This document contains 19 practice problems for an Algebra II study guide. The problems cover a range of algebraic topics including properties of operations, evaluating expressions, solving equations and inequalities, graphing, relations and functions, slope, lines, and systems of equations. Students are to complete the problems, showing the step-by-step work and solutions.
The document provides examples of conditional sentences in the third conditional form, which is used to talk about hypothetical situations in the past that did not happen. It gives sample sentences with blanks to be filled in with the correct verb forms. Additional exercises provide more sentence structures to practice the third conditional, including matching activities, multiple choice questions, sentence completion, and writing original conditional sentences.
The document provides examples of sentences rewritten to replace modal verbs or include modal verbs. It contains two sections:
1) Rewrite sentences using the modal verbs provided in brackets
2) Rewrite sentences using any modal verb
The examples demonstrate how to properly use modal verbs to rewrite sentences in various contexts related to possibility, permission, obligation, advice and certainty.
This document discusses soil science concepts for 5th grade, including defining soil, listing its functions, types of soil that exist, distinguishing between sandy and clay soils, describing soil horizons, and technological developments in agriculture. Questions are posed about each topic to be answered.
The document provides examples of conditional sentences in the third condition (past time - unreal/contrary to fact). It gives 11 sentences where the verbs are missing and asks the reader to fill them in using the correct past tense form. It then provides more examples of third conditional sentences for practice, including matching exercises, sentence completion, comprehension questions, and writing your own conditional sentences.
This document contains an exam on the Cold War for 9th grade students at Colégio Imaculada Conceição. It includes 10 questions about key events and aspects of the Cold War, such as the wars in Korea and Vietnam, characteristics of the Cold War, the Iron Curtain, the Berlin Wall, the UN, Zionism, the Suez Crisis, and social welfare policies in Brazil. Students are asked to describe, cite, and explain facts about these various topics relating to the global Cold War era.
This document provides information and instructions for a student to complete an activity using their campus website and college catalog. The activity has the student:
1) Find various information on the campus website such as events, degree programs, and student organizations.
2) Use the academic calendar to find withdrawal dates and holidays.
3) Use the college catalog to identify scholarship/loan options, required courses for their major, and definitions of academic terms.
4) Visit various campus resources and identify services available at each like the bookstore, library, career services, and more.
The activity has the student familiarize themselves with important resources and terminology to help them succeed at their college.
This document discusses emerging legal trends affecting the workplace presented by Mark Bakker of Wyche, P.A. It outlines increased regulatory scrutiny from agencies like the DOL, EEOC, and NLRB. The DOL is cracking down on misclassifying independent contractors and the EEOC is providing guidance on criminal background checks. The NLRB is also showing signs of more aggressive enforcement of labor laws. Emerging issues around social media, BYOD policies, same-sex marriage benefits, and anti-bullying initiatives are also discussed. Bakker provides best practices for various policies and compliance in this new legal landscape.
This document discusses solving quadratic equations by factoring. It begins by defining a quadratic equation in standard form and explaining the zero factor property. It then provides examples of solving quadratic equations through factoring and setting each factor equal to zero. Finally, it demonstrates solving word problems by setting up and solving the resulting quadratic equation.
The document provides examples of conditional sentences in the third conditional form, which is used to talk about hypothetical situations in the past that did not happen. It gives sample sentences with blanks to be filled in with the correct verb forms. Additional exercises provide more sentence structures to practice the third conditional, including matching activities, multiple choice questions, sentence completion, and writing original conditional sentences.
The document provides examples of sentences rewritten to replace modal verbs or include modal verbs. It contains two sections:
1) Rewrite sentences using the modal verbs provided in brackets
2) Rewrite sentences using any modal verb
The examples demonstrate how to properly use modal verbs to rewrite sentences in various contexts related to possibility, permission, obligation, advice and certainty.
This document discusses soil science concepts for 5th grade, including defining soil, listing its functions, types of soil that exist, distinguishing between sandy and clay soils, describing soil horizons, and technological developments in agriculture. Questions are posed about each topic to be answered.
The document provides examples of conditional sentences in the third condition (past time - unreal/contrary to fact). It gives 11 sentences where the verbs are missing and asks the reader to fill them in using the correct past tense form. It then provides more examples of third conditional sentences for practice, including matching exercises, sentence completion, comprehension questions, and writing your own conditional sentences.
This document contains an exam on the Cold War for 9th grade students at Colégio Imaculada Conceição. It includes 10 questions about key events and aspects of the Cold War, such as the wars in Korea and Vietnam, characteristics of the Cold War, the Iron Curtain, the Berlin Wall, the UN, Zionism, the Suez Crisis, and social welfare policies in Brazil. Students are asked to describe, cite, and explain facts about these various topics relating to the global Cold War era.
