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• Classic-Fiction

7. b(3, 2) = 2

8. b(2, 3) = 5

9. b(1, 1) = 6

10. b(2, 1) = 0

13.2

13.3

13.4

1. 2 × 3

2. Not possible

3. Not possible

4. 3 × 2

5. 2 × 2

6. 3 × 3

7. Not possible

8. Not possible

9. 2 × 1

10. Not possible

11. 1 × 1

12. 3 × 3

13. Not possible

14. [10]

15. [−5]

16. Cannot be multiplied

17. [48 9]

13.5

1. −4

2. −22

3. Not possible

4. 71

5. Not possible

6. 1

7. 7

8. 0

9. 3

10. 5

11. 0

12. 380

13. −145

13.6

1. Inverses

2. Not inverses

3. Not inverses

4. Inverses

5. Inverses

6. Inverses

7. Not inverses

8. Yes

9. No, not square

10. Yes

11. No, determinant = 0

12. Yes

13. Yes

14. Yes

13.7

1. x = 6, y = −1

2. x = 4, y = 1

3. x = −0.5, y = 1.3

4. x = 5, y = 9, z = − 3

5. x = 4, y = −7, z = 3

6. x= −2, y = 3, z = −1

13.8

1. x = 6, y = −1

2. x = 4, y = 1

3. x = −0.5, y = 1.3

4. x = 3, y = 1

5. x = 7, y = −3

6. x = −5, y = 2

7. x = 5, y = 9, z = −3

8. x = 4, y = −7, z = 3

9. x = −2, y = 3, z = −1

10. x = 4, y = −2, z = 3

13.9

6. Dependent

7. Inconsistent

8. Consistent

9. Inconsistent

10. Dependent

Table of Contents

Cover Page

Practice Makes Perfect Algebra

Copyright Page

Contents

Introduction

1 Arithmetic to algebra

The real numbers

Properties of real numbers

Integers

Order of operations

Using variables

Evaluating expressions

2 Linear equations

Addition and subtraction equations

Multiplication and division equations

Two-step equations

Variables on both sides

Simplifying before solving

Absolute value equations

Mixture problems: coffee, coins, cars, and chemicals

3 Linear inequalities

Simple inequalities

Compound inequalities

Absolute value inequalities

4 Coordinate graphing

The coordinate plane

Distance

Midpoints

Slope and rate of change

Graphing linear equations

Vertical and horizontal lines

Graphing linear inequalities

Graphing absolute value equations

Writing linear equations

Parallel and perpendicular lines

5 Systems of linear equations and inequalities

Graphing systems of equations

Graphing systems of inequalities

Solving systems of equations by substitution

Solving systems of equations by combination

Combinations with multiplication

Dependent and inconsistent systems

6 Powers and polynomials

Rules for exponents

More rules

Monomials and polynomials

Adding and subtracting polynomials

Multiplying polynomials

Dividing polynomials

7 Factoring

Greatest common monomial factor

Factoring x2+bx+c

Factoring ax2+bx+c

Special factoring patterns

8 Radicals

Simplifying radical expressions

Adding and subtracting radicals

Solving radical equations

Graphing square root equations

9 Quadratic equations and their graphs

Solving by square roots

Completing the square

The quadratic formula

Solving by factoring

Graphing quadratic functions

10 Proportion and variation

Using ratios and extended ratios

Solving proportions

Variation

Joint and combined variation

11 Rational equations and their graphs

Simplifying rational expressions

Multiplying rational expressions

Dividing rational expressions

Adding and subtracting rational expressions

Complex fractions

Solving rational equations

Graphing rational functions

Work problems

12 Exponential growth and decay

Compound interest

Exponential growth and decay

Graphing the exponential functions

13 Matrix algebra

Rows and columns

Addition and subtraction

Scalar multiplication

Matrix multiplication

Determinants

Inverses

Solving systems with matrices

Answers