the new terms and concepts.Algebra: Nonlinear Functionsand Polynomials
  • 254 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.YOUR VOCABULARYC H A P T E R10This is an alphabetical list of new vocabulary terms you will learn in Chapter 10.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecube rootmonomialnonlinear functionquadratic function
  • Math Connects, Course 3 255Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.MAIN IDEA• Determine whethera function is linear ornonlinear.Nonlinear functions do not have rates ofchange. Therefore, their graphs are not straight lines.BUILD YOUR VOCABULARY (page 254)EXAMPLES Identify Functions Using TablesDetermine whether each table represents a linear ornonlinear function. Explain.+ 2 + 2 + 2x 2 4 6 8y 2 20 54 104+ 18 + 34 + 50As x increases by , y increases by a greater amount eachtime. The rate of change is not , so this functionis .+ 3 + 3 + 3x 1 4 7 10y 0 9 18 27+ 9 + 9 + 9As x increases by , y increases by each time. Therate of change is , so this function is .ORGANIZE ITExplain how to identifylinear and nonlinearfunctions using graphs,equations, and tables onthe Lesson 10-1 section ofyour Foldable.®10–1 Linear and Nonlinear Functions
  • 10–1256 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Determine whether each tablerepresents a linear or nonlinear function. Explain.a.x 1 3 5 7y 3 7 11 15b. x 3 5 7 9y 1 6 12 20EXAMPLES Identify Functions Using GraphsDetermine whether each graph represents a linear ornonlinear function. Explain.yxOy 2 1x2yxOy x 3The graph is a curve, not astraight line. So, it representsa function.The graph is a straightline. So, it represents afunction.Check Your Progress Determine whether each graphrepresents a linear or nonlinear function. Explain.a. yxOy 3x1b. yxOy 2x 3
  • 10–1Math Connects, Course 3 257Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Identify Functions Using EquationsDetermine whether each equation represents a linear ornonlinear function. Explain.y = 5x2+ 3Since x is raised to the power, the equationcannot be written in the form y = mx + b. So, this function is.y - 4 = 5xRewrite the equation as y = . This equation issince it is of the form y = mx + b.Check Your Progress Determine whether eachequation represents a linear or nonlinear function.Explain.a. y = x2- 1b. -3x = y + 6HOMEWORKASSIGNMENTPage(s):Exercises:
  • 258 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.10–2 Graphing Quadratic FunctionsMAIN IDEA• Graph quadraticfunctions.ORGANIZE ITRecord what youlearn about graphingquadratic functions andusing the graphs to solveproblems on theLesson 10-2 section ofyour Foldable.®A quadratic function is a function in which thepower of the is .BUILD YOUR VOCABULARY (page 254)EXAMPLE Graph Quadratic FunctionsGraph y = 5x2.To graph a quadratic function, make a table of values, plot theordered pairs, and connect the points with a smooth curve.x 5x2y (x, y)-2 5(-2)2= (-2, )-1 5(-1)2= (-1, )0 5(0)2= (0, )1 5(1)2 = (1, )2 5(2)2 = (2, )Check Your Progress Graph y = -3x2.yxOyxO
  • 10–2Math Connects, Course 3 259Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Graph Quadratic FunctionsGraph y = 3x2+ 1.x 3x2+ 1 y (x, y)-2 3(-2)2 + 1 = (-2, )-1 3(-1)2 + 1 = 4 4 (-1, 4)0 3(0)2 + 1 = (0, )1 3(1)2 + 1 = 4 4 (1, 4)2 3(2)2 + 1 = 13 13 (2, 13)yxOCheck Your Progress Graph y = -2x2- 1.yxOHOMEWORKASSIGNMENTPage(s):Exercises:
  • 260 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.10–3 Problem-Solving Investigation:Make a ModelEXAMPLE Make a ModelDESKS Caitlyn is arranging desks in her classroom.There are 32 desks, and she wants to have twice asmany desks in each row as she has in each column. Usea model to determine how many desks she should put ineach row and how many rows she will need.UNDERSTAND You know Caitlyn has 32 desks.PLAN Experiment by arranging 32 tiles into differentrows and columns until you have asmany tiles in each row as are in each column.SOLVEThe correct arrangement is rows withdesks in each row.CHECK Check to see if the arrangement meetsCaitlyn’s original requirements.Check Your Progress TABLES Mrs. Wilson wants toarrange tables into a square that is open in the middle andhas 8 tables on each side. How many tables will she needaltogether?MAIN IDEA• Solve problems bymaking a model.HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 261Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 10–4 Graphing Cubic FunctionsEXAMPLE Graph a Cubic FunctionGraph y = -x3_2.Make a table of values.x y = -x3_2(x, y)-2- __2= - _2= -( )=-1 - __2= - _2=0 - __2= - _2=1 - __2= - _2=2 - __2= - _2=Graph the function.xyOy x32Check Your ProgressGraph y = 2x3.MAIN IDEA• Graph cubicfunctions.( )3( )3΂ ΃ ΂ ΃΂ ΃ ΂ ΃( )3΂ ΃ ΂ ΃( )3΂ ΃ ΂ ΃( )3΂ ΃ ΂ ΃
  • 10–4262 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLEGEOMETRY Write a function for thevolume V of the triangular prism.Graph the function. Then estimatethe dimensions of the prism thatwould give a volume of approximately40 cubic meters.V = Bh of a triangular prismV = 1_2· x · x · ( ) Replace B with 1_2· x · x and h with( ).V = (2x + 8) 1_2· x · x =V = x + 4x Distributive PropertyThe function for the volume V of the box is V = .Make a table of values to graph this function. You do not needto include negative values of x since the side length of the prismcannot be negative.x V = x3+ 4x2(x, V)0 (0)3 + 4(0)2 =0.5 (0.5)3 + 4(0.5)2 ≈1 (1)3 + 4(1)2 =1.5 (1.5)3 + 4(1.5)2 ≈2 (2)3 + 4(2)2 =2.5 (2.5)3 + 4(2.5)2 ≈( 2x 8)mx mx m
  • 10–4Math Connects, Course 3 263Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 5040302010-10 1 2 3 4 5 6V x34x 2To obtain a volume of about 40 cubic meters, the legs of thebase are about meters, and the height is (2 · + 8)or about meters.Check Your Progress A rectangular prism has a squarebase of side length x and a height of (x - 4) feet. Use a graphof this function to estimate the dimensions of the prism thatwould give a volume of about 70 cubic feet.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 264 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.10–5 Multiplying MonomialsA monomial is a , , or aof a number and one or more variables.BUILD YOUR VOCABULARY (page 254)EXAMPLE Multiply PowersFind 76· 72. Express using exponents.76· 72= 76 + 2The common base is .= the exponents.Check 76· 72= (7 · 7 · 7 · 7 · 7 · 7) · (7 · 7)= 7 · 7 · 7 · 7 · 7 · 7 · 7 · 7=Check Your Progress Find 25· 24. Express usingexponents.EXAMPLE Multiply MonomialsFind 7x2(11x4). Express using exponents.7x2 (11x4) = (7 · 11) Comm. and Assoc. Properties= (x2 + 4) The common base is .= the exponents.MAIN IDEA• Multiply monomials.KEY CONCEPTProduct of Powers Tomultiply powers withthe same base, add theirexponents.®In theLesson 10–5 section ofyour Foldable, record theproduct of powers rule.
