A)
B)
C)
D)
Solve the problem.
76)
A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius 165
km. Determine an equation for the ellipse, where x and y are measured in km, if the distance of the
satellite from the surface of the moon varies from 238 km to 322 km.
76)
A)
x2
2382+y2
3222= 1
B)
x2
322 +y2
238 = 1
C)
x2
4872+y2
4032= 1
D)
x2
403 +y2
487 = 1
Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
77)
5x2=36 – 5y2
77)
A)
Hyperbola
B)
Circle
C)
Ellipse
D)
Parabola
Graph the function. Give the domain and range.
78)
f(x) =x – 4 + 5
78)
42
A)
Domain: (–, ); Range: [–5, )
B)
Domain: (–, ); Range: [5, )
C)
Domain: (–, ); Range: [5, )
D)
Domain: (–, ); Range: [–5, )
Graph the system of inequalities.
79)
y – x2– 6x – 4
y x2+ 6x + 4
79)
43
A)
B)
C)
D)
Find the center and radius of the circle.
80)
x2+ y2– 10x – 2y + 17 = 0
80)
A)
(5, 1); r =3
B)
(–5, –1); r =9
C)
(–1, –5); r =9
D)
(1, 5); r =3
Solve the system by the substitution method.
81)
x2+ y2= 25
x – y = 1
81)
A)
{(–4, 3), (–3, 4)}
B)
{(4, 3), (–3, –4)}
C)
{(4, –3), (3, –4)}
D)
{(–4, –3), (–3, –4)}
44
Graph the function defined by a radical expression.
82)
y =12 4+ x2
4
82)
A)
B)
C)
D)
45
Decide whether the statement is true or false.
83)
The graph of the equation x
4+y
25 = 1 is an ellipse.
83)
A)
True
B)
False
Graph the inequality.
84)
9x2–16y2144
84)
A)
B)
C)
D)
Graph the system of inequalities.
85)
x + 2y 2
x – y 0
85)
A)
B)
C)
D)
47
Find the center and radius of the circle.
86)
x2+ y2+ 18x – 14y + 94 = 0
86)
A)
(–7, 9); r =36
B)
(–9, 7); r =6
C)
(9, –7); r =36
D)
(7, –9); r =6
Graph the inequality.
87)
36y2–16x2576
87)
A)
B)
C)
D)
D)
Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle.
88)
4y2+ 25x2=100
88)
A)
circle
B)
ellipse
C)
hyperbola
D)
parabola
Decide whether the statement is true or false.
89)
The equation of a circle centered at the origin with radius 4 is x2+ y2=4.
89)
A)
True
B)
False
Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
90)
4x =5y2– 23
90)
A)
Hyperbola
B)
Ellipse
C)
Circle
D)
Parabola
D)
Graph the system of inequalities.
91)
x2
9+y2
25 1
x2
25 +y2
9 1
91)
49
D)
A)
B)
C)
D)
Solve the problem by using a nonlinear system.
92)
Find the dimensions of a rectangular enclosure with perimeter 56 yd and area 187 yd2.
92)
A)
12 yd by 17 yd
B)
12 yd by 16 yd
C)
11 yd by 16 yd
D)
11 yd by 17 yd
Solve the problem.
93)
A rectangular board is 4 by 6. How far from the center of the board will the foci be located to
determine the largest elliptical tabletop? Round your answer to the nearest tenth.
93)
A)
.8
B)
2.0
C)
2.2
D)
1.0
Solve the system by the substitution method.
94)
x2+ y2=181
x + y = – 19
94)
A)
{(9, 10), (10, 9)}
B)
{(9, –10), (10, –9)}
C)
{(–9, 10), (–10, 9)}
D)
{(–9, –10), (–10, –9)}
Graph the circle.
95)
2y2=200 – 2x2
95)
A)
B)
C)
D)
The hyperbola shown in the calculator–generated graph was graphed in function mode with a square viewing window.
What are the two functions y1 and y2 that were used to obtain the graph whose equation is given?
96)
y2
36 –x2
25 = 1
10
–15 15
–10
96)
A)
y1= 6 x2– 25, y2= – 6 x2– 25
B)
y1= 6 x2
25 – 1, y2= – 6x2
25 – 1
C)
y1= 6 x2
25 + 1, y2= – 6x2
25 + 1
D)
y1= 5 x2+ 36, y2= – 5 x2+ 36
Graph the hyperbola.
