,SOLUTION MANUAL College Algebra, 12th edition
Sullivan
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, INSTRUCTOR’S
SOLUTIONS MANUAL
TIM BRITT
Jackson State Community College
COLLEGE ALGEBRA
TWELFTH EDITION
Michael Sullivan
Chicago State University
,Copyright © 2025, 2020, 2016 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. 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/.
PEARSON and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S.
and/or other countries.
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.
PPID: A103000354132
, Table of Contents
Chapter R Review
R.1 Real Numbers ............................................................................................................................ 1
R.2 Algebra Essentials ..................................................................................................................... 5
R.3 Geometry Essentials ................................................................................................................ 11
R.4 Polynomials ............................................................................................................................. 16
R.5 Factoring Polynomials ............................................................................................................ 23
R.6 Synthetic Division ................................................................................................................... 28
R.7 Rational Expressions ............................................................................................................... 30
R.8 nth Roots; Rational Exponents ................................................................................................ 40
Chapter 1 Equations and Inequalities
1.1 Linear Equations ...................................................................................................................... 50
1.2 Quadratic Equations................................................................................................................. 68
1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 86
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations................................ 92
1.5 Solving Inequalities ............................................................................................................... 116
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127
1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ...... 137
Chapter Review ............................................................................................................................ 145
Chapter Test .................................................................................................................................. 153
Chapter Projects ............................................................................................................................ 155
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................... 156
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 169
2.3 Lines ...................................................................................................................................... 183
2.4 Circles .................................................................................................................................... 201
2.5 Variation ................................................................................................................................ 215
Chapter Review ............................................................................................................................ 221
Chapter Test .................................................................................................................................. 227
Cumulative Review ...................................................................................................................... 229
Chapter Project ............................................................................................................................. 231
Chapter 3 Functions and Their Graphs
3.1 Functions................................................................................................................................ 232
3.2 The Graph of a Function ........................................................................................................ 250
3.3 Properties of Functions .......................................................................................................... 259
3.4 Library of Functions; Piecewise-defined Functions .............................................................. 276
3.5 Graphing Techniques: Transformations ................................................................................ 288
3.6 Mathematical Models: Building Functions ........................................................................... 306
Chapter Review ............................................................................................................................ 314
Chapter Test .................................................................................................................................. 321
Cumulative Review ...................................................................................................................... 324
Chapter Projects ............................................................................................................................ 328
iii
Copyright © 2025 Pearson Education, Inc.
,Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ............................................................... 330
4.2 Building Linear Functions from Data .................................................................................... 341
4.3 Quadratic Functions and Their Properties ............................................................................. 347
4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371
4.5 Inequalities Involving Quadratic Functions........................................................................... 378
Chapter Review ............................................................................................................................ 398
Chapter Test .................................................................................................................................. 406
Cumulative Review ...................................................................................................................... 408
Chapter Projects ............................................................................................................................ 411
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions ............................................................................................................ 414
5.2 Graphing Polynomial Functions; Models ............................................................................... 424
5.3 Properties of Rational Functions ........................................................................................... 440
5.4 The Graph of a Rational Function ......................................................................................... 450
5.5 Polynomial and Rational Inequalities .................................................................................... 506
5.6 The Real Zeros of a Polynomial Function ............................................................................. 527
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 558
Chapter Review ............................................................................................................................ 567
Chapter Test .................................................................................................................................. 582
Cumulative Review ...................................................................................................................... 586
Chapter Projects ............................................................................................................................ 591
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ............................................................................................................. 593
6.2 One-to-One Functions; Inverse Functions ............................................................................. 611
6.3 Exponential Functions ........................................................................................................... 634
6.4 Logarithmic Functions ........................................................................................................... 655
6.5 Properties of Logarithms ....................................................................................................... 677
6.6 Logarithmic and Exponential Equations................................................................................ 686
6.7 Financial Models ................................................................................................................... 707
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 715
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 725
Chapter Review ............................................................................................................................ 729
Chapter Test .................................................................................................................................. 742
Cumulative Review ...................................................................................................................... 746
Chapter Projects ............................................................................................................................ 749
iv
Copyright © 2025 Pearson Education, Inc.
