AnswersMO-Algebra II A-CRPerforming Operations with Complex Numbers

Performing Operations with Complex Numbers — Unit test Answers

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1
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What is the rectangular form of the parametric equations x = 6t and y =?

Question illustration
A
y = StartFraction x squared Over 4 EndFraction
Option A
B
y = StartFraction x squared Over 9 EndFraction
Option B
C
y = StartFraction x Over 144 EndFraction
Option C
D
y = StartFraction x Over 9 EndFraction
Option D
2
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Which conic section is represented by the following equation?–5x2 + 9xy + 5y2 + 6x – 4y + 11 = 0

A
circle
B
ellipse
C
parabola
D
hyperbola
3

The graph of a hyperbola is shown.

Question illustration
A
9 units
B
12 units
C
18 units
D
24 units
4

The foci and the vertices of the hyperbola are labeled.

Question illustration
A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
5

Eliminate the parameter in the equations x = and y = t – 4. How can the rectangular equation be described?

Question illustration
A
cubic
B
linear
C
quartic
D
quadratic
6

A player hits a baseball with an initial velocity of 117 ft/sec at an elevation angle of 50°. When struck, the baseball is 2 feet above the ground. What is the maximum height the baseball reaches?

A
31 feet
B
126 feet
C
211 feet
D
421 feet
7

Which graph represents 9x2 – 16y2 – 54x + 64y – 127 = 0?

A
On a coordinate plane, an Ellipse has center (3, 2) and goes through (7, 2), (3, negative 1), (negative 1, 2), and (3, 5).
Option A
B
On a coordinate plane, an Ellipse has center (3, 2) and goes through (6, 2), (3, negative 2), (0, 3), and (3, 6).
Option B
C
Option
Option C
D
On a coordinate plane, one part of a conic graph goes through (negative 1, 6), has a vertex at (0, 2), and goes through (negative 1, negative 1). The second part goes through (7, 6), has a vertex at (6, 2), and goes through (7, negative 1).
Option D
8

Review the graph of circle A.

Question illustration
A
(x – 1)2 + (y – 1)2 = 5
B
(x + 1)2 + (y + 1)2 = 5
C
(x – 1)2 + (y – 1)2 = 25
D
(x + 1)2 + (y + 1)2 = 25
9

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
10

Question text not available

Question illustration
A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
11

Which image shows a plane slicing a double-napped cone to produce a hyperbola?

A
2 cones are stacked at their points. A horizontal plane goes through the center of a cone.
Option A
B
2 cones are stacked at their points. A plane goes diagonally through the center of a cone.
Option B
C
2 cones are stacked at their points. A plane goes diagonally along the sides of the cones.
Option C
D
2 cones are stacked at their points. A plane goes diagonally through both cones.
Option D
12

Which features describe the graph of =1? Select two options.a focus at (104, 0)a focus at (0,−96)a vertex at (−40, 0)a vertex at (0, 96)the center at (0, 0)

Question illustration
A
a focus at (104, 0)
B
a focus at (0,−96)
C
a vertex at (−40, 0)
D
a vertex at (0, 96)
E
the center at (0, 0)
13

A bicycle path starts 5 miles due east of an intersection, and continues in a straight line to finish 8 miles due north of the same intersection. Let the intersection be represented by the point (0, 0). Suppose a cyclist rides the path from start to finish in 2 hours. Which parametric equations model the path of the rider?

A
x (t) = negative five-halves t + 5 and y (t) = 4 t
Option A
B
x (t) = negative five-halves t + 5 and y (t) = 4 t + 8
Option B
C
x(t) = 5t + 2 and y(t) = 8t
D
x(t) = 5t and y(t) = 8t + 2
14

Which equation represents a parabola with its vertex at (1, –5) and its focus at (1, 0)?

A
= (x – 1)2
Option A
B
20(y + 5) = (x – 1)2
C
–20(y + 5) = (x – 1)2
D
= (x – 1)2
Option D
15

One focus of a hyperbola is located at (−1, 7). One vertex of the hyperbola is located at (−1, 5). The center is (−1, −3).What is the equation of the hyperbola?

A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
16

Eliminate the parameter in the equations y = t + 2 and x = . How can the rectangular equation be described?

Question illustration
A
cubic
B
linear
C
quartic
D
quadratic
17

A soccer ball on the ground was kicked with an initial velocity of 35 ft/sec at an elevation angle of 40°. Create a set of parametric equations to model the path of the soccer ball. Approximately how far had the soccer ball traveled when it hit the ground?

A
19 feet
B
26 feet
C
38 feet
D
52 feet
18

Convert 9x2 + 4y2 – 54x – 8y – 59 = 0 into standard form.

A
StartFraction (x + 3) squared Over 4 EndFraction + StartFraction (y + 1) Over 9 EndFraction = 1
Option A
B
StartFraction (x minus 3) squared Over 4 EndFraction + StartFraction (y minus 1) Over 9 EndFraction = 1
Option B
C
StartFraction (x + 3) squared Over 16 EndFraction + StartFraction (y + 1) Over 36 EndFraction = 1
Option C
D
StartFraction (x minus 3) squared Over 16 EndFraction + StartFraction (y minus 1) Over 36 EndFraction = 1
Option D
19

A coach throws a football from a height of 4 feet with an initial velocity of 59 feet per second at an elevation angle of 45°. Which parametric equations represent the path of the football?

A
x(t) = 59sin(45o)t and y(t) = –16t2 + 59cos(45o)t
B
x(t) = 59cos(45o)t and y(t) = –16t2 + 59sin(45o)t
C
x(t) = 59cos(45o)t and y(t) = –16t2 + 59sin(45o)t + 4
D
x(t) = 59sin(45o)t and y(t) = –16t2 + 59cos(45o)t + 4
20

Which rectangular equation represents the parametric equations x = and y = 4t?

Question illustration
A
y = 4x2, for x ≥ 0
B
y = one-fourth x squared, for x greater-than-or-equal-to 0
Option B
C
y = 16x2, for x ≥ 0
D
y = StartFraction 1 Over 16 EndFraction x squared, for x greater-than-or-equal-to 0
Option D

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