Algebra and Trigonometry – 7th Edition
ST
SOLUTIONS
UV
IA
MANUAL
_A
PP
Robert F. Blitzer
RO
Comprehensive Solutions Manual for Instructors
VE
and Students
D?
© Robert F. Blitzer
All rights reserved. Reproduction or distribution without permission is prohibited.
??
©STUDYSTREAM
, TABLE OF CONTENTS for INSTRUCTOR SOLUTIONS
ALGEBRA AND TRIGONOMETRY 7E
ST
Chapter P Fundamental Concepts of Algebra ............................................................................. 1
UV
Chapter 1 Equations and Inequalities ........................................................................................ 75
Chapter 2 Functions and Graphs ............................................................................................. 215
Chapter 3 Polynomial and Rational Functions ........................................................................ 359
IA
Chapter 4 Exponential and Logarithmic Functions ................................................................. 515
Chapter 5 Trigonometric Functions ........................................................................................ 593
Chapter 6 Analytic Trigonometry ........................................................................................... 835
_A
Chapter 7 Additional Topics in Trigonometry ........................................................................ 969
Chapter 8 Systems of Equations and Inequalities ................................................................. 1117
Chapter 9 Matrices and Determinants ................................................................................... 1259
PP
Chapter 10 Conic Sections and Analytic Geometry ................................................................ 1377
Chapter 11 Sequences, Induction, and Probability.................................................................. 1497
RO
VE
D?
??
iii
, Chapter P
Fundamental Concepts of Algebra
Section P.1 6. a. 1− 2
ST
Check Point Exercises Because 2 ≈ 1.4, the number inside the
absolute value bars is negative. The absolute
1. 8 + 6( x − 3)2 = 8 + 6(13 − 3)2 value of x when x < 0 is –x. Thus,
= 8 + 6(10) 2 (
1 − 2 = − 1 − 2 = 2 −1 )
UV
= 8 + 6(100)
= 8 + 600 b. π −3
= 608 Because π ≈ 3.14, the number inside the
absolute value bars is positive. The absolute
2. a. Since 2016 is 16 years after 2000, substitute 16 value of a positive number is the number itself.
for x. Thus,
IA
T = − x 2 + 361x + 3193 π − 3 = π − 3.
= −(16) 2 + 361(16) + 3193
= 8713 x
c.
The average cost of tuition and fees at public
_A
x
U.S. colleges for the school year ending in Because x > 0, x = x.
2016 was $8713.
x x
b. The formula underestimates the actual answer Thus, = =1
x x
by $65.
PP
7. −4 − (5) = −9 = 9
3. The elements common to {3, 4, 5, 6, 7} and
{3, 7, 8, 9} are 3 and 7. The distance between –4 and 5 is 9.
{3, 4,5, 6, 7} ∩ {3, 7,8,9} = {3, 7}
8. 7(4 x 2 + 3x) + 2(5 x 2 + x)
4. The union is the set containing all the elements of = 7(4 x 2 + 3 x) + 2(5 x 2 + x)
either set.
RO
{3, 4,5, 6, 7} ∪ {3, 7,8,9} = {3, 4,5, 6, 7,8,9} = 28 x 2 + 21x + 10 x 2 + 2 x
= 38 x 2 + 23 x
π ½
5. ® −9, − 1.3, 0, 0.3, , 9, 10 ¾
9. 6 + 4[7 − ( x − 2)]
¯ 2 ¿
= 6 + 4[7 − x + 2)]
a. Natural numbers: 9 because 9 =3 = 6 + 4[9 − x]
VE
= 6 + 36 − 4 x
b. Whole numbers: 0, 9 = 42 − 4 x
c. Integers: −9, 0, 9
Concept and Vocabulary Check P.1
D?
d. Rational numbers: −9, − 1.3, 0, 0.3, 9
C1. expression
π C2. b to the nth power; base; exponent
e. Irrational numbers: , 10
2
C3. formula; modeling; models
??
π
f. Real numbers: −9, − 1.3, 0, 0.3, , 9, 10 C4. intersection; A ∩ B
2
C5. union; A ∪ B
Copyright © 2022 Pearson Education, Inc 1
, Chapter P Fundamental Concepts of Algebra
C6. natural 10.