This document provides information and instructions for a student to complete an activity using their campus website and college catalog. The activity has the student:
1) Find various information on the campus website such as events, degree programs, and student organizations.
2) Use the academic calendar to find withdrawal dates and holidays.
3) Use the college catalog to identify scholarship/loan options, required courses for their major, and definitions of academic terms.
4) Visit various campus resources and identify services available at each like the bookstore, library, career services, and more.
The activity has the student familiarize themselves with important resources and terminology to help them succeed at their college.
This document discusses emerging legal trends affecting the workplace presented by Mark Bakker of Wyche, P.A. It outlines increased regulatory scrutiny from agencies like the DOL, EEOC, and NLRB. The DOL is cracking down on misclassifying independent contractors and the EEOC is providing guidance on criminal background checks. The NLRB is also showing signs of more aggressive enforcement of labor laws. Emerging issues around social media, BYOD policies, same-sex marriage benefits, and anti-bullying initiatives are also discussed. Bakker provides best practices for various policies and compliance in this new legal landscape.
This document discusses solving quadratic equations by factoring. It begins by defining a quadratic equation in standard form and explaining the zero factor property. It then provides examples of solving quadratic equations through factoring and setting each factor equal to zero. Finally, it demonstrates solving word problems by setting up and solving the resulting quadratic equation.
This document discusses common myths and misconceptions about wage and hour law. It addresses nine myths, providing the realities of laws regarding overtime exemptions, compensable working time, docking exempt employee pay, and using unpaid interns or independent contractors. The key takeaway is that wage and hour law is complex and employers should regularly audit their pay practices to ensure compliance.
This document discusses polynomial functions. It defines polynomial functions as functions of the form f(x) = anxn + an-1xn-1 + ... + a1x + a0, where the exponents are whole numbers. It describes the leading coefficient, constant term, and degree of a polynomial function. Common types of polynomial functions like constant, linear, quadratic, cubic, and quartic functions are identified based on their degree. Methods for identifying if a function is a polynomial function, evaluating polynomial functions using direct substitution and synthetic substitution, and determining the left and right behavior of a polynomial function's graph are also discussed.
This document discusses how to solve quadratic equations by graphing. It defines the terms of a quadratic equation as the quadratic term, linear term, and constant term. Examples are given of identifying these terms in quadratic functions. The document also discusses that quadratic equations can have 0, 1, or 2 real solutions, which are found by determining where the graph crosses the x-axis. Methods for solving quadratic equations graphically include identifying the x-intercepts of the parabolic graph as well as using a table of x-values to plot the graph.
1) The document is an algebra II study guide containing 50 problems covering various algebra topics including properties, evaluating expressions, solving equations and inequalities, graphing lines and parabolas, working with complex numbers, and other concepts.
2) Many of the problems ask students to reference the specific section of their textbook that covers the relevant concept. The responses provide the answer and cite the textbook reference.
3) The study guide provides practice with essential algebra skills and will help students prepare for an exam or further study of advanced algebra topics.
This document discusses managing social media in the workplace. It notes that most companies now have social media policies and around a third take disciplinary action when policies are violated. The challenges of restricting social media use, addressing personal devices at work, protecting contacts when employees leave, and determining when it's acceptable to fire someone for their social media activity are discussed. The legal implications of using social media in hiring decisions and accessing employee passwords are also covered. Best practices for drafting social media policies that don't restrict lawful employee communications are suggested.
This document discusses polynomial functions. It defines polynomial functions as functions of the form f(x) = anxn + an-1xn-1 + ... + a1x + a0, where the exponents are whole numbers. It describes the leading coefficient, constant term, and degree of a polynomial function. Common types of polynomial functions like constant, linear, quadratic, cubic, and quartic functions are summarized. Methods for identifying if a function is a polynomial function, evaluating polynomial functions using direct substitution and synthetic substitution, and determining the left and right behavior of a polynomial function's graph are also discussed.
This document discusses checking solutions to quadratic inequalities and graphing quadratic inequalities. It provides examples of checking if an ordered pair is a solution to an inequality and finding the vertex of a quadratic function to graph it as a solid curve below or above the vertex based on whether the inequality is ≤ or ≥.
