AnswersMA-PrecalculusUnit Test

Unit Test — Unit test Answers

25 verified answers
1
Free Preview

The equation (x + 11)2 + (y – 27)2 = 2.25, with units in yards, represents a circular fountain in a park. The park entrance maps to (0, 0). If the positive x-axis represents east and the positive y-axis represents north, what is the location of the fountain relative to the park entrance?

A
11 yards east and 27 yards north
B
11 yards west and 27 yards north
C
11 yards east and 27 yards south
D
11 yards west and 27 yards south
2
Free Preview

A farm irrigation system waters a large field. Consider the center of the field as the origin and the rest of the field as a grid measured in yards. The first irrigation unit is located at the point (–400, –200) and waters 500 yards in every direction. The second is located at (200, 300) and waters 400 yards in every direction. The system of inequalities represents this scenario.

Question illustration
A
(100, 100)
B
(–100, 100)
C
(100, –100)
D
(–100, –100)
3

The graph of a hyperbola is shown.

Question illustration
A
(0, −4)
B
(−3, 0)
C
(0, 0)
D
(0, 5)
4

Convert –2y2 + x – 4y + 6 = 0 into standard form.

A
x = 2(y + 1)2 – 6
B
x = 2(y + 1)2 – 8
C
x = 2(y + 1)2 – 7
D
x = 2(y + 1)2 + 8
5

Which point is a solution of x2 + y2 > 49 and y ≤ –x2 – 4?

A
(–8, –1)
B
(–3, 1)
C
(1, –9)
D
(0, –6)
6

What is the radius of the circle with equation ?

Question illustration
A
unit
B
units
C
unit
D
units
7

Which graph represents the hyperbola = 1?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

A plane intersecting a double-napped cone is parallel to the generator. Which conic section is formed?

A
circle
B
ellipse
C
hyperbola
D
parabola
9

An ellipse has vertices along the major axis at (0, 1) and (0, −9). The foci of the ellipse are located at (0, −1) and (0, −7). The equation of the ellipse is in the form below.

Question illustration
A
a = 10
B
b = 4
C
h = 3
D
k = 0
10

The graph of an ellipse is shown.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
11

The cable for a certain suspension bridge is modeled by a parabola with vertex (0, 0) at the center of the bridge. At a point that is 150 ft from the center of the bridge, the height of the cable is 30 ft. Which equation represents the height of the cable at a distance x feet from the center?

A
y = StartFraction 1 Over 3,000 EndFraction x squared
Option A
B
y = StartFraction 1 Over 750 EndFraction x squared
Option B
C
y = StartFraction 1 Over 25 EndFraction x squared
Option C
D
y = StartFraction 1 Over 6 EndFraction x squared
Option D
12

Question text not available

Question illustration
A
(1,−2)
B
(1, 1)
C
(1, 3)
D
(1, 6)
13

Which inequality has (–2.5, –4.5) as part of the solution set?

A
StartFraction (x minus 2) squared Over 16 EndFraction + StartFraction (y minus 6) squared Over 16 EndFraction less-than 1
Option A
B
StartFraction (x + 2) squared Over 16 EndFraction + StartFraction (y minus 6) squared Over 16 EndFraction less-than 1
Option B
C
StartFraction (x + 2) squared Over 16 EndFraction + StartFraction (y + 6) squared Over 16 EndFraction less-than 1
Option C
D
StartFraction (x minus 2) squared Over 16 EndFraction + StartFraction (y + 6) squared Over 16 EndFraction less-than 1
Option D
14

Which statement describes the graph of y + 2 ≥ –4(x – 3)2?

A
a parabola opening up, with shading above the vertex
B
a parabola opening up, with shading below the vertex
C
a parabola opening down, with shading above the vertex
D
a parabola opening down, with shading below the vertex
15

What are the foci of the hyperbola whose equation is = 1?

Question illustration
A
(−6, 2) and (14, 2)
B
(−4, 2) and (12, 2)
C
(4,−8) and (4, 12)
D
(4,−6) and (4, 10)
16

Graph .