  • 12–110–5Math Connects, Course 3 265Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find 3x2(-5x5). Express usingexponents.EXAMPLE Multiply Negative PowersFind 4-8· 43. Express using positive exponents.METHOD 14-8· 43= 4 The common base is .= 4 the exponents.= Simplify.METHOD 24-8· 43= · 4 Write 4-8as 1_48.= 1_____4 × 4 × 4 × 4 × 4 × 4 × 4 × 4× 4 × 4 × 4 Cancel commonvalues.= Simplify.Check Your Progress Find 87· 8-4. Express using positiveexponents.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 266 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.10–6 Dividing MonomialsEXAMPLES Divide PowersSimplify. Express using exponents.612_62612_62= 612 - 2The common base is .= Simplify.a14_a8a14_a8= a14 - 8The common base is .= Simplify.Check Your Progress Simplify. Express usingexponents.a. 310_34b. x11_x3KEY CONCEPTQuotient of Powers Todivide powers with thesame base, subtract theirexponents.MAIN IDEA• Divide monomials.
  • 10–6Math Connects, Course 3 267Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Use Negative ExponentsSimplify. Express using positive exponents.8-5_828-5_82= 8 Quotient of Powers= 8 or Simplify.x-9_x-1x-9_x-1= x Quotient of Powers= x Subtraction of a negative number= x or Simplify.Check Your Progress Simplify. Express using positiveexponents.a. 58_5-3b. n-3_n-1
  • 10–6268 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLETEST EXAMPLE Simplify8y3_16y9. Express using positiveexponents.A 2y6B 1_2y6C 1_2y3Dy6_8Read the ItemYou are asked to simplify the monomial.Solve the Item8y3_16y9= ( 8_16)( ) Group terms= 1_2· y Quotient of Powers.= 1_2· y or Simplify.The correct answer choice is .Check Your ProgressMULTIPLE CHOICE Simplify 2b8_12b3. Express using positiveexponents.F b5_6G 1_6b5H 6b11J 1_6b11HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 269Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLES Find the Power of a PowerSimplify (52)8.(52)8= 5 Power of a Power= Simplify.Simplify (a3)7.(a3)7= a Power of a Power= Simplify.Check Your Progress Simplify.a. (34)5b. (m9)2EXAMPLES Power of a ProductSimplify (3c4)3.(3c4)3= 3 · c Power of a Product= Simplify.Simplify (-4p5q)2.(-4p5q)2= (-4) · p · q Power of a Product= Simplify.KEY CONCEPTPower of a Power Tofind the power of apower, multiply theexponents.®In theLesson 10–7 section ofyour Foldable, record thepower of a power rule.MAIN IDEA• Find powers ofmonomials.10–7 Powers of Monomials
  • 10–7270 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress Simplify.a. (2b2)7b. (-3c3d2)4EXAMPLEGEOMETRY Find the volume of a cube with sides oflength 6mn7as a monomial.V = s3of a cubeV = ( )3Replace s with .V = 6 m n Power of a ProductV = Simplify.The volume of the cube is cubic units.Check Your Progress GEOMETRY Find the volume of acube with sides of length 4a2b as a monomial.
  • Math Connects, Course 3 271Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The cube root of a monomial is one of the equalfactors of the monomial.BUILD YOUR VOCABULARY (page 254)EXAMPLES Simplify Square RootsSimplify √9k4.√9k4= √9 · √ Product Property of Square Roots= 3 · 3 = ; p2· p2=Simplify √400w8x2.√400w8x2= √ · √w8· √x2Product Property of Square Roots= 20 · · ⎪x⎥ 20 · 20 = ; w4· w 4= w ;x · x = x2=Use absolute value to indicate thepositive value of x.Check Your Progress Simplify.a. √16e2b. √81a4b2EXAMPLES Simplify Cube RootsSimplify3√a6.3√a6= (a2)3=MAIN IDEA• Find roots ofmonomials.Roots of Monomials10–8
  • 10–8272 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Simplify3√343m12.3√343m12=3√ ·3√m12Product Property of Cube Roots=3·3√m4× m4× m4= Simplify.Check Your Progress Simplify.a.3√y12b.3√512h3EXAMPLEGEOMETRY Find the length of one side of a cube whosevolume is 729g18cubic units.V = s3of a cube= s3Replace V with .3√729g18=3√s3Definition of root3√729 ·3√g18= Product Property of Cube Roots= s Simplify.The length of one side of the cube is units.Check Your Progress GEOMETRY Find the length of oneside of a cube with a volume of 216x15cubic units.HOMEWORKASSIGNMENTPage(s):Exercises:®In theLesson 10–8 section ofyour Foldable, recordthe Product Property ofSquare Roots and theProduct Property ofCube Roots.
  • Math Connects, Course 3 273Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R10STUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 10 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 10, go to:glencoe.comYou can use your completedVocabulary Builder (page 254)to help you solve the puzzle.10-1Linear and Nonlinear FunctionsWrite linear or nonlinear to name the kind of functiondescribed.1. constant rate change 2. graph that is a curve3. power of x may be greater 4. equation has the formthan one y = mx + b5. Name the kind of function represented. Explain your reasoning.x -3 0 3 6y 10 1 10 3710-2Graphing Quadratic FunctionsDetermine whether each equation represents a quadraticfunction. Write yes or no.6. y = 3x - 5 7. y = 6 - x28.yxO9. Explain how to graph a quadratic function.