,Chapter 7 Analytic Geometry
7.2 The Parabola .......................................................................................................................... 752
7.3 The Ellipse ............................................................................................................................. 767
7.4 The Hyperbola ....................................................................................................................... 784
Chapter Review ............................................................................................................................ 803
Chapter Test .................................................................................................................................. 807
Cumulative Review ...................................................................................................................... 810
Chapter Projects ............................................................................................................................ 812
Chapter 8 Systems of Equations and Inequalities
8.1 Systems of Linear Equations: Substitution and Elimination ................................................. 815
8.2 Systems of Linear Equations: Matrices ................................................................................. 838
8.3 Systems of Linear Equations: Determinants.......................................................................... 862
8.4 Matrix Algebra....................................................................................................................... 876
8.5 Partial Fraction Decomposition ............................................................................................. 895
8.6 Systems of Nonlinear Equations ............................................................................................ 913
8.7 Systems of Inequalities .......................................................................................................... 941
8.8 Linear Programming .............................................................................................................. 956
Chapter Review ............................................................................................................................ 970
Chapter Test .................................................................................................................................. 985
Cumulative Review ...................................................................................................................... 993
Chapter Projects ............................................................................................................................ 997
Chapter 9 Sequences; Induction; the Binomial Theorem
9.1 Sequences .............................................................................................................................. 999
9.2 Arithmetic Sequences .......................................................................................................... 1009
9.3 Geometric Sequences; Geometric Series ............................................................................. 1018
9.4 Mathematical Induction ....................................................................................................... 1030
9.5 The Binomial Theorem ........................................................................................................ 1039
Chapter Review .......................................................................................................................... 1046
Chapter Test ................................................................................................................................ 1050
Cumulative Review .................................................................................................................... 1053
Chapter Projects .......................................................................................................................... 1056
Chapter 10 Counting and Probability
10.1 Counting ............................................................................................................................ 1059
10.2 Permutations and Combinations ........................................................................................ 1062
10.3 Probability.......................................................................................................................... 1067
Chapter Review .......................................................................................................................... 1074
Chapter Test ................................................................................................................................ 1076
Cumulative Review .................................................................................................................... 1077
Chapter Projects .......................................................................................................................... 1080
Appendix Graphing Utilities
Section 1 The Viewing Rectangle ............................................................................................. 1083
Section 2 Using a Graphing Utility to Graph Equations ........................................................... 1084
Section 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry ................. 1089
Section 5 Square Screens ........................................................................................................... 1091
v
Copyright © 2025 Pearson Education, Inc.
,
, Chapter R
Review
Section R.1 16. ( A B) C
1, 3, 4,5, 9 2, 4, 6, 7,8 1,3, 4, 6
1. rational
4 1, 3, 4, 6
2. 4 5 6 3 4 30 3 31
1,3, 4, 6
3. Distributive
17. A 0, 2, 6, 7, 8
4. c
5. a 18. C 0, 2, 5, 7, 8, 9
6. b 19. A B 1, 3, 4, 5, 9 2, 4, 6, 7, 8
7. True 4 0, 1, 2, 3, 5, 6, 7, 8, 9
8. False; The Zero-Product Property states that if a
product equals 0, then at least one of the factors 20. B C 2, 4, 6, 7, 8 1, 3, 4, 6
must equal 0.
1, 2, 3, 4, 6, 7, 8 0, 5, 9
9. False; 6 is the Greatest Common Factor of 12
and 18. The Least Common Multiple is the 21. A B 0, 2, 6, 7, 8 0, 1, 3, 5, 9
smallest value that both numbers will divide
0, 1, 2, 3, 5, 6, 7, 8, 9
evenly. The LCM for 12 and 18 is 36.
10. True 22. B C 0, 1, 3, 5, 9 0, 2, 5, 7, 8, 9
0, 5, 9
11. A B 1, 3, 4,5, 9 2, 4, 6, 7,8
1, 2,3, 4, 5, 6, 7,8, 9
23. a. 2,5
12. A C 1, 3, 4,5, 9 1, 3, 4, 6 b. 6, 2,5
1, 3, 4, 5, 6, 9
13. A B 1, 3, 4,5, 9 2, 4, 6, 7,8 4
c. 1
6, , 1.333..., 2,5
2
d.