3
6 + 5 (8 − 6) = 6 + 5 ( 2)
3
C7. whole = 6 + 5 (8)
= 6 + 40 = 46
ST
C8. integers
C9. rational 11. 82 − 3(8 − 2) = 64 − 3(6)
= 64 − 18 = 46
C10. irrational
12. 82 − 4 ( 8 − 3) = 64 − 4 ( 5 ) = 64 − 20 = 44
UV
C11. rational; irrational
C12. absolute value; x, x 5( x + 2) 5(10 + 2)
13. =
2 x − 14 2(10) − 14
C13. b + a ; ba 5(12)
=
6
C14. a + (b + c) ; ( ab)c
IA
= 5⋅2
C15. ab + ac = 10
C16. 0; inverse; 0; identity 7( x − 3) 7(9 − 3) 7(6)
14. = = = 7 ⋅ 3 = 21
2 x − 16 2(9) − 16 2
_A
C17. inverse; 1; identity
2x + 3y
C18. simplified 15. ; x = −2, y = 4
x +1
C19. a 2 ( −2 ) + 3 ( 4 ) −4 + 12 8
= = = = −8
−2 + 1 −1 −1
PP
Exercise Set P.1
2x + y
16. ; x = −2 and y = 4
1. 7 + 5(10) = 7 + 50 = 57 xy − 2 x
2 ( −2 ) + 4 −4 + 4 0
= = =0
2. 8 + 6 ( 5 ) = 8 + 30 = 38 ( −2 )( 4 ) − 2 ( −2 )
RO
−8 + 4 4
3. 6(3) − 8 = 18 − 8 = 10 5 5
17. C= (50 − 32) = (18) = 10
9 9
4. 8 ( 3) − 4 = 24 − 4 = 20 50°F is equivalent to 10°C.
5. 82 + 3(8) = 64 + 24 = 88 5 5 5
VE
18. C= ( F − 32) = (86 − 32) = (54) = 30
9 9 9
6. 62 + 5 ( 6 ) = 36 + 30 = 66 86°F is equivalent to 30°C.
19. h = 4 + 60t − 16t 2 = 4 + 60(2) − 16(2) 2
7. 7 2 − 6(7) + 3 = 49 − 42 + 3 = 7 + 3 = 10
= 4 + 120 − 16(4) = 4 + 120 − 64
D?
8. 8 − 7 ( 8 ) + 4 = 64 − 56 + 4 = 8 + 4 = 12
2 = 124 − 64 = 60
Two seconds after it is kicked, the ball’s height is
60 feet.
9. 4 + 5(9 − 7)3 = 4 + 5(2)3
= 4 + 5(8) = 4 + 40 = 44
??
2 Copyright © 2022 Pearson Education, Inc
ST
SOLUTIONS
UV
IA
MANUAL
_A
PP
Robert F. Blitzer
RO
Comprehensive Solutions Manual for Instructors
VE
and Students
D?
© Robert F. Blitzer
All rights reserved. Reproduction or distribution without permission is prohibited.
??
©STUDYSTREAM
, TABLE OF CONTENTS for INSTRUCTOR SOLUTIONS
ALGEBRA AND TRIGONOMETRY 7E
ST
Chapter P Fundamental Concepts of Algebra ............................................................................. 1
UV
Chapter 1 Equations and Inequalities ........................................................................................ 75
Chapter 2 Functions and Graphs ............................................................................................. 215
Chapter 3 Polynomial and Rational Functions ........................................................................ 359
IA
Chapter 4 Exponential and Logarithmic Functions ................................................................. 515
Chapter 5 Trigonometric Functions ........................................................................................ 593
Chapter 6 Analytic Trigonometry ........................................................................................... 835
_A
Chapter 7 Additional Topics in Trigonometry ........................................................................ 969
Chapter 8 Systems of Equations and Inequalities ................................................................. 1117
Chapter 9 Matrices and Determinants ................................................................................... 1259
PP
Chapter 10 Conic Sections and Analytic Geometry ................................................................ 1377
Chapter 11 Sequences, Induction, and Probability.................................................................. 1497
RO
VE
D?
??
iii
, Chapter P
Fundamental Concepts of Algebra
Section P.1 6. a. 1− 2
ST
Check Point Exercises Because 2 ≈ 1.4, the number inside the
absolute value bars is negative. The absolute
1. 8 + 6( x − 3)2 = 8 + 6(13 − 3)2 value of x when x < 0 is –x. Thus,
= 8 + 6(10) 2 (
1 − 2 = − 1 − 2 = 2 −1 )
UV
= 8 + 6(100)
= 8 + 600 b. π −3
= 608 Because π ≈ 3.14, the number inside the
absolute value bars is positive. The absolute
2. a. Since 2016 is 16 years after 2000, substitute 16 value of a positive number is the number itself.
for x. Thus,
IA
T = − x 2 + 361x + 3193 π − 3 = π − 3.
= −(16) 2 + 361(16) + 3193
= 8713 x
c.