  • 274 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.10-3Problem-Solving Investigation: Make a Model10. DESIGN Edu-Toys is designing a new package to hold a set of30 alphabet blocks. Each block is a cube with each side of thecube being 2 inches long. Give two possible dimensions forthe package.10-4Graphing Cubic FunctionsDetermine whether each equation represents a cubic function.Write yes or no.11. y = -3x212. y = 1_3x313. y = -x3+ 514. Explain the difference in the graph of a quadratic function andthe graph of a cubic function.10-5Multiplying MonomialsComplete each sentence.15. To multiply powers with the same base, their exponents.Simplify. Express using exponents.16. 52· 5617. 2x2· 4x318. (8x3)(-3x9)Chapter 10 BRINGING IT ALL TOGETHER
  • Math Connects, Course 3 275Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.10-6Dividing Monomials19. To divide powers with the same base, their exponents.Simplify. Express using positive exponents.20. 25_2221. w3_w822. 18a7_6a310-7Powers of Monomials23. To find the power of a power, the exponents.Simplify.24. (82)325. (k4)526. (4a2b4)410-8Roots of MonomialsSimplify.27. √n428. √36x2y829.3√27d930. To find the length of one side of a square when given its area,find the root of the area.Chapter 10 BRINGING IT ALL TOGETHER
  • Checklist276 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FOR THECHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureVisit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 10.Check the one that applies. Suggestions to help you study are given witheach item.I completed the review of all or most lessons without using mynotes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 10 Practice Test onpage 567 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 10 Study Guide and Reviewon pages 563–566 of your textbook.• If you are unsure of any concepts or skills, refer to thespecific lesson(s).• You may also want to take the Chapter 10 Practice Test onpage 567.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in yourStudy Notebook and Chapter 10 Foldable.• Then complete the Chapter 10 Study Guide and Review onpages 563–566 of your textbook.• If you are unsure of any concepts or skills, refer to the specificlesson(s).• You may also want to take the Chapter 10 Practice Test onpage 567.C H A P T E R10
  • ®Chapter11Math Connects, Course 3 277Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with five sheets of 81_2" × 11" paper.Place 4 sheets of paper3_4inch apart.Roll up bottom edges.All tabs should bethe same size.Crease and staplealong the fold.Label the tabswith the topics fromthe chapter. Label thelast tab Vocabulary.NOTE-TAKING TIP: As you take notes on a topic,it helps to write how the subject relates to yourlife. For example, as you learn about differentkinds of statistical measures and graphs, you willunderstand how to evaluate statistical informationpresented in such places as advertisements andpersuasive articles in magazines.C H A P T E R11 Statistics
  • 278 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 11.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleback-to-back stem-and-leaf plotbox-and-whisker plotcircle graphhistograminterquartile rangeleaveslower quartilemeanC H A P T E R11
  • Math Connects, Course 3 279Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Vocabulary TermFoundon PageDefinitionDescription orExamplemeasures of centraltendencymeasures of variationmedianmodeoutlierquartilesrangestem-and-leaf plotstemsupper quartileChapter 11 BUILD YOUR VOCABULARY
  • 280 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.MAIN IDEA• Solve problems bymaking a table.EXAMPLE Make a TableThe list shows the ages of 25 26 42 22 26 2421 27 35 28 1819 25 46 31 2917 56 19 41 2338 20 21 25 22persons selected at randomfrom the audience of a recentshowing of a comedy movie.Make a frequency table of theages using intervals 17–24,25–32, 33–40, 41–48, and 49–56.What is the most commoninterval of attendance ages?UNDERSTAND You have a list of ages. You need to know howmany ages fall into each interval.PLAN Make a tableto show thefrequency, ornumber, of agesin each interval.SOLVE The greatestfrequency isages ,so this is the most commoninterval of attendance ages.CHECK Make sure the frequency tableincludes each age from the list.Check Your ProgressThe list shows the favoritesports of 25 people selectedat random. In the list, Srepresents soccer, B representsbaseball, F represents football,and V represents volleyball.Make a frequency table of thefavorite sports. What is themost popular sport?V B S F VS V F V SS F B S BB S V F SF F B S VHOMEWORKASSIGNMENTPage(s):Exercises:Problem-Solving Investigation:Make a Table11–1
  • Math Connects, Course 3 281Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A histogram is a type of graph used todisplay numerical data that have been organized intointervals.BUILD YOUR VOCABULARY (pages 278–279)EXAMPLE Construct a HistogramFOOD The list shows the 8 47 19 34 3010 58 20 39 3212 4 22 40 9218 85 26 27number of grams of caffeinein certain types of tea. Useintervals 1–20, 21–40, 41–60,61–80, and 81–100 to make afrequency table. Thenconstruct a histogram.Place a tally mark for each value in the appropriate interval.Then add up the tally marks to find the frequency for eachinterval.To construct a histogram, follow these steps.Step 1 Draw and label a horizontal and vertical axis.Include a title.Step 2 Show thefrom the frequency tableon the axis.Step 3 For each caffeineinterval, draw a bar whoseheight is given by thefrequencies.MAIN IDEA• Display and interpretdata in a histogram.ORGANIZE ITUnder the tab forLesson 11–2, explainthe difference betweena bar graph and ahistogram. Describe atype of statistics thatcould be displayed with ahistogram.®Histograms11–2
  • 11–2282 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress The frequency table below showsthe amount of caffeine in certain drinks. Draw a histogram torepresent the data.Caffeine Content of Certain Types of DrinkCaffeine (mg) Tally Frequency0–50 351–100 4101–150 6151–200 7EXAMPLES Analyze and Interpret DataWEATHER How many monthshad 6 or more days of rain?Three months had daysof rain, and one month haddays of rain.Therefore, + ormonths had 6 or more days of rain.WEATHER How many months had exactly 2 days of rain?This cannot be determined from the data presented in thisgraph. The histogram indicates that there werethat had 2 or 3 days of rain, but it is impossible to tell howmany months had days of rain.
  • 11–2Math Connects, Course 3 283Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progressa. How many months had6 or more days of snow?b. How many months had exactly 6 days of snow?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 284 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A circle graph is used to compare parts of a .The entire represents that whole.BUILD YOUR VOCABULARY (pages 278–279)EXAMPLE Construct a Circle Graph from PercentsTORNADOES The table shows when tornadoes occurredin the United States from 1999 to 2001. Make a circlegraph using this information.Tornadoes in the United States, 1999–2001January–March 15%April–June 53%July–September 21%October–December 11%Source: NOAAStep 1 There are in a circle. So, multiply eachpercent by 360 to find the number of degrees for eachof the graph.Jan–Mar:15% of 360 = · 360 orApr–Jun:53% of 360 = · 360 or aboutJul–Sept:21% of 360 = · 360 or aboutOct–Dec:11% of 360 = · 360 or aboutMAIN IDEA• Construct and interpretcircle graphs.ORGANIZE ITUnder the tab forLesson 11–3, find anexample of a circle graphfrom a newspaper ormagazine. Explain whatthe graph shows.®Circle Graphs11–3
  • 11–3Math Connects, Course 3 285Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Step 2 Use a compass to draw a circle and a radius. Thenuse a protractor to draw a angle. This sectionrepresents January–March. From the new radius, drawthe next angle. Repeat for each of the remainingangles. Label each . Then give the grapha .Check Your Progress Hurricanes in theUnited States, 2002Month PercentJuly 7%August 21%September 64%October 8%Source: NOAAHURRICANES The table showswhen hurricanes or tropical stormsoccurred in the Atlantic Oceanduring the hurricane season of2002. Make a circle graph usingthis information.
