answer’key’mat’1033’final’exam’review… ·...
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Answer Key MAT 1033 Final Exam Review (Posted April 2013)
1. ! = − !!
2. ! = !!
3. All reals
4. ! = !!!"!!
! or ! = !
!+ 16!
5. ! = !!! + 2
6. 8 ft by 34 ft
7. $38,000
8. $3500 @ 6% and $2500 @ 8%
9. [−6,∞)
10. (1,∞)
11. x-‐intercept is 4,0 12. x-‐intercept is −5,0
y-‐intercept is 0,−3 y-‐intercept is 0,−6
13. a) ! = !! b) ! = − !
!
c) ! = − !! !!"#! =
!!
14. slope is !! 15. slope is − !
!
y-‐intercept is 0,−2 y-‐intercept is 0,2
16. ! = 2! − 10
17. ! = !!! + 2
18. 2! − ! = −1
19. 3! + 7! = 5
20. ! = 2! − 7
21. ! = !!! + !
!
22. solid line, shade below 23. dashed vertical line, shade left
24. B and D are functions
25. a) ! −4 = −13 b) ! −2 = −6 c) ! !!= −4
26. ! = 24
27. ! = 25
28. ! = 126 pounds
29. 2,−1
30. 4,3
31. −5,3
32. no solution, lines are parallel
33. 18, 32
34. 12 gallons @20% alcohol and 4 gallons @ 60% alcohol
35. shade above both lines, one line is dashed the other line is solid
36. !!
!"!!"
37. !!"!!
!!!!
38. !"!!
!!"
39. a) 2.35 × 10!" b) 4.07 × 10!!
40. 12!! − 5!! + 2! − 5
41. 2!! + !! + 3
42. 21!!!! − 24!!!
43. 8!! + 14! − 15
44. 81!! − 4
45. 9!! − 30! + 25
46. 8!! − 24!! + 4! + 21
47. 19! − 18
48. 8!!!!! 3!! − 2!!
49. 3!!! 2! − 3!
50. 2! + ! 2! − 3
51. 2! − ! 2! + ! ! − !
52. ! − 7 ! − 4
53. ! − 8 ! + 4
54. 2 ! + 4 ! − 3
55. 4! ! − 2 ! − 3
56. 2! − 5 ! − 3
57. 3! − 7 2! + 5
58. 3! − 2! !
59. 6! + 5! !
60. 3! − 2! 3! + 2!
61. 2! − ! 2! + ! 4!! + !!
62. ! + 5! !! − 5!" + 25!!
63. 2! − 3! 4!! + 6!" + 9!!
64. 3! − 4 2! − 1
65. 3! + 4 2! − 5
66. 2 ! + 5 ! − 3
67. 3 2! − 5! 2! + 5!
68. ! = − !!,! = −5
69. ! = !!, ! = −2
70. ! = !!!"#, ! = !
!!"#
71. a) ! ! ≠ 0, ! ≠ 9 b) ! ! ≠ −6
72. a) !!!!!!
b) !!(!!!)!!!
73. 2! + 5 + !!!!!
74. 4!! − 7! + 5 + !!!!!!
75. ! !!!!!
76. a) ! !!!!!! ! b)
!!!!
77. !!!!!!
78. !!!!!!
79. !(!!!")!!! (!!!)
80. !(!!!!)!!! (!!!)
81. !!!!!!
82. !!!!!!
83. ! = 10
84. 4 mph
85. 20 mph
86. t = 60 hours
87. a) !!"/!" b) 4!!/! c) !
!!!!
88. a) 4!!!!!! 3! b) 2!"!! 6!!!!! c) 2!"!! 3!!!!
89. a) ! !! b)
!"! c)
! !!
!
90. −32! 2
91. 11!" 3!!!!
92. 9− 4 5
93. 50− 10 21
94. !"!! !!"
95. 4− 15
96. ! = 8
97. ! = 6 (x = 1 does not check)
98. 52− 16!
99. !"!"− !
!"!
100. a) ! = !!± !"!
b) ! = !!± !"!
c) ! = !!±! !!