# Intermediate Algebra

5^{th}Edition

ISBN10: 1259610233

ISBN13: 9781259610233

Copyright: 2018

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The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

### Program Details

# Intermediate Algebra 5e

### Reference: Review of Basic Algebraic Concepts

#### R.1 Study Skills

#### R.2 Sets of Numbers and Interval Notation

#### R.3 Operations of Real Numbers

#### R.4 Simplifying Algebraic Expressions

### Chapter 1: Linear Equations and Inequalities in One Variable

#### 1.1 Linear Equations in One Variable

Problem Recognition Exercises-Equations versus Expressions

#### 1.2 Applications of Linear Equations in One Variable

#### 1.3 Applications of Geometry and Literal Equations

#### 1.4 Linear Inequalities in One Variable

#### 1.5 Compound Inequalities

#### 1.6 Absolute Value Equations

#### 1.7 Absolute Value Inequalities

Problem Recognition Exercises-Identifying Equations and Inequalities

### Chapter 2: Linear Equations in Two Variables and Functions

#### 2.1 Linear Equations in Two Variables

#### 2.2 Slope of a Line and Rate of Change

#### 2.3 Equations of a Line

Problem Recognition Exercises-Characteristics of Linear Equations

#### 2.4 Applications of Linear Equations and Modeling

#### 2.5 Introduction to Relations

#### 2.6 Introduction to Functions

#### 2.7 Graphs of Functions

Problem Recognition Exercises-Characteristics of Relations

### Chapter 3: Systems of Linear Equations and Inequalities

#### 3.1 Solving Systems of Linear Equations by the Graphing Method

#### 3.2 Solving Systems of Linear Equations by the Substitution Method

#### 3.3 Solving Systems of Linear Equations by the Addition Method

Problem Recognition Exercises-Solving Systems of Linear Equations

#### 3.4 Applications of Systems of Linear Equations in Two Variables

#### 3.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables

#### 3.6 Systems of Linear Equations in Three Variables and Applications

#### 3.7 Solving Systems of Linear Equations by Using Matrices

### Chapter 4: Polynomials

#### 4.1 Properties of Integer Exponents and Scientific Notation

#### 4.2 Addition and Subtraction of Polynomials and Polynomials Functions

#### 4.3 Multiplication of Polynomials

#### 4.4 Division of Polynomials

Problem Recognition Exercises-Operations on Polynomials

#### 4.5 Greatest Common Factor and Factoring by Grouping

#### 4.6 Factoring Trinomials

#### 4.7 Factoring Binomials

Problem Recognition Exercises-Factoring Summary

#### 4.8 Solving Equations by Using the Zero Product Rule

### Chapter 5: Rational Expressions and Rational Equations

#### 5.1 Rational Expressions and Rational Functions

#### 5.2 Multiplication and Division of Rational Expressions

#### 5.3 Addition and Subtraction of Rational Expressions

#### 5.4 Complex Fractions

Problem Recognition Exercises-Operations on Rational Expressions

#### 5.5 Solving Rational Equations

Problem Recognition Exercises-Rational Equations versus Expressions

#### 5.6 Applications of Rational Equations and Proportions

#### Variation

### Chapter 6: Radicals and Complex Numbers

#### 6.1 Definition of an nth Root

#### 6.2 Rational Exponents

#### 6.3 Simplifying Radical Expressions

#### 6.4 Addition and Subtraction of Radicals

#### 6.5 Multiplication of Radicals

Problem Recognition Exercises-Simplifying Radical Expressions

#### 6.6 Division of Radicals and Rationalization

#### 6.7 Solving Radical Equations

#### 6.8 Complex Numbers

### Chapter 7: Quadratic Equations, Functions and Inequalities

#### 7.1 Square Root Property and Completing the Square

#### 7.2 Quadratic Formula

#### 7.3 Equations in Quadratic Form

Problem Recognition Exercises-Quadratic and Quadratic Type Equations

#### 7.4 Graphs of Quadratic Functions

#### 7.5 Vertex of a Parabola: Applications and Modeling

#### 7.6 Polynomial and Rational Inequalities

Problem Recognition Exercises-Recognizing Equations and Inequalities

### Chapter 8: Exponential and Logarithmic Functions and Applications

#### 8.1 Algebra of Functions and Composition

#### 8.2 Inverse Functions

#### 8.3 Exponential Functions

#### 8.4 Logarithmic Functions

Problem Recognition Exercises-Identifying Graphs of Functions

#### 8.5 Properties of Logarithms

#### 8.6 The Irrational Number e and Change of Base

Problem Recognition Exercises-Logarithmic and Exponential Forms

#### 8.7 Logarithmic and Exponential Equations and Applications

### Chapter 9: Conic Sections

#### 9.1 Distance Formula, Midpoint Formula, and Circles

#### 9.2 More on the Parabola

#### 9.3 The Ellipse and Hyperbola

Problem Recognition Exercises-Formulas and Conic Sections

#### 9.4 Nonlinear systems of Equations in Two Variables

#### 9.5 Nonlinear Inequalities and Systems of Inequalities

### Chapter 10: Binomial Expansions, Sequences, and Series

#### 10.1 Binomial Expansions

#### 10.2 Sequences and Series

#### 10.3 Arithmetic Sequences and Series

#### 10.4 Geometric Sequences and Series

Problem Recognition Exercises-Identifying Arithmetic and Geometric Series

### Chapter 11 (Online): Transformations, Piecewise-Defined Functions, and Probability

#### 11.1 Transformations of Graphs and Piecewise-Defined Functions

#### 11.2 Fundamentals of Counting

#### 11.3 Introduction to Probability

### Additional Topics Appendix

#### A.1 Determinants and Cramer’s Rule

# About the Author

**Julie Miller**

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.

**My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students.**

**Molly O'Neill**

Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics.

**I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students.**

**Nancy Hyde**

Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years. During this time she taught the full spectrum of courses from developmental math through differential equations. She received a bachelor of science degree in math education from Florida State University and a master’s degree in math education from Florida Atlantic University. She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom. In addition to this textbook, she has authored a graphing calculator supplement for College Algebra.

**I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.**

#### Affordability

**Find out more about our affordable course material programs.**

Reduce course material costs for your students while still providing full access to everything they need to be successful. It isn't too good to be true - it's Inclusive Access.

Learn more about Inclusive Access here.

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#### How to Access Instructor Tools for your Course

- To get started, you'll need to visit connect.mheducation.com to sign in. (If you do not have an account, you'll need to request one from your MH rep. To find your rep – visit the Find Your Rep page).
- Then, under "Find a Title," you'll search by title, author or subject.
- Select your desired title and create a course. (Note – you do not have to create assignments, just a course instance)
- Then go to your Connect course homepage.
- In the top navigation, select
**library**to access the instructor resources that accompany the title.