  • 11–3286 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLES Construct a Circle Graph from DataBASKETBALL Construct a circle graph using theinformation in the histogram below.Step 1 Find the total number of players.6 + + 1 + + 2 =Step 2 Find the ratio that compares the number in eachpoint range to the total number of players. Round tothe nearest hundredth.11.1 to 13 : 6 ÷ 25 =13.1 to 15 : 12 ÷ 25 =15.1 to 17 : 1 ÷ 25 =17.1 to 19 : 4 ÷ 25 =19.1 to 21 : 2 ÷ 25 =Step 3 Use these ratios to find the number of degrees of eachsection. Round to the nearest degree if necessary.11.1 to 13 : · 360 = or about13.1 to 15 : · 360 = or about 17315.1 to 17 : · 360 = or about17.1 to 19 : · 360 = or about19.1 to 21 : · 360 = or about 29
  • 11–3Math Connects, Course 3 287Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Step 4 Use a compass and protractorto draw a circle and theappropriate sections. Labeleach section and give thegraph a title. Write the ratiosas percents.Use the circle graph from Example 2 to describe themakeup of the average game scores of the 25 top-scoringbasketball players.Almost 3_4of the players had average game scores between 11.1and 15 points. Fewer than 1_4had average game scores greaterthan points.Check Your Progress0–7 24–3116–238–15Points46208NumberofPlayers10Average Points per Football Gamefor Top 10 Scorersa. Construct a circle graphusing the informationin the histogram at right.b. Use the graph to describe the makeup of the average gamescores of the 10 top-scoring football players.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 288 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Measures of central tendency are numbers thata set of data.The mean of a set of data is the of the datathe number of items in the data set.The median of a set of data is the number ofthe data ordered from least to greatest, or the mean of thenumbers.The mode of a set of data is the number or numbers thatoccur often.The range of a set of data is betweenthe greatest and least numbers in a set of data.BUILD YOUR VOCABULARY (pages 278–279)EXAMPLE Find Measures of Central TendencyThe ages, in years, of the actors in a play are 4, 16, 32,19, 27, 32. Find the mean, median, mode, and range ofthe data.Mean4 + 16 + 32 + 19 + 27 + 32_____ =≈Median Arrange the numbers in order fromto .4 16 19 27 32 32+___ =MAIN IDEA• Find the mean, median,mode, and range of aset of data.WRITE ITThe words central andmiddle have similardefinitions. If mean,median, and mode aremeasures of centraltendency, what do theymeasure?11–4 Measures of Central Tendency and Range
  • 11–4Math Connects, Course 3 289Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Mode The data has a mode of .Range 32 - 4 or .Check Your Progress The ages, in years, of the childrenat a daycare center are 3, 5, 3, 7, 6, 4. Find the mean, median,mode, and range of the set of data.EXAMPLE Using Appropriate MeasuresOLYMPICS Select the appropriate measure of centraltendency or range to describe the data in the table.Justify your reasoning.Gold Medals Won by the United States at theWinter Olympics, 1924–2002EventGoldMedalsEventGoldMedalsAlpine skiing 10 Luge 2Bobsleigh 6 Short track speed skating 3Cross country 0 Skeleton 3Figure skating 13 Ski jumping 0Freestyle skiing 4 Snowboarding 2Ice hockey 3 Speed skating 26Find the mean, median, mode, and range of the data.Mean10 + 6 + 0 + 13 + 4 + 3 + 2 + 3 + 3 + 0 + 2 + 26_________ = _=The mean is medals.Median Arrange the numbers from least to greatest.0, 0, 2, 2, 3, 3, 3, 4, 6, 10, 13, 26The median is the middle number, or medals.ORGANIZE ITUnder the tab for Lesson11–4, record how to findthe mean, median, andmode of a set of data.Explain measures ofcentral tendency, mean,median, and mode inyour own words and withexamples.®(continued on the next page)
  • 11–4290 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Mode There is one mode, .Range 26 - 0 or .Check Your Progress Select the appropriate measure ofcentral tendency or range to describe the data in the table.Justify your reasoning.CountryGold Medals(1896–2002 Summer)United States 872Great Britain 180France 188Italy 179Sweden 136Hungary 150Australia 102Finland 101Japan 97Romania 74Brazil 12Ethiopia 12HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 291Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Measures of variation are used to describe theof a set of data.Quartiles are the values that divide the data intoequal parts.The of the lower half of a set of data is thelower quartile.The median of the of the set of data is theupper quartile.Data that are more than times the value of theinterquartile range beyond the quartiles are called outliers.BUILD YOUR VOCABULARY (pages 278–279)EXAMPLE Find Measures of VariationBASKETBALL Find the Average Points per Game Scoredby Top Ten Teams During theNBA Playoffs, 2002Team Points ScoredDallas 109Minnesota 102Sacramento 101.1L.A. Lakers 97.8Charlotte 96.1New Jersey 95.4Orlando 93.8Indiana 91.6Boston 91.3Portland 91.3Source: NBAmeasures of variationfor the data in the table.The range is 109 - 91.3 or.MAIN IDEA• Find the measures ofvariation of a set ofdata.KEY CONCEPTSRange The range of a setof data is the differencebetween the greatestand the least numbers inthe set.Interquartile Range Theinterquartile range isthe range of the middlehalf of the data. It is thedifference between theupper quartile and thelower quartile.Measures of Variation11–5(continued on the next page)
  • 11–5292 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Median, Upper Quartile, and Lower QuartileArrange the numbers in order from least to greatest.lower quartile median upper quartile91.3 91.3 91.6 93.8 95.4 96.1 97.8 101.1 102 109The median is , the lower quartile is , and theupper quartile is .Interquartile Range = upper quartile - lower quartile=Check Your Progress BASEBALL Find the measures ofvariation for the data in the table.Giants Batting AverageAgainst Anaheim in the2002 World SeriesPlayerBattingAverageRueter 0.500Bonds 0.471Snow 0.407Bell 0.304Lofton 0.290Kent 0.276Aurilia 0.250Sanders 0.238Santiago 0.231Source: MLBREMEMBER ITA small interquartilerange means that thedata in the middle ofthe set are close in value.A large interquartilerange means that thedata in the middle arespread out.