The average cost of tuition and fees at public
_A
x
U.S. colleges for the school year ending in Because x > 0, x = x.
2016 was $8713.
x x
b. The formula underestimates the actual answer Thus, = =1
x x
by $65.
PP
7. −4 − (5) = −9 = 9
3. The elements common to {3, 4, 5, 6, 7} and
{3, 7, 8, 9} are 3 and 7. The distance between –4 and 5 is 9.
{3, 4,5, 6, 7} ∩ {3, 7,8,9} = {3, 7}
8. 7(4 x 2 + 3x) + 2(5 x 2 + x)
4. The union is the set containing all the elements of = 7(4 x 2 + 3 x) + 2(5 x 2 + x)
either set.
RO
{3, 4,5, 6, 7} ∪ {3, 7,8,9} = {3, 4,5, 6, 7,8,9} = 28 x 2 + 21x + 10 x 2 + 2 x
= 38 x 2 + 23 x
π ½
5. ® −9, − 1.3, 0, 0.3, , 9, 10 ¾
9. 6 + 4[7 − ( x − 2)]
¯ 2 ¿
= 6 + 4[7 − x + 2)]
a. Natural numbers: 9 because 9 =3 = 6 + 4[9 − x]
VE
= 6 + 36 − 4 x
b. Whole numbers: 0, 9 = 42 − 4 x
c. Integers: −9, 0, 9
Concept and Vocabulary Check P.1
D?
d. Rational numbers: −9, − 1.3, 0, 0.3, 9
C1. expression
π C2. b to the nth power; base; exponent
e. Irrational numbers: , 10
2
C3. formula; modeling; models
??
π
f. Real numbers: −9, − 1.3, 0, 0.3, , 9, 10 C4. intersection; A ∩ B
2
C5. union; A ∪ B
Copyright © 2022 Pearson Education, Inc 1
, Chapter P Fundamental Concepts of Algebra
C6. natural 10.
3
6 + 5 (8 − 6) = 6 + 5 ( 2)
3
C7. whole = 6 + 5 (8)
= 6 + 40 = 46
ST
C8. integers
C9. rational 11. 82 − 3(8 − 2) = 64 − 3(6)
= 64 − 18 = 46
C10. irrational
12. 82 − 4 ( 8 − 3) = 64 − 4 ( 5 ) = 64 − 20 = 44
UV
C11. rational; irrational
C12. absolute value; x, x 5( x + 2) 5(10 + 2)
13. =
2 x − 14 2(10) − 14
C13. b + a ; ba 5(12)
=
6
C14. a + (b + c) ; ( ab)c
IA
= 5⋅2
C15. ab + ac = 10
C16. 0; inverse; 0; identity 7( x − 3) 7(9 − 3) 7(6)
14. = = = 7 ⋅ 3 = 21
2 x − 16 2(9) − 16 2
_A
C17. inverse; 1; identity
2x + 3y
C18. simplified 15. ; x = −2, y = 4
x +1
C19. a 2 ( −2 ) + 3 ( 4 ) −4 + 12 8
= = = = −8
−2 + 1 −1 −1
PP
Exercise Set P.1
2x + y
16. ; x = −2 and y = 4
1. 7 + 5(10) = 7 + 50 = 57 xy − 2 x
2 ( −2 ) + 4 −4 + 4 0
= = =0
2. 8 + 6 ( 5 ) = 8 + 30 = 38 ( −2 )( 4 ) − 2 ( −2 )
RO
−8 + 4 4
3. 6(3) − 8 = 18 − 8 = 10 5 5
17. C= (50 − 32) = (18) = 10
9 9
4. 8 ( 3) − 4 = 24 − 4 = 20 50°F is equivalent to 10°C.
5. 82 + 3(8) = 64 + 24 = 88 5 5 5
VE
18. C= ( F − 32) = (86 − 32) = (54) = 30
9 9 9
6. 62 + 5 ( 6 ) = 36 + 30 = 66 86°F is equivalent to 30°C.
19. h = 4 + 60t − 16t 2 = 4 + 60(2) − 16(2) 2
7. 7 2 − 6(7) + 3 = 49 − 42 + 3 = 7 + 3 = 10
= 4 + 120 − 16(4) = 4 + 120 − 64
D?
8. 8 − 7 ( 8 ) + 4 = 64 − 56 + 4 = 8 + 4 = 12
2 = 124 − 64 = 60
Two seconds after it is kicked, the ball’s height is
60 feet.
9. 4 + 5(9 − 7)3 = 4 + 5(2)3
= 4 + 5(8) = 4 + 40 = 44
??
2 Copyright © 2022 Pearson Education, Inc
