Algebra and Trigonometry (4th Edition, 2010 – Robert Blitzer) | Complete Solutions Manual PDF

ALL CHAPTERS COVERED

, TABLE OF CONTENTS for INSTRUCTOR SOLUTIONS

Algebra and Trigonometry 4e

Chapter P Fundamental Concepts of Algebra ……………………….……….………...…….1

Chapter 1 Equations and Inequalities ………………………………………..………..……72

Chapter 2 Functions and Graphs ………………………………………………………….201

Chapter 3 Polynomial and Rational Functions ……………………………………………317

Chapter 4 Exponential and Logarithmic Functions ……………………………….………461

Chapter 5 Trigonometric Functions ……………………………………………….………537

Chapter 6 Analytic Trigonometry …………………………………………...……….……713

Chapter 7 Additional Topics in Trigonometry ……………………………………………830

Chapter 8 Systems of Equations and Inequalities …………………...……………………994

Chapter 9 Matrices and Determinants ………………………………………….……..…1123

Chapter 10 Conic Sections ………………………………………………………………..1228

Chapter 11 Sequences, Induction, and Probability ……………..……………….………...1344




Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

, Chapter P
Fundamental Concepts of Algebra

Section P.1 6. a. 1− 2
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 )
= 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. Since 2010 is 10 years after 2000, substitute 10 for x. value of a positive number is the number itself.
T = 17 x 2 + 261x + 3257 Thus,
= 17(10)2 + 261(10) + 3257 π − 3 = π − 3.
= 7567
If trends continue, the tuition and fees will be $7567 x
c.
x
3. The elements common to {3, 4, 5, 6, 7} and Because x > 0, x = x.
{3, 7, 8, 9} are 3 and 7.
{3, 4,5, 6, 7} ∩ {3,7,8,9} = {3, 7} x x
Thus, = =1
x x
4. The union is the set containing all the elements of
either set. 7. −4 − (5) = −9 = 9
{3, 4,5, 6, 7} ∪ {3, 7,8,9} = {3, 4,5, 6, 7,8,9} The distance between –4 and 5 is 9.

⎧ π ⎫ 8. 7(4 x 2 + 3x) + 2(5 x 2 + x)
5. ⎨ −9, − 1.3, 0, 0.3, , 9, 10 ⎬
⎩ 2 ⎭ = 7(4 x 2 + 3 x) + 2(5 x 2 + x)
= 28 x 2 + 21x + 10 x 2 + 2 x
a. Natural numbers: 9 because 9 =3
= 38 x 2 + 23x
b. Whole numbers: 0, 9
9. 6 + 4[7 − ( x − 2)]
c. Integers: −9, 0, 9 = 6 + 4[7 − x + 2)]
= 6 + 4[9 − x]
d. Rational numbers: −9, − 1.3, 0, 0.3, 9 = 6 + 36 − 4 x
= 42 − 4 x
π
e. Irrational numbers: , 10
2
Exercise Set P.1
f. Real numbers:
⎧ π ⎫ 1. 7 + 5(10) = 7 + 50 = 57
⎨ −9, − 1.3, 0, 0.3, , 9, 10 ⎬
⎩ 2 ⎭
2. 8 + 6 ( 5 ) = 8 + 30 = 38

3. 6(3) − 8 = 18 − 8 = 10

4. 8 ( 3) − 4 = 24 − 4 = 20




1
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

, Fundamental Concepts of Algebra


5. 82 + 3(8) = 64 + 24 = 88 19. h = 4 + 60t − 16t 2 = 4 + 60(2) − 16(2)2
= 4 + 120 − 16(4) = 4 + 120 − 64
6. 62 + 5 ( 6 ) = 36 + 30 = 66 = 124 − 64 = 60
Two seconds after it is kicked, the ball’s height is
7. 7 2 − 6(7) + 3 = 49 − 42 + 3 = 7 + 3 = 10 60 feet.

8. 82 − 7 ( 8 ) + 4 = 64 − 56 + 4 = 8 + 4 = 12 20. h = 4 + 60t − 16t 2
= 4 + 60(3) − 16(3) 2
9. 4 + 5(9 − 7)3 = 4 + 5(2)3 = 4 + 180 − 16(9)
= 4 + 5(8) = 4 + 40 = 44 = 4 + 180 − 144
3 3
= 184 − 144 = 40
10. 6 + 5 (8 − 6 ) = 6 + 5 ( 2 ) Three seconds after it is kicked, the ball’s height is
= 6 + 5 (8) 40 feet.

= 6 + 40 = 46 21. {1, 2,3, 4} ∩ {2, 4,5} = {2, 4}
2
11. 8 − 3(8 − 2) = 64 − 3(6)
= 64 − 18 = 46 22. {1,3, 7} ∩ {2,3,8} = {3}

12. 82 − 4 ( 8 − 3) = 64 − 4 ( 5 ) = 64 − 20 = 44 23. {s, e, t} ∩ {t , e, s} = {s, e, t}

5( x + 2) 5(10 + 2) 24. {r , e, a, l} ∩ {l , e, a, r} = {r , e, a, l}
13. =
2 x − 14 2(10) − 14
5(12) 25. {1,3,5, 7} ∩ {2, 4, 6,8,10} = { }
=
6 The empty set is also denoted by ∅.
= 5⋅2
= 10
26. {1,3,5, 7} ∩ {−5, −3, −1} = { } or ∅

7( x − 3) 7(9 − 3) 7(6) 27. {a, b, c, d} ∩ ∅ = ∅
14. = = = 7 ⋅ 3 = 21
2 x − 16 2(9) − 16 2
28. {w, y, z} ∩ ∅ = ∅
2x + 3 y
15. ; x = −2, y = 4
x +1 29. {1, 2,3, 4} ∪ {2, 4,5} = {1, 2,3, 4,5}
2 ( −2 ) + 3 ( 4 ) −4 + 12 8
= = = = −8 30. {1,3, 7,8} ∪ {2,3,8} = {1, 2,3, 7,8}
−2 + 1 −1 −1

16.
2x + y
; x = −2 and y = 4
31. {1, 3,5, 7} ∪ {2, 4, 6,8,10}
xy − 2 x = {1, 2, 3, 4, 5, 6, 7,8,10}
2 ( −2 ) + 4 −4 + 4 0
= = =0
( −2 )( 4 ) − 2 ( −2 ) −8 + 4 4 32. {0,1,3,5} ∪ {2, 4, 6} = {0,1, 2,3, 4,5, 6}

5 5 33. {a, e, i, o, u} ∪ ∅ = {a, e, i, o, u}
17. C = (50 − 32) = (18) = 10
9 9
10°C is equivalent to 50°F. 34. {e, m, p, t , y} ∪ ∅ = {e, m, p, t , y}

5 5 5 35. a. 100
18. C = ( F − 32) = (86 − 32) = (54) = 30
9 9 9
30°C is equivalent to 86°F. b. 0, 100




2
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.