  • 11–5Math Connects, Course 3 293Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Find Outliers Item Sold at Football GameConcession StandItem Number SoldColas 196Diet colas 32Water 46Coffee 18Candy bars 39Hotdogs 23Hamburgers 16Chips 41Popcorn 24CONCESSION SALES Findany outliers for the datain the table at the right.First arrange the numbers inorder from least to greatest.Then find the median, upperquartile, and lower quartile.16 18 23 24 32 39 41 46 19618 + 23__2= 3241 + 46__2=Interquartile Range = - or 23Multiply the interquartile range,23, by 1.5. × = 34.5Find the limits for the outliers.Subtract 34.5 from the lower quartile. - 34.5 =Add 34.5 to the upper quartile. + 34.5 =The limits for the outliers are and .The only outlier is .Check Your ProgressItems Sold at School BookstoreItem Number SoldPens 35Pencils 15Erasers 20Candy bars 93Folders 17School pennants 18Calculators 2Find any outliers for thedata in the table at right.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITUnder the tab for Lesson11–5, write what youlearn about finding therange and quartiles of aset of data.®
  • 294 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A box-and-whisker plot uses a to showthe of a set of data.BUILD YOUR VOCABULARY (pages 278–279)EXAMPLE Draw a Box-and-Whisker PlotPOPULATION Use the World’s Most Populous CitiesCityPopulation(millions)Tokyo 34.8New York 20.2Seoul 19.9Mexico City 19.8Sao Paulo 17.9Bombay 17.9Osaka 17.9Los Angeles 16.2Cairo 14.4Manila 13.5Source: Time Almanacdata in the table atthe right to constructa box-and-whisker plot.Step 1 Draw a that includes the least andgreatest number in the data.Step 2 Mark the extremes, the , and the upperand lower above the number line.Since the data have an outlier, mark the greatest valuethat is not an .Step 3 Draw the box and whiskers.MAIN IDEA• Display and interpretdata in a box-and-whisker plot.ORGANIZE ITUnder the tab for Lesson11–6, collect data fromthe Internet, such asnumber of home runshit by the players of abaseball team. Draw abox-and-whisker plot todisplay the data.®11–6 Box-and-Whisker Plots
  • 11–6Math Connects, Course 3 295Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Most Populous U.S. Citiesin a Recent YearCityPopulation(in millions)New York 8.0Los Angeles 3.7Chicago 2.9Houston 2.0Philadelphia 1.5Phoenix 1.3San Diego 1.2Dallas 1.2Use the data in the tableat the right to draw abox-and-whisker plot.EXAMPLE Interpret DataWATERFALLS What do the lengths of the parts of thebox-and-whisker plot below tell you about the data?Data in the quartile are more spread out thanthe data in the quartile. You can see that data inthe quartile are the most spread out because thewhisker is than other parts of the plot.
  • 11–6296 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress What do the lengths of the parts ofthe box-and-whisker plot below tell you about the data?HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 297Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The numerical data are listed in ascending or descendingorder in a stem-and-leaf plot. The placevalue of the data are used for the stems. The leaves formthe place value.BUILD YOUR VOCABULARY (pages 278–279)EXAMPLE Draw a Stem-and-Leaf PlotFOOD Display the data inthe table in a stem-and-leafplot with or without the useof technology.Step 1 Find the least andgreatest number. Thenidentify the greatestplace-value digit in eachnumber.• The least number,, has 2 inthe thousands place.• The greatestnumber, , has 3 in the thousands place.Step 2 Draw a vertical line and write the stems, 2 and 3,to the of the line.Step 3 Write the leaves to the of the line, with thecorresponding stem. For example, for 2,800, write 8 tothe right of .Peanuts Harvested, 2005StateAmount(lb/acre)Alabama 2,800Florida 2,900Georgia 3,000New Mexico 3,200North Carolina 3,100Oklahoma 3,200South Carolina 3,200Texas 3,500Virginia 2,800MAIN IDEA• Display data instem-and-leaf plots.Interpret data in stem-and-leaf plots.Stem Leaf2 8 8 93 0 1 2 2 2 52 8 = 2,800 lb11–7 Stem-and-Leaf Plots
  • 11–7298 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your ProgressBASEBALL Display the datain the table in a stem-and-leafplot with or without the use oftechnology.EXAMPLE Interpret DataMEXICO The stem-and-leaf plot lists the percent ofpeople in each state in 2004 that were born in Mexico,rounded to the nearest whole number.a. Which interval contains the most percentages?Most of the percentages occur in the interval.b. What is the greatest percent of people living in oneU.S. state that were born in Mexico?The greatest percent of people living in one U.S. state bornin Mexico is .Stem Leaf5 8 96 0 1 3 4 5 67 0 35 8 = 58 home runsMost Home Runs in aSingle SeasonPlayer Home RunsBarry Bonds 73Jimmie Foxx 58Roger Maris 61Mark McGwire 65Mark McGwire 70Babe Ruth 59Babe Ruth 60Sammy Sosa 63Sammy Sosa 64Sammy Sosa 66Stem Leaf0 0 0 0 1 1 2 2 3 4 4 5 5 5 6 6 8 8 81 0 1 4 4 72 1 2 3 83 1 2 3 5 5 9 94 0 1 2 3 3 3 4 6 85 2 6 66 4 67 4 3 1 = 31%
  • 11–7Math Connects, Course 3 299Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. c. What is the median percent of people living in oneU.S. state that were born in Mexico?The median percent of people living in one U.S. state born inMexico is .Check Your Progress Refer to the stem-and-leaf plot inExample 2.a. What is the range of the data?b. What is the least percent of people living in one U.S. statethat were born in Mexico?c. What percentages occur most often?A back-to-back stem-and-leaf plot can be used to comparesets of data.BUILD YOUR VOCABULARY (pages 278–279)EXAMPLE Compare DataAGRICULTURE The yearly production of honey inCalifornia and Florida is shown for the years 2000 to2004, in millions of pounds.a. What state produces the most honey?California: 17 + 24 + 28 + 31 + 33 = million lbFlorida: 14 + 20 + 20 + 22 + 24 = million lbproduces the most honey.California Stem Florida7 1 48 4 2 0 0 2 42 1 32 3 = 32 million lb 2 0 = 20 million lb(continued on the next page)
  • 11–7300 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.b. Which state has the most varied production? Explain.The data for are more spread out, while thedata for are clustered. So, hasthe most varied production.Check Your Progress BABYSITTING The amount ofmoney Hanna and Jasmine earned babysitting in 2006 isshown in the back-to-back stem-and-leaf plot.Hanna Stem Jasmine0 0 1 0 2 3 50 0 2 2 5 5 8 2 0 0 50 3 0 24 00 2 = $20 2 5 = $25a. Who earned more money babysitting?b. Who has the most varied earnings? Explain.HOMEWORKASSIGNMENTPage(s):Exercises:
  • Math Connects, Course 3 301Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 9–1EXAMPLES Choose an Appropriate DisplayChoose an appropriate type of display for each situation.Then make a display.FARMS Select an Farms in Maine by Size1–99 acres 46.8%100–499 acres 43.8%500–999 acres 6.9%1,000 or more acres 2.5%Source: USDAappropriate displayto show the acreageof farms in Maine.Justify your answer.This data deals with percents that have a sum of .A would be a good way to show percents.SCHOOLS Select an Favorite School SubjectmathhistoryscienceEnglishotherappropriate displayto show students’favorite schoolsubjects. Justify yourreasoning. Thenconstruct the display.In this case, there arespecific categories. Ifyou want to show thespecific number, use a.11–8MAIN IDEA• Select an appropriatedisplay for a set ofdata.ORGANIZE ITUnder the tab forLesson 11–8, make atable of data from yourscience or social studiestextbook. Draw a circlegraph and bar graphdisplaying the data.Discuss which graph ismost appropriate.®Select an Appropriate Display
  • 11–8302 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progressa. Select an appropriate Favorite Type of Television Programsitcom 54%reality 22%news 10%game show 8%cartoon 6%display to showfavorite types oftelevision programs.Justify your answer.Then construct thedisplay.b. Select an appropriate display to show students’ favoritehobbies. Then construct the display.Hobby Number of Studentsreading 10sports 5listening to music 10photography 7other 18HOMEWORKASSIGNMENTPage(s):Exercises:REMEMBER ITThere are manyways to display the samedata. However, often oneof those ways makes thedata easier to understandthan do the other ways.