Hanging Separately: Why China and Africa are unable to meet as equalsJordan Peacock
China and Africa have had a long historical relationship dating back to the voyages of Zheng He in the early 15th century, but their modern relationships have been complicated by their differing colonial experiences and development paths. China pursued an anti-colonial foreign policy in the 1950s-60s to gain diplomatic recognition and UN votes from newly independent African nations. In the 1970s-80s, China focused domestically and on conflicts with the Soviet Union. Since the 1990s, China has sought to manage its global image and secure natural resource imports from Africa through rapid economic growth and investment. However, concerns remain about the potential for unequal power dynamics between the rising global power of China and individual African states.
The document discusses several key issues related to privacy in the information age:
- Personal data from many major data breaches and hacks has been exposed, including information from Target, Home Depot, Anthem, and the OPM, putting millions of individuals at risk.
- Countries like China, Russia, and the US have significant cyber capabilities and have been accused of hacking for political and economic gains. China in particular has penetrated many US corporations.
- Laws and policies intended to enable surveillance like Section 215 of the PATRIOT Act and Section 702 of the FISA Amendments Act have been criticized for being overly broad and not properly overseen.
- Loss of data privacy and
This document provides an overview of quadratic functions in the form of y = ax^2 + bx + c. It explains that a, b, and c are coefficients that determine the shape of the parabolic graph. The graph will have a line of symmetry and either a maximum or minimum point. Examples are given of how changing the coefficients impacts the graph. Methods for solving quadratic equations by setting y = 0 and finding the x-intercepts are presented, along with examples of graphs with different numbers of solutions.
This document discusses protections for religious beliefs and practices in the workplace. It begins by outlining constitutional and Title VII protections against religious discrimination for both public and private sector employees. It then examines several EEOC cases involving religious discrimination and the types of religious accommodations required by employers. The rest of the document poses hypothetical scenarios and discusses whether certain employer policies or accommodation requests would violate Title VII requirements to reasonably accommodate employees' religious beliefs and practices without imposing an undue hardship.
Okay, let's solve this step-by-step:
1) FOIL the expression: y = 3(x + 2)(x + 2) - 4
= 3(x^2 + 4x + 2x + 4) - 4
= 3x^2 + 12x + 12 - 4
= 3x^2 + 12x + 8
2) This is in the vertex form: y = a(x - h)^2 + k
Where:
a = 3
h = -2
k = 8
So the equation in vertex form is:
y = 3(x - (-2))^2 + 8
y = 3(x + 2)^2 - 4
1) The document discusses solving quadratic equations by factoring, including using the zero factor property.
2) It provides examples of solving quadratic equations by factoring them into two binomial factors and setting each factor equal to zero.
3) The document also shows how to solve word problems by setting up and solving quadratic equations derived from the problem information.
Jordan Peacock discusses using a Magic: The Gathering trading card game deck to illustrate concepts from anarchism and political philosophy. The deck uses different card colors, mechanics, and art to represent conflict pairs like omniscience and control versus foreboding and doom. New game mechanics are introduced to depict technical concepts and idioms in a visual, verbal, and mechanical way. The deck is explored as a potential format for mapping other concepts and themes in the future.
5.2 solve quadratic equations by graphing.vertex and intercept formmorrobea
Okay, let's solve this step-by-step:
1) FOIL the expression: y = 3(x + 2)(x + 2) - 4
= 3(x^2 + 4x + 2x + 4) - 4
= 3x^2 + 12x + 12 - 4
= 3x^2 + 12x + 8
2) This is in the vertex form: y = a(x - h)^2 + k
Where: a = 3
h = 0
k = 8
So the equation in vertex form is:
y = 3(x - 0)^2 + 8
Or simply:
y = 3x^2 + 8
This document discusses how to solve systems of linear inequalities by graphing them. It explains that you first put the inequalities into slope-intercept form, then graph each line as dotted or solid based on the inequality symbols and shade the correct region above or below the line. The solution to the system is the region where the graphs overlap. An example demonstrates these steps to find the solution region between two inequalities.
Back to the Future: Emerging Employment Law Trendswychepa
The document summarizes emerging employment law trends. It discusses that the National Labor Relations Board is expanding protections for private sector employees' rights to discuss workplace issues. It also discusses that the Department of Labor is updating overtime exemption rules to increase the minimum salary threshold and restrict improper classifications of employees as exempt. Additionally, the document discusses evolving standards around joint employer liability and independent contractor classifications that are making it harder to avoid employment relationships.
The document is a summer bucket list with 20 activities left unspecified. It introduces the list as a "Bucketlist Of This Summer" and concludes by stating "Fun Fun Fun Fun", indicating the list is meant to include enjoyable activities to do over the summer months.
The document contains exercises asking to write verbs in sentences and describe what people are doing in sentences. It asks the reader what they will be doing on the weekend.
This document contains two worksheets for students to practice writing numbers. Each worksheet has 5 blank lines for students to write numbers and includes spaces for their name, class, date and grade. The document provides templates for students to complete number writing practice exercises.
