Multiply negative numbers copy
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Here are the solutions to the daily startup problems with explanations: I have 4 groups of 6 black chips. 4x6 = 24 I have 4 groups of 6 red chips. 4x6 = 24 I owe 4 groups of 6 black chips. -4x6 = -24 (Owing chips is a negative amount) I owe 4 groups of 6 red chips. -4x6 = -24 (Owing chips is a negative amount) In the first two situations, having chips is a positive amount. In the last two situations, owing chips is represented as a negative amount since it is a debt that is owed.
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Final Assignment (22 marks)
Each question is worth 1 mark. You must show all your work to obtain full marks.
Marks will be deducted for no work shown.
1. What happens to the graph of 1 if the equation is changed to 1?
2. The graph of y = √ undergoes the transformation (x, y) ( 3,2 5)x y . What is the resulting
equation?
3. Determine the equation of the polynomial in factored form of the least degree that is symmetric
to the y‐axis, touches but does not go through the x‐axis at (3, 0), and has P(0) = 27
4. Determine the measure of all angles that satisfy the following conditions. Give exact answers.
csc =2 in the domain 2 2
Page 2 of 7
5. Solve: 3 cos ² 8 cos 4 0, over all real numbers
6. Use factoring to help to prove each identity for all permissible values of x. Must state
restrictions over all real numbers.
2sin sin tan
cos sin cos
x x x
x x x
Page 3 of 7
7. In a population of moths, 78 moths increase to 1000 moths in 40 weeks. What is the
doubling time for this population of moths?
8. Solve the following equation: log 3 log 5 2
9. Solve for x algebraically: 5 2 3 . State your answer to the nearest hundredth.
10. A radioactive substance has a half‐life of 92 hours. If 48g were present initially, how long will it
take for the substance to decay to 3g? Show algebraically.
Page 4 of 7
11. Given the following two functions √ 1 and 1, evaluate
3 .
12. A sample of 5 people is selected from 3 smokers and 12non‐smokers. In how many ways can
the 5 people be selected?
13. Given the functions 7 and √ , determine an explicit equation for
, then state its domain.
14. Determine the 4th term of 3 2 .
15. Solve by algebra √13 1 0
Page 5 of 7
16. Determine the domain, range, and intercepts of 2√4 2 3. Graph the function.
17. For the graph of , determine an non‐permissible values of , write the coordinates of
any hole and write the equation of any vertical asymptote.
Page 6 of 7
18. Sketch the graph of 3 4 5. State the domain, range, and equation of the
horizontal asymptote.
19. Suppose you play a game of cards in which only 5 cards are dealt from a standard 52 deck. How
many ways are there to obtain at least 3 cards of the same suit? An example of a hand that
contains at least 3 cards of the same suit is 4 hearts and 1 club.
20. Given , determine , the inverse of .
Page 7 of 7
21. Consider the digits 0, 2, 4, 5, 6, 8. How many 3‐digit even numbers less than 700 can be
formed if repetition of digits is not allowed? Note: the first digit cannot be zero.
22. If and 2 3, determine the value of 1 .
Lesson 3.4
Introduction
Course Objectives
This lesson will address the following course outcomes:
· 20. .
Get the facts, jack!
This document appears to be a quiz or game about exponential functions. It asks the player questions to test their knowledge of identifying exponential functions from equations and graphs. It also asks about key properties of exponential functions like their graphical shape as curves and multiplying the base by the same amount each time in a table. The quiz provides feedback and answers for each question to help the player learn.
MATH; discussion_20240304_113651_0000.pdf
This document provides information about comparing different types of numbers on a number line, including integers, fractions, decimals, and whole numbers. It discusses key topics like:
1. Using a number line to compare integers with other numbers like whole numbers, fractions, and decimals.
2. Identifying positive and negative integers.
3. Solving word problems that involve comparing integers to other number types on a number line.
Week 1 - Trigonometry
The document outlines the critical path to success in a course. It states that students should always arrive on time, prepared with materials like notebooks, pencils, and pens. It also emphasizes asking questions when confused and getting extra help from the teacher if falling behind. The document discusses forgetting curves and reviewing notes daily.
Gcf and lcm (1)
This document provides examples and explanations of how to use greatest common factor (GCF) and least common multiple (LCM) to solve word problems involving real-life applications. It discusses how GCF problems involve splitting or distributing items equally into groups, while LCM problems involve events repeating or figuring out when things will happen at the same time. Sample word problems are provided for both GCF and LCM along with step-by-step solutions showing how to apply the concepts. Readers are then given a quiz to practice identifying whether problems require GCF or LCM and to solve some sample real-world application problems.
