A)
B)
C)
D)
Solve the system by the addition method.
50)
y =x2+ 6
y = – x2+ 10
A)
{( 2, 8), ( 2, –8), (–2, 8), (–2, –8)}
B)
{( 2, 8), ( 2, –8)}
C)
{(8, 2), (8, –2)}
D)
{( 2, 8), (–2, 8)}
21
Solve the problem.
51)
An–Mei owns a business making and selling jackets. She has a fixed cost of $720. It costs $66 to
produce each jacket. The selling price is $78 per jacket. Let x represent the number of jackets
produced and sold and write the cost function, C, and revenue function, R.
A)
C(x) =66 +78x
R(x) =720x
B)
C(x) =66x +720x
R(x) =78x
C)
C(x) =66x +720
R(x) =78x
D)
C(x) =66 +720x
R(x) =78
Graph the solution set of the system of inequalities or indicate that the system has no solution.
52)
x2+y236
x2+y21
A)
B)
C)
no solution
D)
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
53)
7x – 5
x2+ 9x + 18
A)
A
x + 6 +B
x + 3 +C
(x + 6)2(x + 3)2
B)
A
x + 6 +B
x + 3 +Cx + D
x2+ 9x + 18
C)
A
x + 6 +B
x + 3
D)
A
x + 6 +B
x + 3 +C
x2+ 9x + 18
Solve the problem.
54)
A right triangle has an area of 11 square inches. The square of the hypotenuse is 125. Find the
lengths of the legs of the triangle. Round your answer to the nearest inch.
A)
1 inches and 22 inches
B)
4 inches and 5.5 inches
C)
4 inches and 121 inches
D)
2 inches and 11 inches
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
55)
x + y = – 2
x – y =19
A)
{(8.5, –10.5)}
B)
{(8.5, 10.5)}
C)
{(x, y) | x + y = – 2}
D)
23
Solve the system by the substitution method.
56)
x2= y2+ 39
x – y = 3
A)
{(8, –5)}
B)
{(–8, –5)}
C)
{(–8, 5)}
D)
{(8, 5)}
Write the partial fraction decomposition of the rational expression.
57)
x
x2– 11x + 30
A)
–6
x – 5 +5
x – 6
B)
–5
x – 5 +
–6
x – 6
C)
5
x – 5 +
–6
x – 6
D)
–5
x – 5 +6
x – 6
Solve the system by the substitution method.
58)
x2+y2=85
x + y = – 13
A)
{(6, –7), (7, –6)}
B)
{(–6, –7), (–7, –6)}
C)
{(–6, 7), (–7, 6)}
D)
{(6, 7), (7, 6)}
Solve the system of equations.
59)
x + y + z =1
x – y + 5z =13
5x + y + z = – 19
A)
{(4, 2, –5)}
B)
{(4, –5, 2)}
C)
{(–5, 2, 4)}
D)
{(2, –5, 4)}
24
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
60)
5x + 2
(x + 5)2
A)
A
x + 5 +B
x + 5 +C
(x + 5)2
B)
A
x + 5 +B
x + 5 +Cx + D
(x + 5)2
C)
A
x + 5 +B
(x + 5)2
D)
A
x + 5 +Bx + C
(x + 5)2
Solve the system by the substitution method.
61)
x – y =5
(x – 2)2+(y + 5)2= 20
A)
{(–1, 4), (–7, –2)}
B)
{(4, –1), (–2, –7)}
C)
{(4, –1), (6, 3)}
D)
{(–1, 4), (3, 6)}
Solve the system of equations.
62)
5x + 4y + z =23
4x – 4y – z =13
5x + y + 2z =19
A)
{(4, –1, 1)}
B)
{(4, 1, –1)}
C)
{(–1, 1, 4)}
D)
{(1, 4, –1)}
25
Solve the problem.
63)
The table shows the percentage of people living below the poverty line in one U.S. city in the years
2000 through 2003.
Year
Percentage of people living
below poverty line
2000 11.6
2001 12.7
2002 13
2003 12.5
The data in the table can be written as ordered pairs (x, y) where x is the number of years after 2000
and y is the percentage of people living below the poverty line in that year. Use the data for 2000,
2002, and 2003 to find the quadratic function y = ax2+ bx + c that models the percentage, y, of
people in this city living below the poverty line x years after 2000.
