Question

Question 2

Two siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account, y, can be represented by the equation y = 10x + 25, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 5x + 50.

Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?

2.5 weeks
5 weeks
15 weeks
75 weeks
Question 3:
What is the slope of the line that contains the points (−3, −1) and (3, 8)?

two thirds
three halves
Undefined
0
Question 4: An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.


Outcome Frequency
Heads, Heads 75
Heads, Tails 40
Tails, Tails 35
Tails, Heads 50


What is the P(No Heads)?
85%
75%
37.5%
17.5%
Question 5:
Which linear equation shows a proportional relationship?

y = −2
y = 3x + 1
y equals three halves times x
y equals one half times x minus 3

Question 6: A fair, 6-sided die is rolled 45 times. Predict how many times it will land on a number greater than 4.

one third
4
10
15

Question 7: Triangle UVW is drawn with vertices at U(−1, 1), V(0, −4), W(−4, −1). Determine the coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 90° counterclockwise.

U′(1, −1), V′(0, 4), W′(4, 1)
U′(−1, −1), V′(4, 0), W′(1, −4)
U′(−1, 1), V′(4, 0), W′(1, 4)
U′(−1, 1), V′(0, −4), W′(−4, −1)

Question 8: Data was collected on the price per cupcake on orders of different amounts from a bakery. The scatter plot shows the data that was gathered.

scatter plot titled cupcake pricing with the x axis labeled number of cupcakes and the y axis labeled cost per cupcake in dollars with points at 1 comma 6, 1 comma 5.5, 2 comma 5, 2 comma 5.5, 3 comma 4, 3 comma 4.5, 4 comma 3.5, 5 comma 3, 6 comma 2.5, 7 comma 2.5, 8 comma 2, and 9 comma 1.5

Which of the following describes the pattern of association for the scatter plot?

There is a strong, positive nonlinear association.
There is a weak, positive nonlinear association.
There is a strong, negative linear association.
There is a weak, negative linear association.

Question 9: Polygon ABCD is rotated to get polygon A′B′C′D′.

Graph of polygon ABCD in quadrant 2 with point A at negative 7 comma 5, point B at negative 2 comma 8, point C at negative 2 comma 4, and point D at negative 4 comma 3 and polygon A prime B prime C prime D prime in quadrant 1 with point A prime at 5 comma 7, point B prime at 8 comma 2, point C prime at 4 comma 2, and point D prime at 3 comma 4

Determine the direction and angle of rotation.

270° clockwise rotation
270° counterclockwise rotation
90° counterclockwise rotation
180° clockwise rotation


Question 11: Romi and her friends ran in a terrain race. Their distance, in miles, from the starting line over time, in minutes, is shown on the graph.

graph titled Romi's Terrain Race with the x axis labeled time in minutes and the y axis labeled distance in miles with line segments going from 0 comma 0 to the 40 comma 4 to 80 comma 4 to 100 comma 3 to 120 comma 3 and to 180 comma 0

Which of the following descriptions could represent the graph?

From the starting line, Romi ran 4 miles in 40 minutes, rested for 20 minutes, jogged back 2 miles toward the starting line in 40 minutes, rested for 20 minutes, and walked the last 2 miles back to the starting line.
From the starting line, Romi ran 4 miles in 40 minutes, rested for 40 minutes, jogged back 1 mile toward the starting line in 20 minutes, rested for 20 minutes, and jogged the last 3 miles back to the starting line.
From the starting line, Romi ran 2 miles in 20 minutes, rested for 20 minutes, jogged 2 more miles away from the starting line in 40 minutes, rested for 40 minutes, and jogged the last 4 miles back to the starting line.
From the starting line, Romi ran 2 miles in 20 minutes, rested for 40 minutes, jogged 1 more mile away from the starting line in 40 minutes, rested for 20 minutes, and jogged the last 4 miles back to the starting line.

Answer 1

Question 2:

We need to find the value of x when the amount of money in both accounts is the same. This means that we need to set the two equations equal to each other and solve for x:

10x + 25 = 5x + 50

5x = 25

x = 5

Therefore, after 5 weeks, both siblings will have the same amount of money. The answer is 5 weeks.

Question 3:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). Therefore, the slope of the line passing through (-3, -1) and (3, 8) is (8 - (-1)) / (3 - (-3)) = 9/6 = 3/2. The answer is three halves.

Question 4:

The total number of trials is 200, so the probability of getting no heads is equal to the frequency of getting tails twice, which is 35/200 = 0.175 or 17.5%. The answer is 17.5%.

Question 5:

A proportional relationship is one in which y varies directly with x, that is, y = kx where k is a constant of proportionality. The equation y = -2 is a horizontal line, which means that y does not vary with x and there is no proportional relationship. The equation y = 3x + 1 does not have a constant ratio of y to x, so it does not represent a proportional relationship. The equation y = (3/2)x and y = (1/2)x - 3 both have a constant ratio of y to x, so they represent proportional relationships. The answer is y equals three halves times x or y equals one half times x minus 3.

Question 6:

A fair, 6-sided die has four outcomes greater than 4, namely 5 and 6 on each of two rolls. The probability of getting a number greater than 4 on one roll is 2/6 = 1/3. Since the rolls are independent, the probability of getting a number greater than 4 on 45 rolls is the same as the probability of getting a head on 45 coin flips, which is approximately 0.5 x 45 = 22.5 or 23. The answer is 23.

Question 7:

To rotate a point (x, y) 90 degrees counterclockwise about the origin, we swap the x and y coordinates and negate the new x coordinate. Therefore, to rotate triangle UVW, we apply the same transformation to each of its vertices:

U' = (1, -1)

V' = (4, 0)

W' = (1, 4)

The answer is U′(1, −1), V′(4, 0), W′(1, 4).

Question 8:

The scatter plot shows a decreasing linear association. As the number of cupcakes increases, the cost per cupcake decreases. The slope of the line of best fit would be negative. The answer is there is a strong, negative linear association.

Question 9:

To rotate polygon ABCD to A′B′C′D′, we need to apply a counterclockwise rotation about the origin. To determine the angle of rotation, we can look at the change in coordinates of a point that is not the origin. For example, the point A moves from (-7, 5) to (5, 7), which is a translation of (12, 2).