The document contains 4 spelling post-tests with 25 blank spaces each for students to fill in spelling words from their lesson. The tests are unlabeled except for blanks for the lesson number and date. They also include a blank for the student's name.
The document is a chapter evaluation that asks students to complete a table with information about a Chinese Fan Dance and Japanese Parasol Dance, describe basic steps from each dance, answer questions comparing and contrasting the two dances, and explain which dance they would prefer to perform and why. It requires students to demonstrate their understanding of key terminology, dance moves, symbols and cultural aspects of the two dances covered in the chapter.
This document discusses common myths and misconceptions about wage and hour law. It addresses nine myths, providing the realities of laws regarding overtime exemptions, compensable working time, docking exempt employee pay, and using unpaid interns or independent contractors. The key takeaway is that wage and hour law is complex and employers should regularly audit their pay practices to ensure compliance.
This document discusses polynomial functions. It defines polynomial functions as functions of the form f(x) = anxn + an-1xn-1 + ... + a1x + a0, where the exponents are whole numbers. It describes the leading coefficient, constant term, and degree of a polynomial function. Common types of polynomial functions like constant, linear, quadratic, cubic, and quartic functions are identified based on their degree. Methods for identifying if a function is a polynomial function, evaluating polynomial functions using direct substitution and synthetic substitution, and determining the left and right behavior of a polynomial function's graph are also discussed.
This document discusses how to solve quadratic equations by graphing. It defines the terms of a quadratic equation as the quadratic term, linear term, and constant term. Examples are given of identifying these terms in quadratic functions. The document also discusses that quadratic equations can have 0, 1, or 2 real solutions, which are found by determining where the graph crosses the x-axis. Methods for solving quadratic equations graphically include identifying the x-intercepts of the parabolic graph as well as using a table of x-values to plot the graph.
1) The document is an algebra II study guide containing 50 problems covering various algebra topics including properties, evaluating expressions, solving equations and inequalities, graphing lines and parabolas, working with complex numbers, and other concepts.
2) Many of the problems ask students to reference the specific section of their textbook that covers the relevant concept. The responses provide the answer and cite the textbook reference.
3) The study guide provides practice with essential algebra skills and will help students prepare for an exam or further study of advanced algebra topics.
This document discusses managing social media in the workplace. It notes that most companies now have social media policies and around a third take disciplinary action when policies are violated. The challenges of restricting social media use, addressing personal devices at work, protecting contacts when employees leave, and determining when it's acceptable to fire someone for their social media activity are discussed. The legal implications of using social media in hiring decisions and accessing employee passwords are also covered. Best practices for drafting social media policies that don't restrict lawful employee communications are suggested.
This document discusses polynomial functions. It defines polynomial functions as functions of the form f(x) = anxn + an-1xn-1 + ... + a1x + a0, where the exponents are whole numbers. It describes the leading coefficient, constant term, and degree of a polynomial function. Common types of polynomial functions like constant, linear, quadratic, cubic, and quartic functions are summarized. Methods for identifying if a function is a polynomial function, evaluating polynomial functions using direct substitution and synthetic substitution, and determining the left and right behavior of a polynomial function's graph are also discussed.
This document discusses checking solutions to quadratic inequalities and graphing quadratic inequalities. It provides examples of checking if an ordered pair is a solution to an inequality and finding the vertex of a quadratic function to graph it as a solid curve below or above the vertex based on whether the inequality is ≤ or ≥.
Hanging Separately: Why China and Africa are unable to meet as equalsJordan Peacock
China and Africa have had a long historical relationship dating back to the voyages of Zheng He in the early 15th century, but their modern relationships have been complicated by their differing colonial experiences and development paths. China pursued an anti-colonial foreign policy in the 1950s-60s to gain diplomatic recognition and UN votes from newly independent African nations. In the 1970s-80s, China focused domestically and on conflicts with the Soviet Union. Since the 1990s, China has sought to manage its global image and secure natural resource imports from Africa through rapid economic growth and investment. However, concerns remain about the potential for unequal power dynamics between the rising global power of China and individual African states.
The document discusses several key issues related to privacy in the information age:
- Personal data from many major data breaches and hacks has been exposed, including information from Target, Home Depot, Anthem, and the OPM, putting millions of individuals at risk.
- Countries like China, Russia, and the US have significant cyber capabilities and have been accused of hacking for political and economic gains. China in particular has penetrated many US corporations.
- Laws and policies intended to enable surveillance like Section 215 of the PATRIOT Act and Section 702 of the FISA Amendments Act have been criticized for being overly broad and not properly overseen.