# Intermediate Algebra 5e

### Reference: Review of Basic Algebraic Concepts

#### R.1 Study Skills

#### R.2 Sets of Numbers and Interval Notation

#### R.3 Operations of Real Numbers

#### R.4 Simplifying Algebraic Expressions

### Chapter 1: Linear Equations and Inequalities in One Variable

#### 1.1 Linear Equations in One Variable

Problem Recognition Exercises-Equations versus Expressions

#### 1.2 Applications of Linear Equations in One Variable

#### 1.3 Applications of Geometry and Literal Equations

#### 1.4 Linear Inequalities in One Variable

#### 1.5 Compound Inequalities

#### 1.6 Absolute Value Equations

#### 1.7 Absolute Value Inequalities

Problem Recognition Exercises-Identifying Equations and Inequalities

### Chapter 2: Linear Equations in Two Variables and Functions

#### 2.1 Linear Equations in Two Variables

#### 2.2 Slope of a Line and Rate of Change

#### 2.3 Equations of a Line

Problem Recognition Exercises-Characteristics of Linear Equations

#### 2.4 Applications of Linear Equations and Modeling

#### 2.5 Introduction to Relations

#### 2.6 Introduction to Functions

#### 2.7 Graphs of Functions

Problem Recognition Exercises-Characteristics of Relations

### Chapter 3: Systems of Linear Equations and Inequalities

#### 3.1 Solving Systems of Linear Equations by the Graphing Method

#### 3.2 Solving Systems of Linear Equations by the Substitution Method

#### 3.3 Solving Systems of Linear Equations by the Addition Method

Problem Recognition Exercises-Solving Systems of Linear Equations

#### 3.4 Applications of Systems of Linear Equations in Two Variables

#### 3.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables

#### 3.6 Systems of Linear Equations in Three Variables and Applications

#### 3.7 Solving Systems of Linear Equations by Using Matrices

### Chapter 4: Polynomials

#### 4.1 Properties of Integer Exponents and Scientific Notation

#### 4.2 Addition and Subtraction of Polynomials and Polynomials Functions

#### 4.3 Multiplication of Polynomials

#### 4.4 Division of Polynomials

Problem Recognition Exercises-Operations on Polynomials

#### 4.5 Greatest Common Factor and Factoring by Grouping

#### 4.6 Factoring Trinomials

#### 4.7 Factoring Binomials

Problem Recognition Exercises-Factoring Summary

#### 4.8 Solving Equations by Using the Zero Product Rule

### Chapter 5: Rational Expressions and Rational Equations

#### 5.1 Rational Expressions and Rational Functions

#### 5.2 Multiplication and Division of Rational Expressions

#### 5.3 Addition and Subtraction of Rational Expressions

#### 5.4 Complex Fractions

Problem Recognition Exercises-Operations on Rational Expressions

#### 5.5 Solving Rational Equations

Problem Recognition Exercises-Rational Equations versus Expressions

#### 5.6 Applications of Rational Equations and Proportions

#### Variation

### Chapter 6: Radicals and Complex Numbers

#### 6.1 Definition of an nth Root

#### 6.2 Rational Exponents

#### 6.3 Simplifying Radical Expressions

#### 6.4 Addition and Subtraction of Radicals

#### 6.5 Multiplication of Radicals

Problem Recognition Exercises-Simplifying Radical Expressions

#### 6.6 Division of Radicals and Rationalization

#### 6.7 Solving Radical Equations

#### 6.8 Complex Numbers

### Chapter 7: Quadratic Equations, Functions and Inequalities

#### 7.1 Square Root Property and Completing the Square

#### 7.2 Quadratic Formula

#### 7.3 Equations in Quadratic Form

Problem Recognition Exercises-Quadratic and Quadratic Type Equations

