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Matthew wants to rent a limousine for the prom. He calls the company to find out that the cost is $150 plus $0.25 per mile. Which equation below shows the cost, y, of renting the limousine for x miles?
A.
Y = (150 + .25)x
B.
Y = 15x + .25
C.
Y = 150 - .25x
D.
Y = .25x + 150
Correct Answer D. Y = .25x + 150
Explanation The equation y = .25x + 150 shows the cost, y, of renting the limousine for x miles. The cost is calculated by multiplying the number of miles by $0.25 and adding it to the base cost of $150.
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2.
Which equation below will have a graph that is parallel to the graph of y = -2x + 6
A.
Y = -2x - 6
B.
Y = 2x - 6
C.
Y = 6x - 2
D.
Y = -6x + 2
Correct Answer A. Y = -2x - 6
Explanation The equation y = -2x - 6 will have a graph that is parallel to the graph of y = -2x + 6 because both equations have the same slope (-2). The only difference is that the y-intercept is -6 in the first equation and +6 in the second equation. Since the slope is the same, the lines will have the same steepness and will never intersect. The only difference is that one line will be shifted up or down compared to the other line.
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3.
For the function f(x) = 2x + 5, find the range when the domain is { 0, 1, 2, 3}.
A.
{0, 1, 2, 3}
B.
{7, 9, 11, 13}
C.
{5, 7, 9, 11}
D.
None of theses
Correct Answer C. {5, 7, 9, 11}
Explanation The correct answer is {5, 7, 9, 11}. When we substitute the given domain values {0, 1, 2, 3} into the function f(x) = 2x + 5, we get the corresponding range values {5, 7, 9, 11}. Therefore, the range for the given domain is {5, 7, 9, 11}.
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4.
Which of the following equations represents a horizontal line?
A.
X = 7
B.
Y = 7
C.
Y = 3x - 4
D.
2x + y = 5
Correct Answer B. Y = 7
Explanation The equation y = 7 represents a horizontal line because it has a constant value for y (7) regardless of the value of x. This means that no matter what x is, the y-coordinate will always be 7, creating a line that is parallel to the x-axis and does not slope.
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5.
Which of the following sets of ordered pairs is NOT a function?
A.
(4, 3) (5, 4) (6, 5) (-4, 6)
B.
(3, 7) (4, 6) (3, -7) (6, 0)
C.
(2, 3) (4, 3) (5, 5) (6, 5)
D.
(0, 5) (5, 0) (1, 2) (2, 3)
Correct Answer B. (3, 7) (4, 6) (3, -7) (6, 0)
Explanation The set of ordered pairs (3, 7) (4, 6) (3, -7) (6, 0) is not a function because it contains two pairs with the same x-value (3), but different y-values (7 and -7). In a function, each x-value should correspond to only one y-value.
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6.
Correct Answer -4/3
7.
Given the graph below, which inequality matches the graph?
A.
Y
B.
Yâ‰¥-x+1
C.
Yâ‰¤x+1
D.
Yâ‰¤-x+1
Correct Answer B. Yâ‰¥-x+1
Explanation The graph shows a shaded region above the line y = -x + 1. This means that all the points above this line satisfy the inequality y â‰¥ -x + 1. Therefore, the correct answer is y â‰¥ -x + 1.
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8.
A.
Y = 1/2x - 5
B.
Y = 2x - 4
C.
Y = -1/2x - 5
D.
Y = x + 1
Correct Answer A. Y = 1/2x - 5
9.
Which equation below contains the ordered pairs (1, 2) and (4, 5)?
A.
Y = -x + 9
B.
Y = -x - 9
C.
Y = x + 9
D.
Y = x + 1
Correct Answer D. Y = x + 1
Explanation The equation y = x + 1 contains the ordered pairs (1, 2) and (4, 5). This can be verified by substituting the x-values of the ordered pairs into the equation and checking if the resulting y-values match. For example, when x = 1, y = 1 + 1 = 2, which matches the y-value of the first ordered pair. Similarly, when x = 4, y = 4 + 1 = 5, which matches the y-value of the second ordered pair. Therefore, the equation y = x + 1 is the correct answer.
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10.
A softball league charges each team $350 plus $10 per player. Which table below shows the correct relationship
between the number of players and the team cost?
A.
Option 1
B.
Option 2
C.
Option 3
D.
Option 4
Correct Answer A. Option 1
Explanation Option 1 shows the correct relationship between the number of players and the team cost. It states that the team cost is $350 plus $10 per player, which means that the cost increases by $10 for each additional player.
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11.
A mobile telephone company charges a flat monthly rate of $25 per month plus $0.25 per minute of airtime. How many minutes did Linda use her cellular phone if her telephone bill was $56?
A.
112 Minutes
B.