  • Math Connects, Course 3 303Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 11 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 11, go to:glencoe.comYou can use your completedVocabulary Builder(pages 278–279) to help yousolve the puzzle.11-1Problem-Solving Investigation: Make a Table1. MONEY The list shows weeklyallowances for a group of 13- and14-year-olds. Organize the data in atable using intervals $2.01–$3.00,$3.01–$4.00, $4.01–$5.00, and so on.What is the most common intervalof allowance amounts?$2.50 $3.00 $3.75 $4.25 $4.25$4.50 $4.75 $4.75 $5.00 $5.00$5.00 $5.00 $5.50 $5.50 $5.75$5.80 $6.00 $6.00 $6.00 $6.50$6.75 $7.00 $8.50 $10.00 $10.00$12.00 $15.0011-2HistogramsUse the histogram at the right.2. How many months have less thantwo days of rain?3. How many months had between twoand seven days of rain?C H A P T E R11
  • 304 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.11-3Circle GraphsUse the circle graph at the right.4. What percent of her time does Luisaspend studying?5. How many degrees are in the sectionthat represents sports?11-4Measures of Central Tendency and Range6. Name the three most common measures of central tendency.7. Which measure of central tendency best represents the data?Why? 9, 9, 20, 22, 25, 2711-5Measures of VariationComplete.8. Measures of variation describe the of data.9. The of a set of data is the difference between thegreatest and the least numbers in the set.10. The range is the difference between theupper and lower quartiles.Chapter 11 BRINGING IT ALL TOGETHER
  • Math Connects, Course 3 305Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.11-6Box-and-Whisker Plots11. Draw a box-and-whisker plot forthe data. 1, 1, 1, 2, 3, 3, 4, 5, 511-7Stem-and-Leaf PlotsFOOTBALL For Exercises12–14, use the all-timeinterception leaders datashown at the right.12. What is the mostinterceptions by an NFLplayer through 2005?13. How many NFL playershave 57 interceptionsthrough 2005?14. What is the median number of interceptions among the leadersrepresented in the stem-and-leaf plot?11-8Select an Appropriate DisplayChoose the letter that best matches the type of display toits use.15. Line Graph a. shows the frequency of data that hasbeen organized into equal intervals16. Bar Graph b. shows the number of items in specificcategories in the data using bars17. Histogram c. shows change over a period of time18. Line Plot d. shows how many times each numberoccurs in the dataChapter 11 BRINGING IT ALL TOGETHERAll-Time NFL InterceptionLeaders (through 2005)Stem Leaf5 7 7 7 7 7 86 2 2 3 5 87 1 98 16 2 = 62 interceptions
  • Checklist306 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FOR THECHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureCheck the one that applies. Suggestions to help you study are givenwith each item.I completed the review of all or most lessons without using mynotes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 11 Practice Test onpage 627 of your textbook as a final check.I used my Foldable or Study Notebook to complete the review ofall or most lessons.• You should complete the Chapter 11 Study Guide and Reviewon pages 622–626 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 11 Practice Test onpage 627.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in yourStudy Notebook and Chapter 11 Foldable.• Then complete the Chapter 11 Study Guide and Review onpages 622–626 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 11 Practice Test onpage 627.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 11.C H A P T E R11
  • ®Chapter12Math Connects, Course 3 307Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a plain sheet of 11" × 17" paper.Fold the sheet inhalf lengthwise.Cut along the fold.Fold each half inquarters alongthe width.Unfold each piece andtape to form onelong piece.Label each page witha key topic as shown.Refold to form a booklet.NOTE-TAKING TIP: It helps to take notes as youprogress through studying a subject. New conceptsoften build upon concepts you have just learned ina previous lesson. If you take notes as you go, youwill know what you need to know for the conceptyou are now learning.ProbabilityC H A P T E R12
  • 308 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 12.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplebiased samplecomposite experimentconvenience sampledependent eventseventexperimentalprobabilityFundamental CountingPrincipleindependent eventsoutcomeC H A P T E R12
  • Math Connects, Course 3 309Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Vocabulary TermFoundon PageDefinitionDescription orExamplepopulationprobabilityrandomsamplesample spacesimple random samplestratified randomsamplesystematic randomsampletheoretical probabilitytree diagramunbiased samplevoluntary responsesampleChapter 12 BUILD YOUR VOCABULARY
  • 310 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A tree diagram is a diagram used to show thenumber of outcomes in a probabilityexperiment. An event is an .An organized of outcomes is called a samplespace. One type of organized list is a tree diagram.BUILD YOUR VOCABULARY (pages 308–309)EXAMPLE Use a Tree DiagramBOOKS A flea market vendor sells new and used booksfor adults and teens. Today she has fantasy novels andpoetry collections to choose from. Draw a tree diagramto determine the number of categories of books.NewFantasy novelsPoetryAdultTeenAdult New, Fantasy Novel, AdultTeenNew, Poetry, AdultNew, Poetry, TeenNew, Fantasy Novel, TeenUsedFantasy novelsPoetryAdultTeenAdult Used, Fantasy Novel, AdultTeenUsed, Poetry, AdultUsed, Poetry, TeenUsed, Fantasy Novel, TeenNew/Used OutcomeAge GroupTypeList new or usedbook.Each type is pairedwith new or used.Each age group ispaired with eachtype and new or used.List all of theoutcomes ofbook categories.There are different categories.MAIN IDEA• Count outcomes byusing a tree diagramor the FundamentalCounting Principle.WRITE ITHow is using a treediagram to find totalnumber of outcomes likeusing a factor tree to findprime factors? (see factortrees in Prerequisite Skillspage 664)Counting Outcomes12–1
  • 12–1Math Connects, Course 3 311Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress A store has spring outfits on sale.You can choose either striped or solid pants. You can also choosegreen, pink, or orange shirts. Finally, you can choose eitherlong-sleeved shirts or short-sleeved shirts. Draw a tree diagramto determine the number of possible outfits.The Fundamental Counting Principle uses tofind the number of in a sample space.BUILD YOUR VOCABULARY (pages 308–309)EXAMPLE Use the Fundamental Counting PrincipleRESTAURANTS A manager assigns different codes toall the tables in a restaurant to make it easier for thewait staff to identify them. Each code consists of thevowel A, E, I, O, or U, followed by two digits from 0through 9. How many codes could the managerassign using this method?number ofpossiblenumbersfor the firstplace×number ofpossiblenumbers forthe secondplace×number ofpossiblenumbers forthe thirdplace=number ofpossiblecodes× × =There are possible codes.KEY CONCEPTFundamental CountingPrinciple If event M anoccur in m ways and isfollowed by event N thatcan occur in n ways, thenthe event M followed bythe event N can occur inm · n ways.
