Algebra: How to for Study Guide

What follows is not the answer key for the final exam but rather a set of hints, plans and strategies for the review sheet.  Not every problem is included but a lot of information on how to approach the problems and some answers here and there.  It is offered up to help you work on your study guide.  Good luck!

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Algebra Study guide How to:

1a Jay minus three

B  four sets of pea

2.  y+5

3.  a.   5/10

b.  6 +5

4.  hours = 2d, replace d with 5, 12, 20

5.  7

6.  -2

7.  19

8.  8.2

9.  -3

10.  -9

11.  18 - -23

12.  -5

13.  2x = 2(-6) = -12

14.  -3

15.  4

16.  -70

17.  21

18. 0

19.  Undefined

22.  – 1/256

23.  -216

24.  216

25.  64

30.  -1

31.  -4

32.  40-4+4 = 40

33.  3(n+ -5), (34-9)/sqrt(25)

34.  evaluate:  3*2*(2+2)

35.  200

36.  8

37.  11.95

38.  78

39.  –x^3

40.  can’t be simplified

41. 300x

42.  b^3 + 3b^2 + 27a

44.  fee = 3x + 50

45.  add 4 to both sides (-4)

46.  add 11/12 to both sides (16/12 = 4/3)

47.  subtract 13 to both sides (71)

48.  subtract 0.6 from both sides (0.15)

49.  add 5 to both sides (27)

50.  multiple both sides by -7 (21) 

51.  multiply both sides by 100 (2.8)

52.  divide both sides by 8 (1/2)

53.  divide both sides by -9 (-14)

54.  multiply both sides by 5/2’s

55.  multiply both sides by 16/15’s

56.  subtract 8 from both, then divide by 4 on both sides

57.  subtract 14 on both sides, then multiply by 4/3rds on both

58.  combine like terms of 2y and -8y to get -6y.  Then subtract 29 on both sides, then divide both sides by -6

59.  divide both sides of the equation by 3, then add 9 to both sides

60.  distribute the – over the parenthesis.  Combine like terms.  Add 12 to both sides, then divide both sides by -2

61.  subtract 5x from both sides.  Subtract 2 from both sides.  Divide both sides by 2

62.  distribute 4 over the parenthesis.  Subtract 5x from both sides.  Add 20 to both sides.  Divide both sides by 3.

67.  578 = y – 89

68.  V = 9/10 E

69.  h = h = 3V / A

70.  C = R –P

71.  y = -2/7 x + 2

72.  m = x(k-6)

73.  C = S + Rt

74.  subtract 2 from both sides, split into the two cases.

75.  split into two cases.  Then in each case, add 1 to both sides, then divide both sides (in both cases) by 3.

76.  Add 3 to both sides, then divide both sides by 5.  Split into two cases.  In each of those two equations subtract 7 from both sides.

77.  84*0.5 + 92*0.3 + 38*0.2

78.  68*0.4 + 65*0.4 + 84*0.2

80.  a number plus four is greater than 7, 7 is smaller than a number plus 4

82.  x > -4    x < 2

83.  x < 250

84.  subtract 7 from both sides,  add 6 to both sides,  subtract 6.7 from both sides.

85.  72+x<120

86.  a.  divide both sides by 8

b.  divide both sides by -5, flip the < to >

c.  multiple both sides by 5.

87.  9.85*n = 77

89.  154 < x < 174

90.  subtract 4 from both sides, in the first OR subtract 3 from both sides, in the second subtract 1 and then divide both sides by -2

91.  x < -7 OR x > 0

92 a.  subtract 10 from both sides, then split into two cases.  Graph using the word OR

b.  add 7.8 to both sides.  Split into two cases (using AND).  In both cases, subtract 1 from both sides.

94.  Domain:  -3 < x < 2, Range:  -2 < y < 4

95.  Domain:  5, 10, 15 Range:  2, 4, 6, 8 not a function because an X (5) goes to two different Y’s (2, 4)

96.  Dependent:  Cost.  Independent:  People.  F(x)= 8.95x

Dependent:  Cost.  Independent:  Miles.  F(x) = 1.5x + 130

97.  g(20) = ¼(20)-3 = 5-3 = 2

F(-5) = 6*-5 -1 = -30 -1 = -31

98.  f(x) = 200x + 100  Domain:  2, 3, 4 Range:  500, 700, 900

100.  a No, b. Yes

101b  a1 = 2.  D = 5.  A40 = 2 + (40-1)5 = 2 + 39*5 = 197

102 a to know for sure you need to check the slopes.  A is not linear.  B is 2/3^rds and is a function.

104.  x intercept is (80, 0) and is the point where the director is out of money.  Y intercept is (0,6000) and is the point where he has not produced anything yet (time is 0).

105.  Slope = (y1-y2)/(x1-x2)  = (-1 – 1)/(3- -3) = -2 / 6 = - 1/3

105 b.  Slope = undefined.

106.  slope = (6-3) / (-1 – 5) = 3 / -6 = -1/2

107.  Solve for y and then check the m from the equation y = mx + b

108.  y = 3x -2 and y = ½

110.  point slope form = y-y1 = m(x-x1)   so slope is (1-7)/(2- -1) = -6 / 3 = -2 equation:  y-7 = -2(x+1)

111.  slope parallel = 4, slope perpendicular = -1/4 parallel line in slope intercept form y-2 = 4(x-3) in slope-intercept form y = 4x -10

112.  a rotation to less steep, b translation of up 7 units, c rotation more steep, d reflection

113.  a translation upwards.  The graph shifts up 75 units so the line is higher.

B  more steep, the graph has a greater slope.