[Hint: Find a, b, and c by substituting each of three ordered pairs into the function and writing and
solving a system of linear equations in three variables.]
A)
y = – 0.5x2+ 1.7x + 11.6
B)
y = – 0.4x2+ 1.5x + 11.6
C)
y = – 0.3x2+ 1.3x + 11.6
D)
y = – 0.5x2+ 1.8x + 11.6
Solve the system by the addition method.
64)
5x2– 4y2= – 99
2x2+ 2y2=90
A)
{(–3, –6), (–6, –3)}
B)
{(3, 6), (–3, 6), (3, –6), (–3, –6)}
C)
{(3, 6), (6, 3), (–3, –6), (–6, –3)}
D)
{(3, –6), (3, 6)}
Graph the inequality.
65)
x + y < – 6
26
A)
B)
C)
D)
Solve the problem.
66)
The following is known about three numbers: If the second number is subtracted from the sum of
the first number and 4 times the third number, the result is 13. The third number plus 2 times the
first number is 4. The first number plus 5 times the second number plus the third number is 19.
Find the three numbers.
[Hint: let x represent the first number, y the second number, and z the third number. Use the given
conditions to write and solve a system of equations.]
A)
x =0, y =2, z =9
B)
x =0, y =3, z =4
C)
x = – 1, y =3, z =6
D)
x =1, y =4, z =4
67)
A woman works out by running and swimming. When she runs, she burns 7 calories per minute.
When she swims, she burns 9 calories per minute. She wants to burn at least 378 calories in her
workout. Graph an inequality that describes the situation. Let x represent the number of minutes
running and y the number of minutes swimming. Because x and y must be positive, limit the
graph to quadrant I only.
27
A)
B)
C)
D)
D)
Graph the inequality.
28
68)
y x – 3
A)
B)
C)
D)
29
Solve the system by the addition method.
69)
2x2+ y2= 66
x2+ y2= 41
A)
{(5, 4), (5, –4), (–5, 4), (–5, –4)}
B)
{(4, 5), (–4, 5), (4, –5), (–4, –5)}
C)
{(4, 5), (–4, –5)}
D)
{(5, 4), (–5, –4)}
Solve the problem.
70)
Find the values of a, b, and c such that the graph of the quadratic equation y = ax2+ bx + c passes
through the points (–3, –25), (2, 5), and (3, –1).
A)
a = – 2; b =5; c =4
B)
a =2; b =5; c =4
C)
a =2; b =4; c =5
D)
a = – 2; b =4; c =5
The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.
71)
Is there a profit when 395 binoculars are produced?
A)
No
B)
Yes
Graph the solution set of the system of inequalities or indicate that the system has no solution.
30
72)
2x + 3y 6
x – y 3
y 2
A)
B)
C)
D)
31
Solve the system of equations by the substitution method.
73)
y=5x – 4
2y + 6x= – 24
A)
{(–1, –9)}
B)
{(1, –9)}
C)
{(–9, –1)}
D)
Solve the problem.
74)
Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food
intake to 120 g protein, 105 g fat, and 159 g carbohydrate. According to the health conscious
hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy
meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein,
15 g fat, and 6 g carbohydrate. How many of each snack can he eat to obtain his goal?
A)
8 mushrooms; 5 meatballs; 2 eggs
B)
2 mushrooms; 8 meatballs; 5 eggs
C)
9 mushrooms; 6 meatballs; 3 eggs
D)
5 mushrooms; 2 meatballs; 8 eggs
D)
75)
As the price of a product increases, the demand for that product decreases. However, at higher
prices, suppliers are willing to produce greater quantities of the product. The weekly supply and
demand models for a certain type of television are as follows:
Demand: N = – 6p +780
Supply: N =2.6p
where p is the price in dollars per television.
How many of these televisions can be sold and supplied at $100 per television?
A)
sold: 180; supplied: 1040
B)
sold: 180; supplied: 260
C)
sold: 260; supplied: 180
D)
sold: 1380; supplied: 260
D)
Graph the inequality.
32
D)
76)
–3x – 4y 12
A)
B)
C)
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
33
77)
x2+ y264
x + y > 1
A)
B)
C)
D)
34
Solve the problem.