14. A C 1, 3, 4,5, 9 1, 3, 4, 6 1, 3, 4
15. ( A B) C
e. 1
6, , 1.333..., , 2,5
2
1, 3, 4,5, 9 2, 4, 6, 7,8 1,3, 4, 6 24. a. 1
1, 2,3, 4,5, 6, 7,8,9 1,3, 4, 6
b. 0,1
1, 3, 4, 6
c. 5
, 2.060606... 2.06,1.25, 0,1
3
d. 5
1
Copyright © 2025 Pearson Education, Inc.
, Chapter R: Review
e. 5
, 2.060606... 2.06,1.25, 0,1, 5
3 34. a.
35. a.
0.054
9.999
b.
b.
0.053
9.998
25. a. 1
36. a. 1.001 b. 1.000
b. 0,1 37. a. 0.429 b. 0.428
c. 1 1 1
0,1, , ,
2 3 4 38. a. 0.556 b. 0.555
d. None 39. a. 34.733 b. 34.733
e. 1 1 1
0,1, , ,
2 3 4 40. a. 16.200
41. 3 2 5
b. 16.200
26. a. None
42. 5 2 10
b. 1
43. x 2 3 4
c. 1.3, 1.2, 1.1, 1
44. 3 y 2 2
d. None
e. 1.3, 1.2, 1.1, 1 45. 3 y 1 2
46. 2 x 4 6
27. a. None
b. None 47. x 2 6
c. None
48. 2 y 6
d. 2, , 2 1,
1
2 49.
x
6
2
e. 2, , 2 1,
1
2 50.
2
6
x
28. a. None
b. None 51. 9 4 2 5 2 7
c. 1
2
10.3
52. 6 4 3 2 3 5
53. 6 4 3 6 12 6
d. 2, 2 54. 8 4 2 8 8 0
e. 1
2, 2, 10.3
2 55. 18 5 2 18 10 8
56. 100 10 2 100 20 80
29. a. 18.953 b. 18.952
1 12 1 13
30. a. 25.861 b. 25.861 57. 4
3 3 3
31. a. 28.653 b. 28.653
1 4 1 3
58. 2
32. a. 99.052 b. 99.052 2 2 2
33. a. 0.063 b. 0.062
2
Copyright © 2025 Pearson Education, Inc.
Sullivan
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, INSTRUCTOR’S
SOLUTIONS MANUAL
TIM BRITT
Jackson State Community College
COLLEGE ALGEBRA
TWELFTH EDITION
Michael Sullivan
Chicago State University
,Copyright © 2025, 2020, 2016 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. 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/.
PEARSON and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S.
and/or other countries.
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.
PPID: A103000354132
, Table of Contents
Chapter R Review
R.1 Real Numbers ............................................................................................................................ 1
R.2 Algebra Essentials ..................................................................................................................... 5
R.3 Geometry Essentials ................................................................................................................ 11
R.4 Polynomials ............................................................................................................................. 16
R.5 Factoring Polynomials ............................................................................................................ 23
R.6 Synthetic Division ................................................................................................................... 28
R.7 Rational Expressions ............................................................................................................... 30
R.8 nth Roots; Rational Exponents ................................................................................................ 40
Chapter 1 Equations and Inequalities
1.1 Linear Equations ...................................................................................................................... 50
1.2 Quadratic Equations................................................................................................................. 68
1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 86
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations................................ 92
1.5 Solving Inequalities ............................................................................................................... 116
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127
1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ...... 137
Chapter Review ............................................................................................................................ 145
Chapter Test .................................................................................................................................. 153
Chapter Projects ............................................................................................................................ 155
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................... 156
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 169
2.3 Lines ...................................................................................................................................... 183
2.4 Circles .................................................................................................................................... 201
2.5 Variation ................................................................................................................................ 215
Chapter Review ............................................................................................................................ 221
Chapter Test .................................................................................................................................. 227
Cumulative Review ...................................................................................................................... 229
Chapter Project ............................................................................................................................. 231
Chapter 3 Functions and Their Graphs
3.1 Functions................................................................................................................................ 232
3.2 The Graph of a Function ........................................................................................................ 250
3.3 Properties of Functions .......................................................................................................... 259
3.4 Library of Functions; Piecewise-defined Functions .............................................................. 276
3.5 Graphing Techniques: Transformations ................................................................................ 288
3.6 Mathematical Models: Building Functions ........................................................................... 306
Chapter Review ............................................................................................................................ 314
Chapter Test .................................................................................................................................. 321
Cumulative Review ...................................................................................................................... 324
Chapter Projects ............................................................................................................................ 328
iii
Copyright © 2025 Pearson Education, Inc.
,Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ............................................................... 330
4.2 Building Linear Functions from Data .................................................................................... 341
4.3 Quadratic Functions and Their Properties ............................................................................. 347
4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371
4.5 Inequalities Involving Quadratic Functions........................................................................... 378
Chapter Review ............................................................................................................................ 398
Chapter Test .................................................................................................................................. 406
Cumulative Review ...................................................................................................................... 408
Chapter Projects ............................................................................................................................ 411
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions ............................................................................................................ 414
5.2 Graphing Polynomial Functions; Models ............................................................................... 424
5.3 Properties of Rational Functions ........................................................................................... 440
5.4 The Graph of a Rational Function ......................................................................................... 450
5.5 Polynomial and Rational Inequalities .................................................................................... 506
5.6 The Real Zeros of a Polynomial Function ............................................................................. 527
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 558
Chapter Review ............................................................................................................................ 567
Chapter Test .................................................................................................................................. 582
Cumulative Review ...................................................................................................................... 586
Chapter Projects ............................................................................................................................ 591
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ............................................................................................................. 593
6.2 One-to-One Functions; Inverse Functions ............................................................................. 611
6.3 Exponential Functions ........................................................................................................... 634
6.4 Logarithmic Functions ........................................................................................................... 655
6.5 Properties of Logarithms ....................................................................................................... 677
6.6 Logarithmic and Exponential Equations................................................................................ 686
6.7 Financial Models ................................................................................................................... 707
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 715
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 725
Chapter Review ............................................................................................................................ 729
Chapter Test .................................................................................................................................. 742
Cumulative Review ...................................................................................................................... 746
Chapter Projects ............................................................................................................................ 749
iv
Copyright © 2025 Pearson Education, Inc.
,Chapter 7 Analytic Geometry
7.2 The Parabola .......................................................................................................................... 752
7.3 The Ellipse ............................................................................................................................. 767
7.4 The Hyperbola ....................................................................................................................... 784
Chapter Review ............................................................................................................................ 803
Chapter Test .................................................................................................................................. 807
Cumulative Review ...................................................................................................................... 810
Chapter Projects ............................................................................................................................ 812
Chapter 8 Systems of Equations and Inequalities
8.1 Systems of Linear Equations: Substitution and Elimination ................................................. 815
8.2 Systems of Linear Equations: Matrices ................................................................................. 838
8.3 Systems of Linear Equations: Determinants.......................................................................... 862
8.4 Matrix Algebra....................................................................................................................... 876
8.5 Partial Fraction Decomposition ............................................................................................. 895
8.6 Systems of Nonlinear Equations ............................................................................................ 913
8.7 Systems of Inequalities .......................................................................................................... 941
8.8 Linear Programming .............................................................................................................. 956
Chapter Review ............................................................................................................................ 970
Chapter Test .................................................................................................................................. 985
Cumulative Review ...................................................................................................................... 993
Chapter Projects ............................................................................................................................ 997
Chapter 9 Sequences; Induction; the Binomial Theorem
9.1 Sequences .............................................................................................................................. 999
9.2 Arithmetic Sequences .......................................................................................................... 1009
9.3 Geometric Sequences; Geometric Series ............................................................................. 1018
9.4 Mathematical Induction ....................................................................................................... 1030
9.5 The Binomial Theorem ........................................................................................................ 1039
Chapter Review .......................................................................................................................... 1046
Chapter Test ................................................................................................................................ 1050
Cumulative Review .................................................................................................................... 1053
Chapter Projects .......................................................................................................................... 1056
Chapter 10 Counting and Probability
10.1 Counting ............................................................................................................................ 1059
10.2 Permutations and Combinations ........................................................................................ 1062
10.3 Probability.......................................................................................................................... 1067
Chapter Review .......................................................................................................................... 1074
Chapter Test ................................................................................................................................ 1076
Cumulative Review .................................................................................................................... 1077
Chapter Projects .......................................................................................................................... 1080
Appendix Graphing Utilities
Section 1 The Viewing Rectangle ............................................................................................. 1083
Section 2 Using a Graphing Utility to Graph Equations ........................................................... 1084
Section 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry ................. 1089
Section 5 Square Screens ........................................................................................................... 1091
v
Copyright © 2025 Pearson Education, Inc.