#### 7.4 Graphs of Quadratic Functions

#### 7.5 Vertex of a Parabola: Applications and Modeling

#### 7.6 Polynomial and Rational Inequalities

Problem Recognition Exercises-Recognizing Equations and Inequalities

### Chapter 8: Exponential and Logarithmic Functions and Applications

#### 8.1 Algebra of Functions and Composition

#### 8.2 Inverse Functions

#### 8.3 Exponential Functions

#### 8.4 Logarithmic Functions

Problem Recognition Exercises-Identifying Graphs of Functions

#### 8.5 Properties of Logarithms

#### 8.6 The Irrational Number e and Change of Base

Problem Recognition Exercises-Logarithmic and Exponential Forms

#### 8.7 Logarithmic and Exponential Equations and Applications

### Chapter 9: Conic Sections

#### 9.1 Distance Formula, Midpoint Formula, and Circles

#### 9.2 More on the Parabola

#### 9.3 The Ellipse and Hyperbola

Problem Recognition Exercises-Formulas and Conic Sections

#### 9.4 Nonlinear systems of Equations in Two Variables

#### 9.5 Nonlinear Inequalities and Systems of Inequalities

### Chapter 10: Binomial Expansions, Sequences, and Series

#### 10.1 Binomial Expansions

#### 10.2 Sequences and Series

#### 10.3 Arithmetic Sequences and Series

#### 10.4 Geometric Sequences and Series

Problem Recognition Exercises-Identifying Arithmetic and Geometric Series

### Chapter 11 (Online): Transformations, Piecewise-Defined Functions, and Probability

#### 11.1 Transformations of Graphs and Piecewise-Defined Functions

#### 11.2 Fundamentals of Counting

#### 11.3 Introduction to Probability

### Additional Topics Appendix

#### A.1 Determinants and Cramer’s Rule

# About the Author

**Julie Miller**

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.

**My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students.**

**Molly O'Neill**

Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics.

**I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students.**

**Nancy Hyde**

Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years. During this time she taught the full spectrum of courses from developmental math through differential equations. She received a bachelor of science degree in math education from Florida State University and a master’s degree in math education from Florida Atlantic University. She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom. In addition to this textbook, she has authored a graphing calculator supplement for College Algebra.

**I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.**

#### Affordability

**Find out more about our affordable course material programs.**

Reduce course material costs for your students while still providing full access to everything they need to be successful. It isn't too good to be true - it's Inclusive Access.

Learn more about Inclusive Access here.

When your students still want a book but don't want to keep it, McGraw-Hill's Textbook Rental program provides students with our latest editions at our most affordable hardcover prices.

Learn more about our Textbook Rental program.

Want more information?

#### How to Access Instructor Tools for your Course

- To get started, you'll need to visit connect.mheducation.com to sign in. (If you do not have an account, you'll need to request one from your MH rep. To find your rep – visit the Find Your Rep page).
- Then, under "Find a Title," you'll search by title, author or subject.
- Select your desired title and create a course. (Note – you do not have to create assignments, just a course instance)
- Then go to your Connect course homepage.
- In the top navigation, select
**library**to access the instructor resources that accompany the title.

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