97)
y2
64 –x2
16 = 1
97)
52
A)
B)
C)
D)
Decide whether the statement is true or false.
98)
The circle with equation x2+ y2=9 has center at (3, 3).
98)
A)
True
B)
False
53
Graph the step function.
99)
Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each
additional ounce or fraction of an ounce. Let L(x) be the cost of mailing a letter weighing x ounces.
Graph y = L(x). Use the interval (0, 4].
99)
A)
B)
C)
D)
Find the equation of a circle satisfying the given conditions.
100)
Center: (8, 0); radius: 14
100)
A)
x2+ (y + 8)2=196
B)
(x + 8)2+ y2=14
C)
(x – 8)2+ y2=14
D)
x2+ (y – 8)2=196
Solve the nonlinear system.
101)
xy = 1
–6x – y =5
101)
A)
–1
2, –2, –1
3, –3
B)
no real solution
C)
–2, –1
2, –3, –1
3
D)
{(2, –2), (3, –3)}
Provide an appropriate response.
102)
True or false? The hyperbola with equation y2
16 –x2
9= 1 opens up and down.
102)
A)
False
B)
True
103)
True or false? The x–intercepts of the hyperbola with equation x2
9–y2
64 = 1 are (8, 0) and (–8, 0).
103)
A)
True
B)
False
Solve the problem by using a nonlinear system.
104)
In 1979, City #1 and City #2 had the same population. The population of City #2 continued to
increase steadily, while the rate of population growth of City #1 (although initially less than that of
City #2) eventually overtook the growth rate of City #2. The populations of two cities are modeled
by the following equations: City #1: y = 2x2+ 15x +1031; City #2: y = 25x +1031, where x = 0
corresponds to the year 1979. In what year after 1979 did the cities have the same population?
104)
A)
1984
B)
1983
C)
1982
D)
1985
The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one
of the solutions. Find the other solution.
105)
y =1
2x2– 3
x + y = 1
105)
A)
(4, –3)
B)
(–4, 5)
C)
(6, –5)
D)
(5, –4)
Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
106)
y2=100 – x2
106)
A)
Hyperbola
B)
Ellipse
C)
Parabola
D)
Circle
Graph the function.
107)
f(x) =x + 4
107)
56
A)
B)
C)
D)
Decide whether the statement is true or false.
108)
The equation of a semicircle that is the upper half of the circle centered at the origin with radius 4 is
y =16 –x2.
108)
A)
True
B)
False
Graph the hyperbola.
57
109)
x2
16 –y2
36 = 1
109)
A)
B)
C)
D)
Solve the problem.
110)
A railroad tunnel has the shape of half an ellipse. The height of the tunnel at the center is 42 ft and
the vertical clearance must be 6 ft at a point 12 ft from the center. Find an equation for the ellipse,
where x and y are measured in ft.
110)
A)
x2
144 +y2
1764 = 1
B)
x2
147 +y2
1764 = 1
C)
x2
147 +y2
36 = 1
D)
x2
1764 +y2
147 = 1
Answer the question.
111)
The lowest point on the graph of f(x) =x+14 has what coordinates?
111)
A)
(0, 0)
B)
(14, 0)
C)
(0, 14)
D)
(14, 14)
Solve the nonlinear system.
112)
4x2+2y2=4
x2+2y2=1
112)
A)
{(–1, –2), (–1, 2), (1, –2), (1, 2)}
B)
{(–1, 0), (1, 0)}
C)
{(–1i, 0), (1i, 0)}
D)
{(1, 0)}
59
The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one
of the solutions. Find the other solution.
113)
y =1
3x2– 3
x + y = 3
113)
A)
(0, –3)
B)
(0, 3)
C)
(3, 0)
D)
(–3, 0)
D)
The hyperbola shown in the calculator–generated graph was graphed in function mode with a square viewing window.
What are the two functions y1 and y2 that were used to obtain the graph whose equation is given?
114)
y2
25 –x2
9= 1
10
–15 15
–10
114)
A)
y1= 5 x2
9+ 1, y2= – 5x2
9+ 1
B)
y1= 5 x2
9– 1, y2= – 5x2
9– 1
C)
y1= 5 x2– 9, y2= – 5 x2– 9
D)
y1= 3 x2+ 25, y2= – 3 x2+ 25
D)