- Loss of data privacy and
This document provides an overview of quadratic functions in the form of y = ax^2 + bx + c. It explains that a, b, and c are coefficients that determine the shape of the parabolic graph. The graph will have a line of symmetry and either a maximum or minimum point. Examples are given of how changing the coefficients impacts the graph. Methods for solving quadratic equations by setting y = 0 and finding the x-intercepts are presented, along with examples of graphs with different numbers of solutions.
This document discusses protections for religious beliefs and practices in the workplace. It begins by outlining constitutional and Title VII protections against religious discrimination for both public and private sector employees. It then examines several EEOC cases involving religious discrimination and the types of religious accommodations required by employers. The rest of the document poses hypothetical scenarios and discusses whether certain employer policies or accommodation requests would violate Title VII requirements to reasonably accommodate employees' religious beliefs and practices without imposing an undue hardship.
Okay, let's solve this step-by-step:
1) FOIL the expression: y = 3(x + 2)(x + 2) - 4
= 3(x^2 + 4x + 2x + 4) - 4
= 3x^2 + 12x + 12 - 4
= 3x^2 + 12x + 8
2) This is in the vertex form: y = a(x - h)^2 + k
Where:
a = 3
h = -2
k = 8
So the equation in vertex form is:
y = 3(x - (-2))^2 + 8
y = 3(x + 2)^2 - 4
1) The document discusses solving quadratic equations by factoring, including using the zero factor property.
2) It provides examples of solving quadratic equations by factoring them into two binomial factors and setting each factor equal to zero.
3) The document also shows how to solve word problems by setting up and solving quadratic equations derived from the problem information.
Jordan Peacock discusses using a Magic: The Gathering trading card game deck to illustrate concepts from anarchism and political philosophy. The deck uses different card colors, mechanics, and art to represent conflict pairs like omniscience and control versus foreboding and doom. New game mechanics are introduced to depict technical concepts and idioms in a visual, verbal, and mechanical way. The deck is explored as a potential format for mapping other concepts and themes in the future.
5.2 solve quadratic equations by graphing.vertex and intercept formmorrobea
Okay, let's solve this step-by-step:
1) FOIL the expression: y = 3(x + 2)(x + 2) - 4
= 3(x^2 + 4x + 2x + 4) - 4
= 3x^2 + 12x + 12 - 4
= 3x^2 + 12x + 8
2) This is in the vertex form: y = a(x - h)^2 + k
Where: a = 3
h = 0
k = 8
So the equation in vertex form is:
y = 3(x - 0)^2 + 8
Or simply:
y = 3x^2 + 8
This document discusses how to solve systems of linear inequalities by graphing them. It explains that you first put the inequalities into slope-intercept form, then graph each line as dotted or solid based on the inequality symbols and shade the correct region above or below the line. The solution to the system is the region where the graphs overlap. An example demonstrates these steps to find the solution region between two inequalities.
Back to the Future: Emerging Employment Law Trendswychepa
The document summarizes emerging employment law trends. It discusses that the National Labor Relations Board is expanding protections for private sector employees' rights to discuss workplace issues. It also discusses that the Department of Labor is updating overtime exemption rules to increase the minimum salary threshold and restrict improper classifications of employees as exempt. Additionally, the document discusses evolving standards around joint employer liability and independent contractor classifications that are making it harder to avoid employment relationships.
The document is a summer bucket list with 20 activities left unspecified. It introduces the list as a "Bucketlist Of This Summer" and concludes by stating "Fun Fun Fun Fun", indicating the list is meant to include enjoyable activities to do over the summer months.
The document contains exercises asking to write verbs in sentences and describe what people are doing in sentences. It asks the reader what they will be doing on the weekend.
This document contains two worksheets for students to practice writing numbers. Each worksheet has 5 blank lines for students to write numbers and includes spaces for their name, class, date and grade. The document provides templates for students to complete number writing practice exercises.
The document contains 4 spelling post-tests with 25 blank spaces each for students to fill in spelling words from their lesson. The tests are unlabeled except for blanks for the lesson number and date. They also include a blank for the student's name.
The document is a chapter evaluation that asks students to complete a table with information about a Chinese Fan Dance and Japanese Parasol Dance, describe basic steps from each dance, answer questions comparing and contrasting the two dances, and explain which dance they would prefer to perform and why. It requires students to demonstrate their understanding of key terminology, dance moves, symbols and cultural aspects of the two dances covered in the chapter.