Multiplication Algorithm
The document discusses the integers multiplication algorithm. It states that the product of an even number of negative numbers is positive, while the product of an odd number of negative numbers is negative. To determine the sign and magnitude of the product of signed numbers, one should first determine if the number of negative numbers is even or odd, write down the sign if it is negative, and then compute the magnitude by multiplying the absolute values of the numbers.
N) Multiply Integers Day 1
The document provides instruction on multiplying integers. It explains that multiplication is repeated addition and presents rules for determining the sign of the product when multiplying integers. Examples are worked through step-by-step using models to represent multiplication as groups of numbers. Practice problems are provided for students to simplify expressions involving integer multiplication.
G8 Math Q2- Week 8- Transforming Contrapositive, Converse and Inverse.pptx
This document discusses conditional statements and their transformations. It defines the hypothesis and conclusion of an if-then statement and shows examples of converting a statement to its converse, inverse, and contrapositive. Specifically, it demonstrates that the converse switches the hypothesis and conclusion, the inverse negates both, and the contrapositive switches and negates both. The document provides examples, activities for students to practice the transformations, and emphasizes the importance of identifying the hypothesis and conclusion of an if-then statement.
Taller de recuperacion
The document is about INFOTEC, the National Institute of Technical Training. It does not provide any details about specific activities.
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This document outlines ratios, proportions, and how to solve ratio and proportion problems. It discusses:
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- Properties of proportions including the cross product property (ad = bc) and reciprocal property.
- Examples of setting up and solving proportions for an unknown variable using the cross product property.
- An example problem walking through setting up and solving a multi-step ratio and proportion word problem about how many gallons of gas Mr. Yu uses in a week for his commute to school.
Math stars grade 4
The document contains a collection of math word problems and exercises for students. It includes problems involving geometry, algebra, time, money, fractions, probability and other topics. After each problem section, it provides the answers and an explanation of the problem solving strategies and concepts involved. The purpose is to challenge students with complex multi-step problems and help them improve their problem solving skills.
QL-8Z65MgMR
1. The standard bowling lane setup has pins arranged in four rows, with the number of pins in each row increasing by one from front to back.
2. If a fifth row is added, the total number of pins can be calculated using the formula for the sum of the first n positive integers, which is n(n+1)/2.
3. For 100 rows of pins, this same formula can be used to calculate that there would be 100*101/2 = 5,050 total pins.
G6 m3-a-lesson 4-t
This document provides a lesson on the concept of opposites of numbers. It includes:
1) An opening exercise asking students to identify relationships between sets of opposites words.
2) Examples of locating numbers and their opposites on a number line. The key points are that opposites are the same distance from zero but on opposite sides, and zero is its own opposite.
3) A word problem example modeling a real-world situation involving opposites on a number line, with questions to discuss the representation.
The lesson emphasizes that opposites are equidistant from zero but on opposite sides, and that zero represents the point of reference or no change in various contexts.
Ratios and Proportions.pptx
This document discusses ratios, proportions, and their uses. It provides examples of ratios comparing quantities like shaded area to unshaded area in rectangles. Proportions are defined as ratios that are equal, such as fractions that reduce to the same value. Examples are given for solving proportions to find unknown values. Similar figures are discussed as having the same shape but not necessarily the same size, with corresponding angles being congruent and sides proportional. Methods are presented for using proportions to solve for unknown sides or values in similar or scaled figures.
1.3 Real Numbers and the Number Line
The document discusses classifying, graphing, and comparing real numbers, including finding and estimating square roots. It defines real numbers as numbers that can be located on the number line, including integers, rational numbers, and irrational numbers. The document also discusses the differences between finding the square root of a perfect square versus a non-perfect square.
john-michaels-lp-editedmee.docx
The document summarizes a Grade 8 mathematics lesson on if-then statements. The lesson included the following:
1. Students reviewed linear functions from the previous lesson and completed a drill on basic math problems.
2. They participated in a motivation activity where they analyzed pictures in pairs and explained the relationships using if-then statements.
3. The teacher explained that an if-then statement has two clauses - a hypothesis (if clause) and conclusion (then clause). Students practiced writing statements in this form using more picture examples.
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Multiply negative numbers copy
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