INSTRUCTOR’S
SOLUTIONS MANUAL
JUDITH A. PENNA
ALGEBRA AND
T RIGONOMETRY :
GRAPHS AND MODELS
SEVENTH EDITION
Bittinger/Beecher/Penna/Johnson
,Copyright © 2025 by Pearson Education, Inc. or its affiliates, 221 River Street, Hoboken, NJ 07030. All Rights
Reserved. This publication is protected by copyright, and permission should be obtained from the publisher
prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means,
electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request
forms, and the appropriate contacts within the Pearson Education Global Rights and Permissions department,
please visit www.pearsoned.com/permissions/.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are
the property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade
dress are for demonstrative or descriptive purposes only. Such references are not intended to imply any
sponsorship, endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or
any relationship between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or
distributors.
Pearson Product ID: A103000345958
, Contents
Just-in-Time Review …………………………………………………………...1
Chapter 1 ……………………………………………………………………...13
Chapter 2 ……………………………………………………………………...71
Chapter 3 ………………………………………………………..……..…….129
Chapter 4 …………………………………………………………………….189
Chapter 5 …………………………………………………………………….279
Chapter 6 …………………………………………………………………….341
Chapter 7 …………………………………………………………………….399
Chapter 8 …………………………………………………………………….445
Chapter 9 …………………………………………………………………….499
Chapter 10 …………………………………………………….…….……….601
Chapter 11 ………………………………………………………..………….687
iii
, Just-in-Time Review
√ √ √ √
4. 6 = 6, so it is true that 6 ≤ 6.
1. Real Numbers
5. −30 is to the left of −25 on the number line, so it i
that −30 > −25.
2 √ 8 4 16 5 25 16
1. Rational numbers: , 6, −2.45, 18.4, −11, 3 27, − , 6. − =− and − = − ; − is to the right of
√ 3 7 5 20 4 20 20
0, 16 4 5
so it is true that − > − .
2 8 5 4
2. Rational numbers but not integers: , −2.45, 18.4, −
3 7
√ √ √ √
3. Irrational numbers: 3, 6 26, 7.151551555 . . . , − 35, 5 3 4. Absolute Value
(Although there is a pattern in 7.151551555 . . . , there is
no repeating block of digits.)
√ √ 1. | − 98| = 98 (|a| = −a, if a < 0.)
4. Integers: 6, −11, 3 27, 0, 16
2. |0| = 0 (|a| = a, if a ≥ 0.)
√ √
5. Whole numbers: 6, 3 27, 0, 16
3. |4.7| = 4.7 (|a| = a, if a ≥ 0.)
6. Real numbers: All of them
2 2
4. − = (|a| = −a, if a < 0.)
3 3
2. Properties of Real Numbers 5. | − 7 − 13| = | − 20| = 20, or
|13 − (−7)| = |13 + 7| = |20| = 20
1. −24 + 24 = 0 illustrates the additive inverse property. 6. |2 − 14.6| = | − 12.6| = 12.6, or
2. 7(xy) = (7x)y illustrates the associative property of mul- |14.6 − 2| = |12.6| = 12.6
tiplication.
7. | − 39 − (−28)| = | − 39 + 28| = | − 11| = 11, or
3. 9(r − s) = 9r − 9s illustrates a distributive property. | − 28 − (−39)| = | − 28 + 39| = |11| = 11
4. 11 + z = z + 11 illustrates the commutative property of 3 15 6 15 21 21
addition. 8. − − = − − = − = , or
4 8 8 8 8 8
5. −20 · 1 = −20 illustrates the multiplicative identity prop- 15
− − 3 = 15 + 6 = 21 = 21
erty. 8 4 8 8 8 8
6. 5(x + y) = (x + y)5 illustrates the commutative property
of multiplication.
5. Operations Using Fraction Notation
7. q + 0 = q illustrates the additive identity property.
1 1 3 1 4 3 5 4 15 4 + 15 19
8. 75 · = 1 illustrates the multiplicative inverse property. 1. + = · + · = + = =
75 5 4 5 4 4 5 20 20 20 20
9. (x+y)+w = x+(y+w) illustrates the associative property 3 1 3 1 5 3 5 8 4·2 4
2. + = + · = + = = =
of addition. 10 2 10 2 5 10 10 10 5·2 5
10. 8(a + b) = 8a + 8b illustrates a distributive property. 3 5 3 3 5 4 9 20 29
3. + = · + · = + =
8 6 8 3 6 4 24 24 24
5 5 9 5 27 32
4. +3= +3· = + =
3. Order on the Number Line 9 9 9 9 9 9
7 3 7 3 2 7 6 1
5. − = − · = − =
1. 9 is to the right of −9 on the number line, so it is false 8 4 8 4 2 8 8 8
that 9 < −9. 10 2 10 3 2 11 30 22 8
6. − = · − · = − =
2. −10 is to the left of −1 on the number line, so it is true 11 3 11 3 3 11 33 33 33
that −10 ≤ −1. 3 7 3 14 3 11
7. 2 − =2· − = − =
√ √ √ 7 7 7 7 7 7
3. −5 = − 25, and − 26 is to the left of√− 25, or −5, on
the number line. Thus it is true that − 26 < −5. 5 3 5·3 15 5·3 3
8. · = = = =
8 10 8 · 10 80 5 · 16 16
Copyright
c 2025 Pearson Education, Inc.