,
, Chapter R
Review
Section R.1 16. ( A B) C
1, 3, 4,5, 9 2, 4, 6, 7,8 1,3, 4, 6
1. rational
4 1, 3, 4, 6
2. 4 5 6 3 4 30 3 31
1,3, 4, 6
3. Distributive
17. A 0, 2, 6, 7, 8
4. c
5. a 18. C 0, 2, 5, 7, 8, 9
6. b 19. A B 1, 3, 4, 5, 9 2, 4, 6, 7, 8
7. True 4 0, 1, 2, 3, 5, 6, 7, 8, 9
8. False; The Zero-Product Property states that if a
product equals 0, then at least one of the factors 20. B C 2, 4, 6, 7, 8 1, 3, 4, 6
must equal 0.
1, 2, 3, 4, 6, 7, 8 0, 5, 9
9. False; 6 is the Greatest Common Factor of 12
and 18. The Least Common Multiple is the 21. A B 0, 2, 6, 7, 8 0, 1, 3, 5, 9
smallest value that both numbers will divide
0, 1, 2, 3, 5, 6, 7, 8, 9
evenly. The LCM for 12 and 18 is 36.
10. True 22. B C 0, 1, 3, 5, 9 0, 2, 5, 7, 8, 9
0, 5, 9
11. A B 1, 3, 4,5, 9 2, 4, 6, 7,8
1, 2,3, 4, 5, 6, 7,8, 9
23. a. 2,5
12. A C 1, 3, 4,5, 9 1, 3, 4, 6 b. 6, 2,5
1, 3, 4, 5, 6, 9
13. A B 1, 3, 4,5, 9 2, 4, 6, 7,8 4
c. 1
6, , 1.333..., 2,5
2
d.
14. A C 1, 3, 4,5, 9 1, 3, 4, 6 1, 3, 4
15. ( A B) C
e. 1
6, , 1.333..., , 2,5
2
1, 3, 4,5, 9 2, 4, 6, 7,8 1,3, 4, 6 24. a. 1
1, 2,3, 4,5, 6, 7,8,9 1,3, 4, 6
b. 0,1
1, 3, 4, 6
c. 5
, 2.060606... 2.06,1.25, 0,1
3
d. 5
1
Copyright © 2025 Pearson Education, Inc.
, Chapter R: Review
e. 5
, 2.060606... 2.06,1.25, 0,1, 5
3 34. a.
35. a.
0.054
9.999
b.
b.
0.053
9.998
25. a. 1
36. a. 1.001 b. 1.000
b. 0,1 37. a. 0.429 b. 0.428
c. 1 1 1
0,1, , ,
2 3 4 38. a. 0.556 b. 0.555
d. None 39. a. 34.733 b. 34.733
e. 1 1 1
0,1, , ,
2 3 4 40. a. 16.200
41. 3 2 5
b. 16.200
26. a. None
42. 5 2 10
b. 1
43. x 2 3 4
c. 1.3, 1.2, 1.1, 1
44. 3 y 2 2
d. None
e. 1.3, 1.2, 1.1, 1 45. 3 y 1 2
46. 2 x 4 6
27. a. None
b. None 47. x 2 6
c. None
48. 2 y 6
d. 2, , 2 1,
1
2 49.
x
6
2
e. 2, , 2 1,
1
2 50.
2
6
x
28. a. None
b. None 51. 9 4 2 5 2 7
c. 1
2
10.3
52. 6 4 3 2 3 5
53. 6 4 3 6 12 6
d. 2, 2 54. 8 4 2 8 8 0
e. 1
2, 2, 10.3
2 55. 18 5 2 18 10 8
56. 100 10 2 100 20 80
29. a. 18.953 b. 18.952
1 12 1 13
30. a. 25.861 b. 25.861 57. 4
3 3 3
31. a. 28.653 b. 28.653
1 4 1 3
58. 2
32. a. 99.052 b. 99.052 2 2 2
33. a. 0.063 b. 0.062
2
Copyright © 2025 Pearson Education, Inc.
