AnswersMA-PrecalculusCumulative Exam

Cumulative Exam — Cumulative exam Answers

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Air traffic controllers are watching two planes on radar to ensure there is enough distance between them. Plane A took off at 10:00 a.m., and plane B took off at the same runway 5 minutes later. Both planes are flying at the same direction angle and the same path. At 10:10 a.m., the airport’s radar system detected plane A at (24, 18) and plane B at (8, 6). The scale on the radar is 1 unit = 25 miles.Which vector represents the path from plane A to plane B, and what is the actual distance between them?

A
components:, distance between planes: about 20 miles
Option A
B
components:, distance between planes: about 500 miles
Option B
C
components:, distance between planes: about 20 miles
Option C
D
components:, distance between planes: about 500 miles
Option D
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Review the diagram.

Question illustration
A
11.49 foot-pounds
B
38.30 foot-pounds
C
574.53 foot-pounds
D
750.00 foot-pounds
3

Given vectors u = ⟨3, 4⟩ and v = ⟨4, 3⟩, what is the measure of the angle between the vectors?

A
0°
B
16.3°
C
163.7°
D
Undefined
4

Heron’s formula: Area =

Question illustration
A
square units
Option A
B
square units
Option B
C
square units
Option C
D
square units
Option D
5

What are the values of x and z in the solution to the system of linear equations below?

Question illustration
A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
6

A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10 units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units.

Question illustration
A
(14)(10)(8) – π(2.52)(8)
Option A
B
(14)(10)(8) + π(2.52)(8)
Option B
C
(10)(8)(14) – π(2.52)(8)
Option C
D
(10)(8)(14) + π(2.52)(8)
Option D
7

Which matrix equation can be used to solve the systems of equations below?3x - 2y = -36x - 5y = -9

A
mc016-1.jpg
Option A
B
mc016-2.jpg
Option B
C
mc016-3.jpg
Option C
D
mc016-4.jpg
Option D
8

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)
9

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
10

What is the diameter of a circle with the equation (x – 4)2 + (y + 6)2 = 64?

A
4
B
8
C
16
D
64
11

The table below shows the number of different types of faucets sold over three months and the total selling price of the items. Number of Faucets Sold and Total Selling Price Kitchen SinkBathroom SinkShowerTotal Selling PriceJanuary1587$2,830February17128$3,450March242521$6,680The company makes a profit of 15% on every faucet sold. What is the profit on one shower faucet?

A
$12.00
B
$13.50
C
$14.15
D
$18.00
12

Which equation can be used to solve for y-value of the solution in the system of linear equations below?

Question illustration
A
=
Option A
B
= 9
Option B
C
= 9
Option C
D
=
Option D
13

Points D, E, and F are on circle C and EF ≅ DF.

Question illustration
A
14°
B
19°
C
26°
D
38°
14

Based on the sketch below, how far is Joey’s house from the park?

Question illustration
A
0.74 mi.
B
0.86 mi.
C
2.21 mi.
D
2.35 mi.
15

Review the graph.

Question illustration
A
y ≤ x2 – 8 and x > y2 + 1
B
y ≥ x2 – 8 and x < y2 + 1
C
y ≤ x2 + 1 and x > y2 – 8
D
y ≥ x2 + 1 and x < y2 – 8
16

Given vectors u = ⟨–2, 1⟩ and v = ⟨4, –2⟩, which statement is true concerning u and v?

A
The vectors form an obtuse angle of approximately 93°.
B
The vectors form an obtuse angle of approximately 96°.
C
The vectors form an obtuse angle of approximately 127°.
D
The vectors point in opposite directions.
17

Amir encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. The matrix representing the encoded text is . What is the secret phrase? Determine the location of spaces after you decode the text.

Question illustration
A
THE BEAN IS GREEN
B
BLUE IS THE GLOVE
C
GREEN IS THE BEAN
D
THE GLOVE IS BLUE
18

What is one possible solution for the triangle below?

Question illustration
A
Y Z similar to 43 point 0, m angle X similar to 94 point 6 degree, m angle Z similar to 17 point 4 degree.
Option A
B
Y Z similar to 19 point 3, m angle X similar to 85 point 4 degree, m angle Z similar to 26 point 6 degree.
Option B
C
Y Z similar to 12 point 9, m angle X similar to 17 point 4 degree, m angle Z similar to 94 point 6 degree.
Option C
D
Y Z similar to 95 point 4, m angle X similar to 26 point 7 degree, m angle Z similar to 85 point 4 degree.
Option D
19

A row operation is performed on a matrix as shown below.What is the value of x?

Question illustration
A
–2
B
–1
C
0
D
3
20

The vertices of a triangle are given in the columns of the matrix . If is found to perform a transformation, what are the coordinates of the transformed triangle?

Question illustration
A
(0, 0), (–4, 0), (0, –5)
B
(0, 0), (–4, 0), (0, 5)
C
(0, 0), (4, 0), (0, –5).
D
(0, 0), (4, 0), (0, 5).

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