SOLUTIONS MANUAL
JUDITH A. PENNA
ALGEBRA AND
T RIGONOMETRY :
GRAPHS AND MODELS
SEVENTH EDITION
Bittinger/Beecher/Penna/Johnson
,Copyright © 2025 by Pearson Education, Inc. or its affiliates, 221 River Street, Hoboken, NJ 07030. All Rights
Reserved. This publication is protected by copyright, and permission should be obtained from the publisher
prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means,
electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request
forms, and the appropriate contacts within the Pearson Education Global Rights and Permissions department,
please visit www.pearsoned.com/permissions/.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are
the property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade
dress are for demonstrative or descriptive purposes only. Such references are not intended to imply any
sponsorship, endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or
any relationship between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or
distributors.
Pearson Product ID: A103000345958
, Contents
Just-in-Time Review …………………………………………………………...1
Chapter 1 ……………………………………………………………………...13
Chapter 2 ……………………………………………………………………...71
Chapter 3 ………………………………………………………..……..…….129
Chapter 4 …………………………………………………………………….189
Chapter 5 …………………………………………………………………….279
Chapter 6 …………………………………………………………………….341
Chapter 7 …………………………………………………………………….399
Chapter 8 …………………………………………………………………….445
Chapter 9 …………………………………………………………………….499
Chapter 10 …………………………………………………….…….……….601
Chapter 11 ………………………………………………………..………….687
iii
, Just-in-Time Review
√ √ √ √
4. 6 = 6, so it is true that 6 ≤ 6.
1. Real Numbers
5. −30 is to the left of −25 on the number line, so it i
that −30 > −25.
2 √ 8 4 16 5 25 16
1. Rational numbers: , 6, −2.45, 18.4, −11, 3 27, − , 6. − =− and − = − ; − is to the right of
√ 3 7 5 20 4 20 20
0, 16 4 5
so it is true that − > − .
2 8 5 4
2. Rational numbers but not integers: , −2.45, 18.4, −
3 7
√ √ √ √
3. Irrational numbers: 3, 6 26, 7.151551555 . . . , − 35, 5 3 4. Absolute Value
(Although there is a pattern in 7.151551555 . . . , there is
no repeating block of digits.)
√ √ 1. | − 98| = 98 (|a| = −a, if a < 0.)
4. Integers: 6, −11, 3 27, 0, 16
2. |0| = 0 (|a| = a, if a ≥ 0.)
√ √
5. Whole numbers: 6, 3 27, 0, 16
3. |4.7| = 4.7 (|a| = a, if a ≥ 0.)
6. Real numbers: All of them
2 2
4. − = (|a| = −a, if a < 0.)
3 3
2. Properties of Real Numbers 5. | − 7 − 13| = | − 20| = 20, or
|13 − (−7)| = |13 + 7| = |20| = 20
1. −24 + 24 = 0 illustrates the additive inverse property. 6. |2 − 14.6| = | − 12.6| = 12.6, or
2. 7(xy) = (7x)y illustrates the associative property of mul- |14.6 − 2| = |12.6| = 12.6
tiplication.
7. | − 39 − (−28)| = | − 39 + 28| = | − 11| = 11, or
3. 9(r − s) = 9r − 9s illustrates a distributive property. | − 28 − (−39)| = | − 28 + 39| = |11| = 11
4. 11 + z = z + 11 illustrates the commutative property of 3 15 6 15 21 21
addition. 8. − − = − − = − = , or
4 8 8 8 8 8
5. −20 · 1 = −20 illustrates the multiplicative identity prop- 15
− − 3 = 15 + 6 = 21 = 21
erty. 8 4 8 8 8 8
6. 5(x + y) = (x + y)5 illustrates the commutative property
of multiplication.
5. Operations Using Fraction Notation
7. q + 0 = q illustrates the additive identity property.
1 1 3 1 4 3 5 4 15 4 + 15 19
8. 75 · = 1 illustrates the multiplicative inverse property. 1. + = · + · = + = =
75 5 4 5 4 4 5 20 20 20 20
9. (x+y)+w = x+(y+w) illustrates the associative property 3 1 3 1 5 3 5 8 4·2 4
2. + = + · = + = = =
of addition. 10 2 10 2 5 10 10 10 5·2 5
10. 8(a + b) = 8a + 8b illustrates a distributive property. 3 5 3 3 5 4 9 20 29
3. + = · + · = + =
8 6 8 3 6 4 24 24 24
5 5 9 5 27 32
4. +3= +3· = + =
3. Order on the Number Line 9 9 9 9 9 9
7 3 7 3 2 7 6 1
5. − = − · = − =
1. 9 is to the right of −9 on the number line, so it is false 8 4 8 4 2 8 8 8
that 9 < −9. 10 2 10 3 2 11 30 22 8
6. − = · − · = − =
2. −10 is to the left of −1 on the number line, so it is true 11 3 11 3 3 11 33 33 33
that −10 ≤ −1. 3 7 3 14 3 11
7. 2 − =2· − = − =
√ √ √ 7 7 7 7 7 7
3. −5 = − 25, and − 26 is to the left of√− 25, or −5, on
the number line. Thus it is true that − 26 < −5. 5 3 5·3 15 5·3 3
8. · = = = =
8 10 8 · 10 80 5 · 16 16
Copyright
c 2025 Pearson Education, Inc.
