2. is not a real number. (Can’t take the square root of a negative number)

4.

6.

8.

10.

12.

14.

16.

18.

20.

22.

24.

26.

28.

30.

32.

34. 3x² + 15x = 0

3x(x + 5) = 0

3x = 0 or x +5 = 0

x = 0 x = -5

36.

38.

40. OMIT

42.

Opens downward

Vertex: (0,0)

y-intercept: (0,0)

x-intercept(s): (0,0)

other points:
(2,-2) (-2,2) (4, -8) (-4,-8)

44. g(x) = 1 – 2x – x² = –x² – 2x +1

Opens downward

Vertex: (-1, 2)

y-intercept: (0,1)

x-intercept(s): (0.41,0) and (-2.41,0)

Other point(s): (-2,1)

46. y = 25x – 0.2x²

Find vertex.

The high point is (62.5, 781.25)

48. P = R – C

They would make a profit of $200 if they sold 15 items or 100 items.

50. x = smaller #

x + 4 = larger #

The numbers are approximately 1.24 and 5.24 or –3.24 and 0.76.

52. l = length

2l – 4 = width

l(2l – 4) = 390

2l² – 4l – 390 = 0

l² – 2l – 195 = 0

(l – 15)(l + 13) = 0

l – 15 = 0 or l + 13 = 0

l = 15 l = -13

(The length can’t be negative.)

The length is 15 meters and the width is 26 meters. {(2)(15) – 4 = 26}

54. x + 2y = 4 ® 2y = -x + 4 ® y = -½x + 2

2x + 4y = 16 ® 4y = -2x +16 ® y = -½x + 4

Since the two equations have the same slope and the y-intercepts are different, the lines are parallel and the system of equations has no solution.

56. x – 2y = 6 ® x – 2y = 6 ® x – 2y = 6

3x + y = 3 ® 2(3x + y = 3) ® 6x + 2y = 6

7x = 12

x = 12/7

3(12/7) + y = 3 ® 36/7 + y = 3 ® y = 3 – 36/7 = 21/7 – 36/7 = -15/7

So x = 12/7 and y = -15/7

58.

® ®

7 = 5x +2(3x + 9)

7 = 5x + 6x + 18

-11 = 11x

-1 = x

y = 3(-1) + 9 = -3 + 9 = 6

x = -1 and y = 6

60. a = 3

® ® ® 6 – 5b = 9 ® -5b = 3
® b = -3/5

a = 3 and b = -3/5

62. 0.4u + v = 800 ® -2(0.4u + v = 800) ® -0.8u – 2v = -1600

0.7u + 2v = 1850 ® 0.7u + 2v = 1850 ® 0.7u + 2v = 1850

-0.1u = 250

u = -2500

0.4(-2500) + v = 800

-1000 + v = 800

v = 1800

Check: 0.4u + v = 800 0.7u + 2v = 1850

0.4(-2500) + 1800 ? 800 0.7(-2500) +2(1800) ? 1850

-1000 + 1800 ? 800 -1750 + 3600 ? 1850

800 = 800 1850 = 1850

Both equations check.

64. Let b = rate of boat

Let c = rate of current

	Rate	Time	Distance
Downstream	b + c	4	32
Upstream	b – c	6	12

(b + c)(4) = 32 ® 4b + 4c = 32 ® 3(4b + 4c = 32) ® 12b + 12c = 96

(b – c)(6) = 12 ® 6b – 6c = 12 ® 2(6b – 6c = 12) ® 12b – 12c = 24

24b = 120

b = 5

(5 + c)4 = 32

5 + c = 8

c = 3

The speed of the boat is 5 mph and the speed of the current is 3 mph.

66.

	Price/ticket	# tickets	Total revenue
Adult	5	x	5x
Child	2	Y	2y
Total		500	1945

x + y = 500 ® -2(x + y = 500) ® -2x –2y = -1000

5x + 2y = 1945 ® 5x + 2y = 1945 ® 5x + 2y = 1945

3x = 945

x = 315

315 + y = 500 ® y = 185

There were 315 adults and 185 children in attendance.

68.

	Amount invested	Interest rate	Interest earned
CD	x	0.085	0.085x
Mutual fund	y	0.11	0.11y
Total	10000		1050

x + y = 10000 ® y = 10000 - x

0.085x + 0.11y = 1050 ® 0.085x + 0.11(10000 – x) = 1050

0.085x + 1100 – 0.11x = 1050

-0.025x = -50

x = 2000

y = 10000 – 2000 = 8000

Invest $2000 in the CD and $8000 in the mutual fund.