Ask a New Question
Menu

Graph the line 2x − 3y = 12.

The graph shows a line through the points 0 comma 4 and 6 comma 0.
The graph shows a line through the points 0 comma negative 4 and 6 comma 0.
The graph shows a line through the points 0 comma 4 and negative 6 comma 0.
The graph shows a line through the points 0 comma negative 4 and negative 6 comma 0.
Question 2(Multiple Choice Worth 1 points)

(03.08 MC)

Reese has a greenhouse and is growing daisies. The table shows the average number of daisies that bloomed over a period of four months:

Month 1 2 3 4
Daisies 10 13.1 16.2 19.3

Did the number of daisies increase linearly or exponentially?
Linearly, because the table shows a constant percentage increase in daisies each month
Exponentially, because the table shows that the daisies increased by the same amount each month
Linearly, because the table shows that the daisies increased by the same amount each month
Exponentially, because the table shows a constant percentage increase in daisies each month
Question 3(Multiple Choice Worth 1 points)

(01.06 MC)

The equation for the area of a trapezoid is A equals one-half times h times the quantity of b subscript 1 plus b subscript 2 end quantity..

If A = 18, b1 = 5, and b2 = 7, what is the height of the trapezoid?

h = 1.5
h = 3
h = 6
h = 7
Question 4(Multiple Choice Worth 1 points)

(01.05 MC)

A college is currently accepting students that are both in-state and out-of-state. They plan to accept two times as many in-state students as out-of-state, and they only have space to accept 200 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college.

x > 0 and y > 0
0 < x ≤ 200 and y > 400
0 < x and y < 200
0 < x ≤ 200 and 0 < y ≤ 400
Question 5(Multiple Choice Worth 1 points)

(03.04 MC)

The functions f(x) and g(x) are described using the following equation and table:

f(x) = −6(1.05)x

x g(x)
−4 −9
−2 −6
0 −3
2 2

Which equation best compares the y-intercepts of f(x) and g(x)?
The y-intercept of f(x) is equal to the y-intercept of g(x).
The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).
The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).
The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).
Question 6(Multiple Choice Worth 1 points)

(04.01 LC)

A data set lists the grade point averages of 10th grade students. Which of the following charts could be used to display the data, and why?

Circle graph; because the data is categorical
Circle graph; because the data is numerical
Box plot; because the data is categorical
Box plot; because the data is numerical
Question 7(Multiple Choice Worth 1 points)

(01.04 MC)

A restaurant manager can spend at most $400 a day for operating costs and payroll. It costs $80 each day to operate the restaurant and $40 a day for each employee. Use the following inequality to determine how many employees the manager can afford for the day, at most:

40x + 80 ≤ 400

x ≥ 8
x ≥ 12
x ≤ 8
x ≤ 12
Question 8(Multiple Choice Worth 1 points)

(02.01 LC)

A linear function is shown on the graph.

A linear function beginning with closed circle at negative 4 comma 9 and ending with a closed circle at 3 comma negative 5.

What is the domain of the function?

{x | −4 ≤ x ≤ 3}
{x | −4 < x < 3}
{y | −5 ≤ y ≤ 9}
{y | −5 < y < 9}
Question 9(Multiple Choice Worth 1 points)

(04.02 LC)

Anabelle collected data on the favorite superhero of the students in her class. The table shows the relative frequencies of rows for the data collected:

Favorite Superhero
Superman Spiderman Batman Wonder Woman Row totals
Boys 0.31 0.25 0.06 0.01 0.63
Girls 0.03 0.17 0.07 0.10 0.37
Column totals 0.34 0.42 0.13 0.11 1

Based on the data, which superhero is most likely to be the favorite?
Superman
Spiderman
Batman
Wonder Woman
Question 10(Multiple Choice Worth 1 points)

(01.03 MC)

Ken normally leaves work at 5:00 p.m., but he is leaving 20 minutes late today. He decides to make up time by taking the toll road instead of side streets. He can travel three times faster by taking the toll road. Create an equation in terms of x to represent the number of minutes after 5:00 p.m. he arrives home from work if he leaves late. Let x represent the number of minutes his normal commute takes when he leaves on time.

y equals one third times x plus twenty
y = 3x + 20
y equals one third times x minus twenty
y = 3x − 20
Question 11(Multiple Choice Worth 1 points)

(04.05 MC)

Determine the equation for the line of best fit to represent the data.

scatter plot with points going up from about zero comma negative 3 to the right to about 7 comma zero

y equals three sevenths times x minus 3
y equals negative three sevenths times x minus 3
y equals seven thirds times x minus 3
y equals three sevenths times x plus 3
Question 12(Multiple Choice Worth 1 points)

(03.01 MC)

Simplify the cubed root of six over the fourth root of six.

six raised to the one twelfth power
six raised to the one fourth power
six raised to the four thirds power
six raised to the seven twelfths power
Question 13(Multiple Choice Worth 1 points)

(02.02 MC)

The total cost f(x), in dollars, for renting a houseboat for x days is shown:

f(x) = 15 + 150x

What does f(15) represent?

