Algebra Problems: Solutions and Answers - Comprehensive Guide

This document provides a complete set of solutions to a wide range of algebra problems. The solutions cover various topics, including solving equations, working with functions, graphing, and analyzing algebraic expressions. The problems range in complexity, providing a valuable resource for students seeking to check their work, practice problem-solving techniques, and deepen their understanding of algebraic concepts. The document includes detailed answers to all the problems, making it an effective tool for self-assessment and exam preparation. The solutions provided are comprehensive and cover a wide range of algebraic concepts, ensuring that students can gain a thorough understanding of the subject matter. This assignment is designed to help students with their algebra homework and exam preparation.

Algebra problems2
Answers only
1. ( ) = + −
2. (− ) − ( ) = −
3. .
i) ( ) =
ii) A 200 square foot garden require 1 cubic yard of compost
4. : [− , . ] : [− . , . ]
5. ( ) = − , >
+ , ≤ −
:(−∞, − ] ∪ ( , ∞) :(−∞, − ] ∪ (− , ∞)
6. .

i) Fixed cost is $ 1, 750
ii) C(65) = $ 3, 750
iii) :[ , ], :[ , ]
7. Average rate of change: −
8.
9. Increasing: (-1.5, ∞); Decreasing: (-∞, 1.5)
10. Absolute maximum at (0.85, 7.3) and local maximum at (4.5, 0.38); local minimumat (-
4.5, 0.85) and absolute minimum at (1.2, -4.3)
11. ( ∘ )( ) = ( ) = ; : (−∞, − ) ∪ (− , ∞)
12. ( ) = + + − +
13. Find:
i) ( ∘ )( ) = ( ) =
ii) ( ∘ )( ) = ( ) = +
14. ( ) = ( ) = −
15. ( ) = +
16. The graph is increasing on (3, ∞) and decreasing on (-∞, 3)
17. Reflection across the x-axis, horizontal compressed by a factor of 4, translated down 3
units.
18. ( ) = −
19. −intercept: none
−Intercept (0, -19)

20. = | − | +
21. The plot is given below:
22. | − . | ≤ .
23. ( ) =
∶ −∞, ∪ , ∞
: (−∞, − ) ∪(− , ∞)
24. Domain: (-7, ∞)
25. ( ) = ±√ ( ) = ±
This means that when the radius is 13 units the area is 169π
26. Slope is : −

27. P(t) = 13255t+133550
28. Slope of = −
Slope of =
The lines are neither parallel nor perpendicular
29. ( ) = +
30. = +
31. Population in 2018: 52, 290
The population will reach 41, 940 in 2027
32. .
i) ( ) = − +
ii) 2008
iii) 2022
33. You would need to sell $83,333.33
34. There is maximum: (− , )
The axis if symmetry: = −
35. = − +
36. $12.50
37. Degree 10
Leading coefficient: 1
38. = ( − )( − ) = − +
39. = ( − )( − ) = − +
40. The graph is shown below

The x-intercepts are: (− , ), − , , ( , )
The y-intercept is: ,
= − :
= − − :
= :
The end behavior the graph of the given polynomial falls to the left and rises to the
right
41. − ( + )( − )( − )( + )( + ) NOTE: Options given has no correct answer
42. ( ) = ( − ) ( + )
43. Quotient: − +
Remainder: −
44. + −

45. − +
46. ( + )( − )( − )
47. = , = , = , =
48. The radius is 7 feet and the height is 48 feet
49. Horizontal intercept: ( , ), (− , )
Vertical intercept: , −
Vertical asymptote: = − , = −
Horizontal asymptote: =
50. ( ) = ( )( )
( )( ) : ( ) =
51. ( ) = .
52. ( ) = √
53. Domain of f(x) is [− , ∞)
( ) = √ + −
54. = − ; =
55. = √
56. = .
57. =
58. ( ) ( )
59. ( ) + ( ) − ( ) − ( )

60. ( )
( ) = .
61. √
62. =
63. √
64. .1 years
65. − .
66. = .
67. = .
68. =
69. ( )
( )
70. ( ) + ( ) + ( ) − ( ) − ( )
71. ( )
( ) = . Repeated
72. √
73. =
74. √
75. 2.4 years
76. K=-0.014
77. = .
78. = .
79. =

80. = ; =
81. = ; =
82. x=162.3 hot dogs
83. The truck was travelling 51.63 miles per hour and the Lamborghini was driving 76.63
miles per hour
84. = ; = ; =
85. = ; = − ; =
86. The solution has infinitely may solution; the given answers, 3 of them applies
Loading dock manager $50 500; Office manager 36 500; and truck driver $33 500
Loading dock manager $51 500; Office manager 35 500; and truck driver $32 500
Loading dock manager $52 500; Office manager 34 500; and truck driver $31 500
87. The graph is shown below
88. 199.6 tons