  • 12–1312 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress A middle school assigns eachstudent a code to use for scheduling. Each code consists ofa letter, followed by two digits from 0 though 9. How manycodes are possible?Outcomes are random if each outcome is likelyto occur. Probability is the of outcomes of anevent to the total number of outcomes.BUILD YOUR VOCABULARY (pages 308–309)EXAMPLE Find ProbabilityCOMPUTERS What is the probability that Liana willguess her friend’s computer password on the first try ifall she knows is that it consists of three letters?Find the number of possible outcomes. Use the FundamentalCounting Principle.choicesfor the fistletter×choices forthe secondletter×choices forthe thirdletter=totalnumber ofoutcomes× × =There are possible outcomes. There iscorrect password. So, the probability of guessing on the firsttry is .Check Your Progress What is the probability that Shaunawill guess her friend’s locker combination on the first try if allshe knows is that it consists of three digits from 0 through 9?HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITUnder Tree Diagram andFundamental CountingPrinciple, write notes onwhat you learned aboutcounting outcomes byusing a tree diagram andby using the CountingPrinciple. Includeexamples of each.®
  • Math Connects, Course 3 313Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A compound event consists of simpleevents.Independent events are events inwhich the outcome of one event affect theoutcome of the other events.BUILD YOUR VOCABULARY (pages 308–309)EXAMPLE Probability of Independent EventsThe two spinners below are spun. What is theprobability that both spinners will show a numbergreater than 6?1234567890 1234567890P(first spinner is greater than 6) =P(second spinner is greater than 6) =P(both spinners are greater than 6) = 3_10· 3_10orCheck Your Progress The two spinners below are spun.What is the probability that both spinners will show a numberless than 4?KEY CONCEPTProbability of TwoIndependent EventsThe probability of twoindependent events canbe found by multiplyingthe probability ofthe first event by theprobability of thesecond event.MAIN IDEA• Find the probabilityof independent anddependent events.12–2 Probability of Compound Events
  • 12–2314 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLETEST EXAMPLE A red number cube and a white numbercube are rolled. The faces of both cubes are numberedfrom 1 to 6. What is the probability of rolling a 3 on thered number cube and rolling the number 3 or less on thewhite number cube?A 1_2B 1_6C 1_9D 1_12Read the ItemYou are asked to find the probability of rolling a 3 on the rednumber cube and rolling a number 3 or less on the whitenumber cube. The events are because rollingone number cube affect rolling the other cube.Solve the ItemFirst, find the probability of each event.P(rolling a 3 on the red number cube) =P(rolling 3 or less on the white number cube) =Then, find the probability of both events occurring.P(3 red and 3 or less white) = · P(A and B)= P(A) · P(B)= Multiply.The probability is , which is .Check Your Progress MULTIPLE CHOICE A whitenumber cube and a green number cube are rolled. The faces ofboth cubes are numbered from 1 to 6. What is the probability ofrolling an even number on the white number cube and rolling a3 or a 5 on the green number cube?F 1_12G 1_6H 1_3J 1_2KEY CONCEPTProbability of TwoDependent EventsIf two events, A andB, are dependent,then the probability ofboth events occurringis the product of theprobability of A and theprobability of B after Aoccurs.
  • 12–2Math Connects, Course 3 315Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.If the outcome of one event does the outcome ofanother event, the compound events are calleddependent events.BUILD YOUR VOCABULARY (pages 308–309)EXAMPLE Probability of Dependent EventsThere are 4 red, 8 yellow, and 6 blue socks mixed up in adrawer. Once a sock is selected, it is not replaced. Findthe probability of reaching into the drawer withoutlooking and choosing 2 blue socks.Since the first sock replaced, the first event affectsthe second event. These are dependent events.P(first sock is blue) =number of blue sockstotal number of socksP(second sock is blue) =number of blue socksafter one blue sock isremovedtotal number of socksafter one blue sock isremovedP(two blue socks) = orCheck Your Progress There are 6 green, 9 purple,and 3 orange marbles in a bag. Once a marble is selected,it is not replaced. Find the probability that two purplemarbles are chosen.ORGANIZE ITUnder IndependentEvents and DependentEvents, write what youlearned about how tofind the probabilityof independent anddependent events.®HOMEWORKASSIGNMENTPage(s):Exercises:
  • 316 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A probability that is based on obtainedby conducting an is called anexperimental probability.A probabililty that is based onis called a theoretical probability.BUILD YOUR VOCABULARY (pages 308–309)EXAMPLES Experimental ProbabilityNikki is conducting an experiment to find theprobability of getting various results when threecoins are tossed. The results of her experiment aregiven in the table.ResultNumber ofTossesall heads 6two heads 32one head 30no heads 12What is the theoretical probability of tossing all headson the next turn?The theoretical probability is = .According to the experimental probability, is Nikki morelikely to get all heads or no heads on the next toss?Based on the results so far, heads is more likely.MAIN IDEA• Find experimental andtheoretical probabilitiesand use them to makepredictions.Experimental and Theoretical Probability12–3
  • 12–3Math Connects, Course 3 317Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your ProgressResultNumber ofTossesall heads 6three heads 12two heads 20one head 7no heads 5Marcus is conducting anexperiment to find theprobability of gettingvarious results when fourcoins are tossed. Theresults of his experimentare given in the table.a. What is the theoretical probability of tossing all tails on thenext turn?b. According to the experiment probability, is Marcus morelikely to get all heads or no heads on the next toss?EXAMPLE Experimental ProbabilityMARKETING Eight hundred adults were asked whetherthey were planning to stay home for winter vacation.Of those surveyed, 560 said that they were. What is theexperimental probability that an adult planned to stayhome for winter vacation?There were people surveyed and said that theywere staying home.The experimental probability is or .ORGANIZE ITUnder ExperimentalProbability, write a fewwords to compare andcontrast experimentaland theoreticalprobabilities.®
  • 12–3318 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Explain what aproportion is andhow you can solve aproportion. (Lesson 4-3)REVIEW ITCheck Your Progress Five hundred adults were askedwhether they were planning to stay home for New Year’sEve. Of those surveyed, 300 said that they were. What is theexperimental probability that an adult planned to stay homefor New Year’s Eve?EXAMPLE Use Probability to PredictMATH TEAM Over the past three years, the probabilitythat the school math team would win a meet is 3_5.Is this probability experimental or theoretical? Explain.This is an experimental probability since it is based on whathappened in the .If the team wants to win 12 more meets in the next3 years, how many meets should the team enter?This problem can be solved using a proportion.3 out of 5 meetswere wins.3_5× 12_x12 out of x meetsshould be wins.Solve the proportion.3_5= 12_xWrite the proportion.= Find the cross products.= Multiply.= Divide each side by .x =They should enter meets.
