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

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A pair of listening posts picks up a sound, with one listening post recording the sound after the other. The equation represents possible locations of the sound source with units in feet. How far apart are the listening posts?

A

1,375 ft

B

2,750 ft

C

3,000 ft

D

6,000 ft

3

Which equation represents a hyperbola?

A

4x2 + 3x + 4y2+ 5 = 0

B

2x2 – 5xy + 4y2 + 10x – y + 12 = 0

C

3x2 – 6xy + 3y2 + 5x – 2y + 1 = 0

D

3x2 + xy – 9y2 + 2x + 5 = 0

4

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

5

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

B

StartFraction (x + 2) squared Over 16 EndFraction + StartFraction (y minus 6) squared Over 16 EndFraction less-than 1

C

StartFraction (x + 2) squared Over 16 EndFraction + StartFraction (y + 6) squared Over 16 EndFraction less-than 1

D

StartFraction (x minus 2) squared Over 16 EndFraction + StartFraction (y + 6) squared Over 16 EndFraction less-than 1

6

Which ordered pair is a solution of 9(x – 2)2 – 4(y + 5)2 ≥ 36?

A

(2, –3.5)

B

(2, 5.5)

C

(–7.5, –5)

D

(1.5, –5)

7

A yard dart is thrown from a height of 3 feet with an initial velocity of 25 feet per second at an elevation angle of 70°. How long is the dart in the air? Round to the nearest tenth.

A

0.7 seconds

B

0.8 seconds

C

1.5 seconds

D

1.6 seconds

8

Eliminate the parameter in the equations x = 5cos(t) – 7 and y = 5sin(t) + 9. How can the rectangular equation be described?

A

circle

B

ellipse

C

parabola

D

hyperbola

9

Which graph is represented by the equation (x + 3)2 + (y – 4)2 = 9?

A

On a coordinate plane, a circle has center (negative 3, 4) and radius 3.

B

On a coordinate plane, a circle has center (3, negative 4) and radius 9.

C

On a coordinate plane, a circle has center (3, negative 4) and radius 3.

D

On a coordinate plane, a circle has center (negative 3, 4) and radius 9.

10

A parabola has the following properties.Vertex at (–2, 1)Directrix is x = 5Which equation represents this parabola?

A

(x + 2) = (y – 1)2

B

28(x + 2) = (y – 1)2

C

–28(x + 2) = (y – 1)2

D

(x + 2) = (y – 1)2

11

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.

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.

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.

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.

12

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)

13

A graphic designer creates a logo in the shape of an ellipse. The equation , with units in centimeters, represents the outer edge of the logo. How tall is the logo?