78)
A candy company has 130 pounds of cashews and 170 pounds of peanuts which they combine into
two different mixes. The deluxe mix has half cashews and half peanuts and sells for $7 per pound.
The economy mix has one third cashews and two thirds peanuts and sells for $5.40 per pound.
How many pounds of each mix should be prepared for maximum revenue?
A)
90 pounds of deluxe and 40 pounds of economy
B)
130 pounds of deluxe and 0 pounds of economy
C)
180 pounds of deluxe and 120 pounds of economy
D)
270 pounds of deluxe and 80 pounds of economy
Write the partial fraction decomposition of the rational expression.
79)
2x3+4x2
(x2+ 5)2
A)
2x + 4
x2+ 5
+
–10x – 20
(x2+ 5)2
B)
2x + 4
x2+ 5
+10x + 20
(x2+ 5)2
C)
2x – 4
x2+ 5
+
–10x + 20
(x2+ 5)2
D)
2x + 4
x2+ 5
+10x – 20
(x2+ 5)2
Explanation:
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
80)
3x +y=8
9x +3y =24
A)
{(0, 8)}
B)
{(5, –7)}
C)
{(x, y) 3x + y =8}
D)
Explanation:
Decide if the system of equations in two variables is linear or nonlinear.
81)
x2=2y +4
8x – y =7
A)
Linear
B)
Nonlinear
Explanation:
35
Explanation:
Solve the system by the addition method.
82)
2x2+ y2= 17
3x2– 2y2= – 6
A)
{(2, –3), (–2, 3)}
B)
{(1, 3), (–1, –3)}
C)
{(2, 3), (2, –3), (–2, 3), (–2, –3)}
D)
{(1, 3), (1, –3), (–1, 3), (–1, –3)}
Solve the problem.
83)
A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3
hours to prepare, 2 hours to paint, and 9 hours to fire. A tree takes 16 hours to prepare, 3 hours to
paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 17 hours to paint, and 7 hours to fire. If
the workshop has 135 hours for prep time, 87 hours for painting, and 126 hours for firing, How
many of each can be made?
A)
6 wreaths, 3 trees, 9 sleighs
B)
10 wreaths, 7 trees, 4 sleighs
C)
3 wreaths, 9 trees, 6 sleighs
D)
9 wreaths, 6 trees, 3 sleighs
Solve the system of equations.
84)
x + 3y + 4z = – 13
3y + 2z = – 9
z = – 3
A)
{(2, –1, –3)}
B)
{(–1, 2, –3)}
C)
{(–3, –1, 2)}
D)
{(2, –3, –1)}
Graph the inequality.
85)
x2+y2>1
36
A)
B)
C)
D)
86)
y <1
4x
37
A)
B)
C)
D)
Solve the problem.
87)
The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle
and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth,
if necessary.
A)
width = 3.9 ft, length = 9.7 ft
B)
width = 2 ft, length = 9 ft
C)
width = 4 ft, length = 11 ft
D)
width = 9.7 ft, length = 22.4 ft
38
88)
A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter Festival.
A serving bowl takes 3 hours to prepare, 2 hours to paint, and 8 hours to fire. A platter takes 15
hours to prepare, 3 hours to paint, and 4 hours to fire. A bread basket takes 4 hours to prepare, 13
hours to paint, and 7 hours to fire. If the workshop has 122 hours for prep time, 60 hours for
painting, and 102 hours for firing, how many of each can be made?
A)
2 serving bowls, 8 platters, 6 bread baskets
B)
9 serving bowls, 7 platters, 3 bread baskets
C)
8 serving bowls, 6 platters, 2 bread baskets
D)
6 serving bowls, 2 platters, 8 bread baskets
89)
A twin–engined aircraft can fly 816 miles from city A to city B in 4 hours with the wind and make
the return trip in 6 hours against the wind. What is the speed of the wind?
A)
51 mph
B)
17 mph
C)
68 mph
D)
34 mph
Graph the solution set of the system of inequalities or indicate that the system has no solution.
90)
–x +3y < – 15
x 2
A)
B)
39
C)
D)
Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of the feasible points.
91)
Objective Function: z =6x +7y
Find maximum and minimum.
A)
maximum value: 75; minimum value: 21
B)
maximum value: 117; minimum value: 18
C)
maximum value: 75; minimum value: 18
D)
maximum value: 117; minimum value: 21
40