Question illustration
A
On a coordinate plane, an Ellipse has center point (0, negative 1) and goes through points (0, 1), (7, negative 1), (0, negative 3), and (negative 7, negative 1).
B
On a coordinate plane, an Ellipse has center point (0, 1) and goes through points (0, 3), (7, 1), (0, negative 1), and (negative 7, 1).
C
On a coordinate plane, an ellipse has center point (0, 0) and goes through (0, 8), (2, 0), (0, negative 8), and (negative 2, 0).
D
On a coordinate plane, an ellipse has center point (0, 0.5) and goes through (0, 8), (2, 0), (0, negative 9), and (negative 2, 0).
17

Convert the equation –9x2 + 25y2 – 100y – 125 = 0 into standard form.

A
StartFraction (y + 2) squared Over 9 EndFraction minus StartFraction x squared Over 25 EndFraction = 1
B
StartFraction (y minus 2) squared Over 5 EndFraction minus StartFraction 9 x squared Over 125 EndFraction = 1
C
StartFraction (y minus 2) squared Over 9 EndFraction minus StartFraction x squared Over 25 EndFraction = 1
D
StartFraction (y + 2) squared Over 5 EndFraction minus StartFraction 9 x squared Over 125 EndFraction = 1
18

Given –9x2 + 4y2 – 18x + 16y – 29 ≤ 0, which graph represents the inequality?

A
On a coordinate plane, one part of a conic graph goes through (negative 6, 7), has a vertex at (negative 2, 5), and goes through (4, 10). The second part goes through (negative 6, negative 6), has a vertex at (negative 1, negative 1), and goes through (4, negative 6). Everything inside of the conic graph is shaded.
Option A
B
On a coordinate plane, one part of a conic graph goes through (negative 5, 4), has a vertex at (negative 1, 1), and goes through (2, 3). The other part goes through (negative 3, negative 6), has a vertex at (negative 1, negative 5), and goes through (4, negative 10). Everything inside of the graph is shaded.
Option B
C
On a coordinate plane, one part of a conic graph goes through (negative 5, 4), has a vertex at (negative 1, 1), and goes through (2, 3). The other part goes through (negative 3, negative 6), has a vertex at (negative 1, negative 5), and goes through (4, negative 10). Everything outside of the graph is shaded.
Option C
D
On a coordinate plane, one part of a conic graph goes through (negative 6, 7), has a vertex at (negative 2, 5), and goes through (4, 10). The second part goes through (negative 6, negative 6), has a vertex at (negative 1, negative 1), and goes through (4, negative 6). Everything outside of the conic graph is shaded.
Option D
19

Which graph represents the solution of y ≤ x2 + 1 and x > y2 – 5?

A
On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 1) and goes through (2, 6). Another parabola opens to the right and goes through (4, 3), has vertex (negative 5, 0), and goes through (4, negative 3). Everything outside of the first parabola and inside of the second parabola is shaded.
Option A
B
On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 1) and goes through (2, 6). Another parabola opens to the right and goes through (4, 3), has vertex (negative 5, 0), and goes through (4, negative 3). Everything inside of both parabolas is shaded.
Option B
C
On a coordinate plane, a parabola opens up and goes through (negative 3, 4), has vertex (0, negative 5), and goes through (3, 4). Another parabola opens to the right and goes through (5, 2), has vertex (1, 0), and goes through (5, negative 2). Everything inside of both parabolas is shaded.
Option C
D
On a coordinate plane, a parabola opens up and goes through (negative 3, 4), has vertex (0, negative 5), and goes through (3, 4). Another parabola opens to the right and goes through (5, 2), has vertex (1, 0), and goes through (5, negative 2). Everything inside the first parabola and outside of the second parabola is shaded.
Option D
20

The center of a hyperbola is located at the origin. One focus is located at (0, 20), and its associated directrix is represented by the line y = . What is the equation of the hyperbola?

Question illustration
A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D

Did you find these answers helpful?

More from this Course

RC
25 verified answers

Cumulative Exam

Quiz
50 verified answers

Cumulative Exam