Give Your Students a Voice With Interactive Notebooks
Interactive Notebooks will change the way your students organize their thoughts, show creativity and express their knowledge of a subject. Using Interactive Notebooks, your students will have a significant decrease in lost papers and a more personalized education. Though this session is directed towards Science, Interactive Notebooks are easily adaptable for other subjects.
Presenter: Catie DiVito - Broad Creek Middle School - Newport, NC
This document contains a science exam with multiple choice, labeling, matching, and fill-in-the-blank questions about engineering, technology, and biology. The exam tests understanding of key terms like the design process, materials, engineers, and solutions. It also requires identifying examples of technology used at home, school, and for safety. Students must demonstrate knowledge of lungs, gills, shelter, oxygen, and how different animals survive.
This daily lesson log outlines lessons, objectives, references, and materials used for multiple classes. Details include the lesson topics, objectives, textbook and module pages, and teacher guides referenced. Remarks note the number of students who achieved mastery of the material and those needing remediation or reinforcement. Other activities are also listed.
The document lists 25 words with their American English meanings and asks the reader to choose the matching British English term for each. It includes common vocabulary differences like apartment/flat, candy/sweets, truck/lorry, and theater/cinema. The purpose is to test knowledge of alternate terms used in British versus American English.
This document contains a spelling list for Grade 5 students. It includes 24 sets of homophones and commonly misspelled words from their curriculum. After the students spell the words, another 24 vocabulary words from the story "Two Old Women" will be given as an assignment.
This document discusses checking solutions to quadratic inequalities and graphing quadratic inequalities. It provides examples of checking if an ordered pair is a solution to an inequality and finding the vertex of a quadratic function to graph it as a solid curve below or above the vertex based on whether the inequality is ≤ or ≥.
This document discusses checking solutions to quadratic inequalities and graphing quadratic inequalities. It provides examples of checking if an ordered pair is a solution to an inequality and finding the vertex of a quadratic function to graph it as a solid curve below or above the vertex based on whether the inequality is ≤ or ≥.
This document discusses checking solutions to quadratic inequalities and graphing quadratic inequalities. It provides examples of checking if an ordered pair is a solution to an inequality and finding the vertex of a quadratic function to graph it as a solid curve below or above the vertex based on whether the inequality is ≤ or ≥.
This document discusses checking solutions to quadratic inequalities and graphing quadratic inequalities. It provides examples of checking if an ordered pair is a solution to an inequality and finding the vertex of a quadratic function to graph it as a solid curve below or above the vertex based on whether the inequality is ≤ or ≥.
1. The document contains 50 math problems involving ordering numbers, evaluating expressions, solving equations and inequalities, graphing functions and relations, and other topics.
2. For each problem, the key steps are shown and the solution is provided in brackets at the end in reference to the problem number.
3. The document serves as an expert summary by providing concise solutions to each problem in 3 sentences or less.
1) The document is an algebra II study guide containing 50 problems covering various algebra topics including properties, evaluating expressions, solving equations and inequalities, graphing lines and parabolas, working with complex numbers, and other concepts.
2) Many of the problems ask students to reference the specific section of their textbook that covers the relevant concept. The responses provide the answer and cite the textbook reference.
3) The study guide is designed to help students review major algebra II concepts in preparation for a test or exam through practicing worked examples. The answers allow students to check their work and understanding of these essential skills.
1. The document contains 50 math problems involving ordering numbers, evaluating expressions, solving equations and inequalities, graphing functions and relations, and other topics.
2. For each problem, the key steps are shown and the solution is provided in brackets at the end in reference to the problem number.
3. The document serves as an expert summary by providing concise 3-sentence or less solutions for each of the 50 math problems.
This document discusses graphing quadratic functions in vertex and intercept forms. It defines key terms like vertex, axis of symmetry, and parabola. It explains how to graph quadratic functions written in vertex form and intercept form. Examples are provided for graphing functions in each form. The document also discusses how to change between the vertex, intercept, and standard forms of a quadratic equation.
This document discusses quadratic functions in the form of y = ax^2 + bx + c. It explains that a, b, and c are coefficients and the graph will be a parabola with either a maximum or minimum point. Changing the values of a and c affects whether the parabola opens up or down and if it moves above or below the x-axis. Setting a quadratic function equal to 0 allows it to be solved for the x-intercepts, though there may be 0, 1, or 2 solutions depending on the equation. The document presents various examples and explores how changing the coefficients impacts the graph.
3.5 solving systems of equations in three variablesmorrobea
This document discusses solving systems of three linear equations in three variables using the elimination method. It provides examples of setting up systems of equations, eliminating a variable to create a system of two equations with two variables, solving the reduced system, back-substituting to find the third variable, and checking that the solution satisfies all three original equations. The solution is written as an ordered triple (x, y, z). Graphing is not recommended due to difficulty accurately graphing three-dimensional planes. Examples are worked through to demonstrate the full elimination method.