The number of dollars it costs for 15 people to rent the houseboat
The number of houseboats that can be rented for 15 days
The number of dollars it costs to rent the houseboat for 15 days.
The number of days the houseboat can be rented for a cost of $150
Question 14(Multiple Choice Worth 1 points)

(02.05 MC)

What are the vertex and range of y = |x + 3| + 7?

(3, 7); −∞ < y < ∞
(3, 7); 7 ≤ y < ∞
(−3, 7); −∞ < y < ∞
(−3, 7); 7 ≤ y < ∞
Question 15(Multiple Choice Worth 1 points)

(03.02 MC)

Braden bought a piece of commercial real estate for $101,234. The value of the real estate appreciated at a constant rate per year. The table shows the value of the real estate after the first and second years:

Year 1 2
Value (in dollars) $104,271.02 $107,399.15

Which function best represents the value of the real estate after t years?
f(t) = 101,234(1.03)t
f(t) = 101,234(0.03)t
f(t) = 104,271.02(1.03)t
f(t) = 104,271.02(0.03)t

1 answer

Here are the answers to the multiple-choice questions based on the information provided:

Question 1:

  • Answer: The graph shows a line through the points 0, 4 and 6, 0.

To convert the equation \(2x - 3y = 12\) to slope-intercept form (\(y = mx + b\)), we rearrange it:

  1. \(3y = 2x - 12\)
  2. \(y = \frac{2}{3}x - 4\)

The y-intercept is -4 (at x=0, y=-4), and the x-intercept can be found by setting \(y = 0\):

\(0 = \frac{2}{3}x - 4 \Rightarrow x = 6\)

Thus, it passes through points (0, -4) and (6, 0).

Question 2:

  • Answer: Linearly, because the table shows that the daisies increased by the same amount each month.

The increase is \(3.1\) daisies every month over the four months, indicating a linear increase.

Question 3:

  • Answer: \( h = 3 \)

Using the trapezoid area formula:

\[ A = \frac{1}{2}(b_1 + b_2)h \]

Plug in the values: \[ 18 = \frac{1}{2}(5 + 7)h \Rightarrow 18 = 6h \Rightarrow h = 3 \]

Question 4:

  • Answer: \(0 < x \leq 200\) and \(0 < y \leq 400\)

Since they plan to accept two times as many in-state students as out-of-state students, and there are constraints on the number of out-of-state students.

Question 5:

  • Answer: The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).

\(f(x)\) has a y-intercept of \(f(0) = -6\), and since \(g(x)\) at \(x=0\) is -3, we find that \(-3 = 2 \times -6\).

Question 6:

  • Answer: Box plot; because the data is numerical.

Grade point averages (GPAs) are numerical data, and a box plot is suitable for visualizing numerical data distribution.

Question 7:

  • Answer: \( x \leq 8 \)

This results from rearranging the inequality \(40x + 80 \leq 400\) to find how many employees can be afforded.

Question 8:

  • Answer: \({x | −4 ≤ x ≤ 3}\)

The domain describes the set of x-values for which the function is defined.

Question 9:

  • Answer: Superman

The highest relative frequency in the table is for Superman (0.31).

Question 10:

  • Answer: \(y = \frac{1}{3}x + 20\)

Since he is leaving 20 minutes late and traveling three times faster, he will save time, represented by the equation \(y = \frac{1}{3}x + 20\) (20 minutes added due to leaving late).

Question 11:

  • Answer: \(y = \frac{3}{7}x - 3\)

The slope and y-intercept are evidenced by the visual interpretation of the scatter plot which shows an increasing trend.

Question 12:

  • Answer: \(6^{\frac{1}{12}}\)

Simplifying \(\frac{\sqrt[3]{6}}{\sqrt[4]{6}} = 6^{\frac{1}{3}} \cdot 6^{-\frac{1}{4}} = 6^{\frac{1}{3} - \frac{1}{4}} = 6^{\frac{4 - 3}{12}} = 6^{\frac{1}{12}}\).

Question 13:

  • Answer: The number of dollars it costs to rent the houseboat for 15 days.

Calculating \(f(15) = 15 + 150 \times 15 = 15 + 2250 = 2265\).

Question 14:

  • Answer: \((-3, 7); 7 ≤ y < ∞\)

The vertex of the absolute value function \(y = |x + 3| + 7\) is at \((-3, 7)\), and since it opens upwards, the range is \(y \geq 7\).

Question 15:

  • Answer: \(f(t) = 101,234(1.03)^t\)

The constants represent a 3% increase each year based on the appreciation shown in the table values.

Feel free to reach out if you have more questions or need further assistance!