124 minutes
C.
156 minutes
D.
200 minutes
Correct Answer B. 124 minutes
Explanation Linda's telephone bill was $56. The flat monthly rate is $25, so the remaining $31 must be for airtime usage. Each minute of airtime costs $0.25, so to find the number of minutes Linda used, we divide $31 by $0.25. This gives us 124 minutes. Therefore, Linda used 124 minutes of airtime.
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12.
Jake started with $75 in his savings account. Each week he withdraws $10 to use as spending money. Which equation best describes a, the amount in Jake’s savings account after a certain number of weeks, w?
A.
A = 75w - 10
B.
A = 75w + 10
C.
A = 75 - 10w
D.
A = 10w - 75
Correct Answer C. A = 75 - 10w
Explanation The equation a = 75 - 10w best describes the amount in Jake's savings account after a certain number of weeks. This equation represents that Jake starts with $75 in his savings account (the constant term 75) and then withdraws $10 each week (the coefficient of w is -10). The negative sign indicates that the amount in his savings account decreases each week due to the withdrawals.
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13.
Which of the equations below represents the second step of the solution process?
A.
5(5x + 7) + 3 = â€“ 78
B.
5(5x + 10) = â€“ 78
C.
25x + 15 + 7 = â€“ 78
D.
25x + 3 + 7 = â€“ 78
Correct Answer C. 25x + 15 + 7 = â€“ 78
Explanation The second step of the solution process is to simplify the expression on the left side of the equation. In this case, the equation 5(5x + 10) = -78 represents the second step because it simplifies the expression 5(5x + 7) + 3 by distributing the 5 to both terms inside the parentheses.
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14.
Solve for y: 4x + 2y = 6
A.
Y = -2x + 3
B.
Y = 2x + 3
C.
Y = 2x + 6
D.
Y = -2x + 6
Correct Answer A. Y = -2x + 3
Explanation The given equation is in the form of y = mx + c, where m is the slope and c is the y-intercept. Comparing the equation 4x + 2y = 6 with y = mx + c, we can see that the coefficient of x is -2, which means the slope is -2. The constant term on the right side of the equation is 3, which means the y-intercept is 3. Therefore, the correct equation is y = -2x + 3.
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15.
Which equation below best describes the graph below?
A.
3x - y = 6
B.
2x + y = -6
C.
2x - 3y = -12
D.
-2x + 3y = 4
Correct Answer C. 2x - 3y = -12
Explanation The equation 2x - 3y = -12 best describes the graph below because it has the same slope-intercept form as the graph. The equation represents a linear relationship between x and y, where the coefficient of x is 2 and the coefficient of y is -3. The constant term on the right side of the equation is -12, which corresponds to the y-intercept of the graph. Therefore, this equation accurately represents the relationship between x and y shown in the graph.
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16.
Megan decided to earn some extra money for the holidays by wrapping gifts at the mall. She would earn $15 plus $0.50 for each package she wrapped. The equation for this situation is
y = 0.50x + 15
What is the rate of change and what does it represent in this problem?
A.
$0.50.the amount earned for each package
B.
$0.50, amount earned for coming to work
C.
$15, amount earned for each package
D.
$15, amount earned for coming to work
Correct Answer A. $0.50.the amount earned for each package
Explanation The rate of change in this problem is $0.50. It represents the amount earned for each package that Megan wraps. For every package she wraps, she will earn an additional $0.50.
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17.
Solve the equation for y: 3x - 3y = 12
A.
Y = -x + 4
B.
Y = -x - 4
C.
Y = x - 4
D.
Y = x + 12
Correct Answer C. Y = x - 4
Explanation The given equation is in the form of "3x - 3y = 12". To solve for y, we need to isolate it on one side of the equation. By moving the 3x term to the other side, we get "-3y = -3x + 12". To get y alone, we divide both sides by -3, resulting in "y = x - 4". Therefore, the correct answer is "y = x - 4".
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18.
Which of the following represents a function?
A.
B.
C.
D.
X = 6
Correct Answer B.
Explanation This equation represents a function because it assigns a unique output value (6) to a given input value (x). In a function, each input has only one corresponding output, and in this case, the input value of x will always result in an output value of 6. Therefore, it satisfies the definition of a function.
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19.
If (c, 5c) amd (3c, 2c) are two points on the graph of a line, and c is not equal to 0, what is the slope of the line?
Correct Answer -3/2
Explanation The slope of a line can be determined by finding the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the change in y-coordinates is 2c - 5c = -3c and the change in x-coordinates is 3c - c = 2c. Therefore, the slope of the line is -3c/2c = -3/2.
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20.
Which graph does not represent y as a function of x?
A.
B.
C.
D.
Correct Answer B.
Explanation Remember the vertical line test
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