3.5 solving systems of equations in three variables
Algebra ii study guide
1. Algebra II Regular Study Guide
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1. State the property that is illustrated. 3 ⋅ (5 ⋅ 7) = (3 ⋅ 5) ⋅ 7
2. Evaluate –3y + x + 30 when x = –3 and y = 9.
3. Evaluate the expression. 60 – (15)(2) ÷ 3
2. Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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1
x=
6 and y = 3.
4. Evaluate (7 + 5y) ÷ 3x when
5. Solve the equation. − 3x + 5 = −7 x − 4
6. Solve the equation. − x + 3 = 7 x + 8
3. Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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7. For 1980 through 1990, the population, P, (in thousands), of
Hawaii can be modeled by P = 17(t + 56.6) where t = 0
represents 1980. What was the population in 1987?
5
( F − 32)
8. Solve for F C = 9
4. Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
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9. Solve for P A = P + Prt
10. A rectangle is 5 feet longer than it is wide. The perimeter of
the rectangle is 34 feet. What is the length of the rectangle?
11. Solve the inequality. Then graph your solution.
2 x + 5 ≥ 2 − ( x − 9)
5. Algebra II Regular Study Guide
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12. Is x = –7 a solution of the inequality 5x − 7 ≤ 3( x − 7) ?
Solve
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13. x − 4 ≥ 3
14. x + 7 ≥ 9
15. Is the relation
4
–
–
la, – 2f, a5, – 2f, a6, – 2fqa function?
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16. Find the range of the relation {(4, – 3), (– 5, 1), (– 1, 2)}.
17. Find
F1I. f ( x) = 18x
H3K
f −
2
− 12 x − 3
18. Find the slope of the line passing through the points (–3, 3)
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and (6, 2).
5
[A] 3
[B] 1
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[C] −9
[D]
−
1
9
19. Find the slope and y-intercepts of the line. 5x − 4 y = 20
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2
y = − x−2
3
20. Graph the line.
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21. Find the slope and y-intercepts of the line. 4 x − 3y = 36
22. Write the equation of the line, in slope-intercept form, that
passes through the point (− 2, − 2) and has slope − 3 .
23. Write the equation in slope-intercept form. Then identify the
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slope and y-intercept. 18x − 42 y = 24
24. The variables x and y vary directly and y = –7 when x = 14.
Write an equation that relates the variables.
25. For the following data
A. Make a scatter plot of the data.
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B. Approximate the best fitting line for the data.
C. Find an equation of your line of best fit.
x 1 2 3 4 5 6
7
8
y 175 41 4.95 7 815 111 1195 14
.
.
.
.
.
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y
x
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2
4
y>−
3
26. Graph the inequality in a coordinate plane. 3
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27. Is the ordered pair (–7, 2) a solution of the inequality
3x + 10 y ≥ −1 ?
28. Graph − y ≤ 4 x − 7
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29. Graph the equation. y = 2 x + 5
30. Find the solution to the system by graphing.
x+ y = –7
2x − y = – 2
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31. Is (5, –2) a solution of the system?
2x + 6y = –2
2x + y = 6
32. The drama club sold 1500 tickets for the end-of-year
performance. Admission prices were $12 for adults and $6 for
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students. The total amount collected at the box office was
$16,200. How many students attended the play?
4x − 4 y = 4
33. Solve the linear system 3x + 4 y = – 25
34. Graph the system of linear inequalities
22. Algebra II Regular Study Guide
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y ≥ x−3
3x + y ≥ – 1
35. Decide if the given ordered triple is a solution of the
following system of equations (1, –2, 4)
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3x + 2 y + 3z = 11
2 x − 4 y + z = 14
x + y − 5z = – 21
36. Solve the system of equations
x + y + z = 5
− 2 x − y + z = – 15
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x − 2y − z = 6
2
37. Does the parabola open up or down? y = 4 + 6x − 2 x
2
38. Sketch the graph of the equation. y = x − 2 x + 3
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2
39. Write in standard form and graph y = ( x − 1) + 2
40. Factor the expression 8x 2 − 25 + 10x
41. The height of a triangle is three feet longer than the base.
The area of the triangle is 44 square feet. Find the height and
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base of the triangle.
42. Find the zeros of the equation. x 2 + 2 x − 15 = y
43. Simplify the expression 175
44. Solve for x 5 x 2 = 405
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45. Solve the equation. Round the solutions to two decimal
places. 7 x 2 − 2 = 23
46. Solve x 2 + 2 x + 5 = 0
Write the expression as a complex number in standard form.