  • 12–3Math Connects, Course 3 319Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Over the past three years, theprobability that the school speech and debate teamwould win a meet is 4_5.a. Is this probability experimental or theoretical? Explain.b. If the team wants to win 20 more meets in the next 3 years,how many meets should the team enter?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 320 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Act It OutMelvin paid for a $5 sandwich with a $20 bill. Thecashier has $1, $5, and $10 bills in the register. Howmany different ways can Melvin get his change?UNDERSTAND You know that Melvin should receive $20 – $5or in change. You need to determinehow many different ways the cashier can make$15 in change with $1, $5, and $10 bills.PLAN Use manipulatives such as play money to actout the problem. Record the different ways thecashier can make $15 in change.SOLVE$1 $5 $10Method 1 1 1Method 2 1Method 3Method 4Method 5Method 6The cashier can make the change indifferent ways.CHECK Make sure each method adds up to inchange.Check Your Progress SHOPPING Amanda paid for an $8CD with a $20 bill. The cashier has $1, $5, and $10 bills in theregister. How many different ways can Amanda get her change?MAIN IDEA• Solve problems byacting them out.HOMEWORKASSIGNMENTPage(s):Exercises:Problem-Solving Investigation:Act It Out12–4
  • Math Connects, Course 3 321Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A sample is a selected group chosen forthe purpose of collecting data.The population is the from which thesamples under consideration are taken.An unbiased sample is selected so that it isof the entire population.In a simple random sample, each part of the population isequally likely to be chosen.In a stratified random sample, the population is dividedinto , nonoverlapping groups.In a systematic random sample, the items or people areselected according to a specific or item interval.BUILD YOUR VOCABULARY (pages 308–309)EXAMPLES Determine Validity of ConclusionsDetermine whether each conclusion is valid. Justifyyour answer.To determine which school lunches students like most,the cafeteria staff surveyed every tenth student whowalk into the cafeteria. Out of 40 students surveyed,19 students stated that they liked the burgers best.The cafeteria staff concludes that about 50% of thestudents like burgers best.The conclusion is . Since the population is thestudents of the school, the sample is a. It is .MAIN IDEA• Predict the actions of alarger group by using asample.12–5 Using Sampling to Predict
  • 12–5322 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.In a biased sample, one or more parts of the population areover others. Two types of samplesare convenience sample and voluntary response sample.BUILD YOUR VOCABULARY (pages 308–309)To determine what sports teenagers like, Janetsurveyed the student athletes on the girls’ field hockeyteam. Of these, 65% said that they like field hockey best.Janet concluded that over half of teenagers like fieldhockey best.The conclusion is . The students surveyedprobably prefer field hockey. This is .The sample is because the peopleare easily accessed.Check Your Progress Determine whether eachconclusion is valid. Justify your answer.a. To determine what ride is most popular, every tenth personto walk through the gates of a theme park is surveyed. Outof 290 customers, 98 stated that they prefer The Zip. Thepark manager concludes that about a third of the park’scustomers prefer The Zip.b. To determine whether people prefer dogs or cats, aresearcher surveys 80 people at a dog park. Of thosesurveyed, 88% said that they prefer dogs, so the researcherconcludes that most people prefer dogs.
  • 12–5Math Connects, Course 3 323Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Using Sampling to PredictBOOKS The student council is Book TypeNumber ofStudentsmystery 12adventurenovel9sports 11shortstories8trying to decide what types ofbooks to sell at its annual bookfair to help raise money for theeighth-grade trip. It surveys 40students at random. The booksthey prefer are in the table.If 220 books are to be sold at thebook fair, how many shouldbe mysteries?First, determine whether the sample method is valid. Thesample is since the studentswere randomly selected. Thus, the sample .12_40or of the students prefer mysteries. So, find.0.30 × =About books should be mysteries.Check Your Progress The student shop sells pens. Itsurveys 50 students at random. The pens they prefer are in thetable. If 300 pens are to be sold at the student shop, how manyshould be gel pens?Type Numbergel pens 22ball point 8glitter 10roller balls 10ORGANIZE ITUnder Sampling, listthe different typesof samples and howto use them to makepredictions. Giveexamples.®HOMEWORKASSIGNMENTPage(s):Exercises:
  • 324 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 12 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 12, go to:glencoe.comYou can use your completedVocabulary Builder(pages 308–309) to help yousolve the puzzle.12-1Counting Outcomes1. Complete the tree diagram shown below for how many boys andand how many girls are likely to be in a family of three children.Child 1 Child 2 Child 3 Sample OutcomeB BBBBBGGGBGBG2. Use the Fundamental Counting Principle to find the numberof possible outcomes if there are 4 true-false questions on a test.× × × =C H A P T E R12
  • Math Connects, Course 3 325Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.12-2Probability of Compound Events3. What is a compound event?4. Are the events of spinning a spinner and rolling a number cubeindependent events? Why or why not?A number cube is rolled and a penny is tossed. Find eachprobability.5. P(4 and tails) 6. P(3 or less, heads)12-3Experimental and Theoretical ProbabilityThe table at the right shows the results of a survey.7. How many people bought balloons?8. How many people were surveyed?9. What is the experimental probability thata person surveyed preferred balloons?10. A bag contains 15 red marbles, 25 purple marbles, and 10 yellowmarbles. Describe an experiment that you could conduct with themarbles to find an experimental probability.ItemNumber ofPeopleballoons 75cards 15decorations 25cake 50Chapter 12 BRINGING IT ALL TOGETHER
  • 326 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.12-4Problem-Solving Investigation: Act It Out11. SPORTS There are 32 tennis players in a tournament. If eachlosing player is eliminated from the tournament, how manytennis matches will be played during the tournament?12-5Using Sampling to Predict12. When you conduct a survey by asking ten students selected atrandom from each grade at your school what their favorite class is,what type of random sample have you taken?13. A grocery store owner asks the shoppers in his store wherethey prefer to shop for groceries. What type of sample has heconducted?Chapter 12 BRINGING IT ALL TOGETHER
  • Math Connects, Course 3 327Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ChecklistARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureVisit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 12.Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R12Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 12 Practice Test on page 663of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 12 Study Guide and Reviewon pages 659–662 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 12 Practice Test on page 663of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 12 Foldables.• Then complete the Chapter 12 Study Guide and Review onpages 659–662 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 12 Practice Test onpage 663.