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Linear Programming — Cumulative exam Answers

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For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: Table A a b c up or down y-intercept 0 0 7 up (0, 7) Table B a b c up or down y-intercept 7 0 0 up (0, 0) Table C a b c up or down y-intercept 7 0 0 up (0, 7) Table D a b c up or down y-intercept 0 7 0 up (0, 0)

Question illustration
A
Table A
B
Table B
C
Table C
D
Table D
2
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Complete the following table using the equation: x -3 -1 0 1 3 y Plot the points on a graph and determine which graph best represents the equation. Graph A Graph B

Question illustration
A
-9, -1, 0, -1, -9; Graph B
B
9, 1, 0, 1, 9; Graph B
C
9, 1, 0, 1, 9; Graph A
D
-9, -1, 0, -1, -9; Graph A
3

Complete the following table using the equation: x -2 -1 0 1 2 y Plot the points on a graph and determine which graph best represents the equation. Graph A Graph B

Question illustration
A
8, 2, 0, 2, 8; Graph A
B
-8, -2, 0, -2, -8; Graph A
C
8, 2, 0, 2, 8; Graph B
D
-8, -2, 0, -2, -8; Graph B
4

Make a scatter plot of the data below. x y 25 150 50 178 75 216 100 265 125 323 150 392 175 470.4 Use the quadratic regression feature of a graphing calculator to find a quadratic model. Round to the nearest thousdandths place. a. b. c. d. Please select the best answer from the choices provided

Question illustration
A
A
B
B
C
C
D
D
5

Suppose that the speed of a car, measured in miles per hour (mph), is monitored for a short period of time after the driver applies the brakes. The following table relates the speed of the car to the amount of time, measured in seconds (sec), elapsed from the moment that the brakes are applied. Elapsed Time (sec) 2 4 6 8 10 Speed of Car (mph) 44 29 19 9 4 The data is represented in the table graphically with elapsed time on the horizontal axis and speed on the vertical axis. What general trend does the data reflect?

Question illustration
A
With increasing elapsed time, the speed remains the same.
B
With increasing elapsed time, the speed decreases.
C
There is no apparent trend in the data.
D
With increasing elapsed time, the speed increases.
6

The Air Quality Index, or AQI, measures how polluted the air is in your city and assigns a number based on the quality of the air. Over 100 is "Unhealthy". The following quadratic regression equation, models the AQI over time, where n represents the number of days the AQI exceeded 100, and t represents the number of years since 1990. Estimate the number of days the AQI exceeded 100 in the year 2002. Round to the nearest whole day. (Hint: t = 0 corresponds to the year 1990.)

Question illustration
A
281 days
B
97 days
C
135 days
D
52 days
7

Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.

Question illustration
A
both f and g open downward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis
B
both f and g open upward; low point of f is 3 units above the x-axis; the low point of g is 3 units below the x-axis
C
both f and g open upward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis
D
both f and g open downward; low point of f is 3 units above the x-axis; the low point of g is 3 units below the x-axis
8

The graph represents a mechanic’s labor costs for a given number of hours of car repair.

Question illustration
A
All repairs requiring 1 hour or less have the same labor cost.
B
Labor costs the same no matter how many hours are used for a repair.
C
Labor costs for a repair are less expensive as the number of hours increases.
D
There is no cost of labor for a repair requiring less than 1 hour.
9

Which linear function represents the line given by the point-slope equation y + 7 = –(x + 6)?

Question illustration
A
f(x) = –x – 11
Option A
B
f(x) = –x – 1
Option B
C
f(x) = –x + 3
Option C
D
f(x) = –x + 13
Option D
10

Giselle graphs the function f(x) = x2. Robin graphs the function g(x) = –x2. How does Robin’s graph relate to Giselle’s?

A
Robin’s graph is a reflection of Giselle’s graph over the x-axis.
B
Robin’s graph is a reflection of Giselle’s graph over the y-axis.
C
Robin’s graph is a translation of Giselle’s graph 1 unit down.
D
Robin’s graph is a translation of Giselle’s graph 1 unit left.
11

Which graph represents the solution of x2 + (y – 2)2 8x?

A
On a coordinate plane, a circle has center (0, 2) and radius 3. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and inside of the parabola is shaded.
Option A
B
On a coordinate plane, a circle has center (0, 2) and radius 3. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and outside of the parabola is shaded.
Option B
C
On a coordinate plane, a circle has center (2, 0) and radius 6. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and outside of the parabola is shaded.
Option C
D
Option
Option D
12

What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36?

A
(−4, 0) and (9, 0)
B
(4, 0) and (−9, 0)
C
(−3, 0) and (12, 0)
D
(3, 0) and (−12, 0)
13

Describe what is happening in this graph.

Question illustration
Answer:

The skater’s speed decreases at first, then increases to a peak. After that, the speed decreases and eventually stays constant.

14

The graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants.

Question illustration
A
1.5
B
2
C
13
D
15.5
15

Which system of equations is consistent and dependent?

A
mc014-1.jpg
Option A
B
mc014-2.jpg
Option B
C
mc014-3.jpg
Option C
D
mc014-4.jpg
Option D
16

A coordinate plane with a line passing through points at (0, negative 2) and (4, negative 1).

Question illustration
A
y = 4x – 2
B
y = –4x – 2
C
y = x – 2
Option C
D
y = – x – 2
Option D
17

What is the range of the function f(x) = −(x + 3)2 + 7?

A
all real numbers less than or equal to 7
B
all real numbers greater than or equal to 7
C
all real numbers less than or equal to −3
D
all real numbers greater than or equal to −3
18

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach negative infinity. To which family of functions might the described function belong?

A
absolute value
B
exponential
C
cube root
D
square root
19

The members of the drama club have 100 tickets to sell to the school play. Students pay $5 per ticket, and nonstudents pay $10 per ticket. The drama club needs to collect at least $800 in total ticket sales. The system of inequalities represents the number of student tickets, s, and the number of nonstudent tickets, n, the members must sell. s + n ≤ 1005s + 10n ≥ 800

A
40
B
60
C
80
D
100
20

The system of inequalities in the graph represents the change in an account, y, depending on the days delinquent, x.

Question illustration
A
≤
B
≥
C
<
D
>

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