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a f
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2
3 − 2i
47.
48. − i + (7 − 5i) − 3(2 − 3i)
49. Solve the equation by completing the square.
x 2 + 2 x − 35 = 0
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2
50. Sketch the graph of the inequality. y ≥ 2 x + 4 x − 1
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33. Algebra II Regular Study Guide
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Reference [1.1.2.13]
[1] Associative property for multiplication
Reference [1.2.1.21]
[2] 0
34. Algebra II Regular Study Guide
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Reference [1.2.1.25]
[3] 50
35. Algebra II Regular Study Guide
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Reference [1.2.1.27]
[4] 44
Reference [1.3.1.46]
36. Algebra II Regular Study Guide
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9
x=−
4
[5]
Reference [1.3.1.42]
37. Algebra II Regular Study Guide
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5
x=−
8
[6]
Reference [1.3.2.52]
[7] 1,081,200
38. Algebra II Regular Study Guide
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Reference [1.4.2.62]
9
C + 32
5
[8] F =
39. Algebra II Regular Study Guide
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Reference [1.4.2.64]
A
P=
1 + rt
[9]
40. Algebra II Regular Study Guide
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Reference [1.5.2.75]
[10] 11 feet
Reference [1.6.1.81]
[11] x ≥ 2
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– 0 1 2 3 4 5
1
x
Reference [1.6.1.85]
[12] Yes
42. Algebra II Regular Study Guide
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Reference [1.7.1.92]
[13] x ≤ 1 or x ≥ 7
43. Algebra II Regular Study Guide
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Reference [1.7.1.90]
[14] x ≤ – 16 or x ≥ 2
Reference [2.1.1.3]
[15] Yes
44. Algebra II Regular Study Guide
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Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [2.1.1.1]
[16] {–3, 1, 2}
45. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [2.1.2.10]
[17] 3
Reference [2.2.1.15]
[18] [D]
46. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [2.3.1.32]
5
slope =
4 ; y-intercept = (0, -5)
[19]
47. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [2.3.1.40]
48. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
1
1 x
–5 –4 –3
–3
–4
–5
[20]
y
49. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [2.3.1.34]
4
slope =
3 ; y-intercept = (0, –12)
[21]
50. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [2.4.1.46]
[22] y = − 3x − 8
Reference [2.4.1.50]
51. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
3
4
3
4
y= x−
−
7
7 ; Slope 7 ; y-intercept (0, 7 )
[23]
Reference [2.4.2.63]
52. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
1
y=− x
2
[24]
Reference [2.5.2.72]
53. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
y
[25]
x
54. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
.
y = 175x
Reference [2.6.1.85]
55. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
y
3
2
1
–3 –2 –1
[26]
–3
1 2 3
x
56. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [2.6.1.80]
[27] Yes
Reference [2.6.1.74]
57. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
y
10
–10
[28]
10
–10
x
58. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [2.8.1.114]
59. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
y
10
–10
[29]
10
–10
x
60. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [3.1.1.3]
61. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
y
10
–10
[30]
10
–10
x
62. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
(–3, –4)
Reference [3.1.1.11]
[31] No
63. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [3.1.2.18]
[32] 300
Reference [3.2.1.23]
64. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
[33] (–3, –4)
Reference [3.3.1.45]
65. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
10
−10
[34]
y
10
−10
x
66. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [3.6.1.74]
[35] yes
67. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [3.6.1.77]
[36] (6, 1, –2)
Reference [5.1.1.5]
[37] Down
68. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [5.1.1.11]
69. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
y
3
2
(1, 2)
1
–2
[38]
1
2
3
4
x
70. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [5.1.1.15]
2
[39] y = x – 2 x + 3
71. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
y
5
−5
5
−5
x
72. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [5.2.1.27]
[40] (2 x + 5)(4 x − 5)
73. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [5.2.1.36]
[41] Base 8 ft; Height 11 ft
Reference [5.2.2.39]
[42] –5, 3
74. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [5.3.1.41]
[43] 5 7
75. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [5.3.1.44]
[44] 9
Reference [5.3.1.52]
.
[45] ± 189
76. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [5.4.1.58]
[46] – 1 + 2i, – 1 – 2i
77. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [5.4.1.81]
[47] 5 − 12i
Reference [5.4.1.77]
[48] 1 + 3i
78. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [5.5.1.101]
[49] 5, –7
79. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Reference [5.7.1.140]
80. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
y
2
1
–4 –3
1
–1
(–1, –3)
[50]
–4
2
x
81. Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______
Period____Algebra II Regular Study Guide
Name________________________________ Date_______