1
In the figure, line n intersects lines r and s. Line r is parallel to line s. What is the value of x ?
164
2024.6 B
Math · 44 questions Go to Reading and Writing
Module 1 (Medium)
2
During a portion of a flight, a small airplane's cruising speed varied between 175 miles per hour and 195 miles per hour. Which inequality best represents this situation, where s is the cruising speed, in miles per hour; during this portion of the flight?
- As≤20
- Bs≤175
- Cs≤195
- Ds<=20175≤s≤195
D
3
If 5x = 9, what is the value of 20x?
- A5
- B13
- C36
- D49
C
4
Which expression is equivalent to(x^3+9^()x^2^()-8x)+5(x^2+8) ?
- Ax^3+14x^2-8x+40
- Bx^3+9x^2-8x+40
- Cx^3+5x^2-8x+40
- Dx^3+8x^2-8x+40
A
5
The function f is defined by f(x)=x^3+9 . What is the value of f (2)?
17
6
The function g is defined by g(x)=x/2 . For what value of x does g(x)=620 ?
1240
The scatterplot shows the relationship between two variables, x and y.
7
Which of the following equations is the most appropriate linear model for the data shown?
- Ay=0.8+8.7x
- By=0.8-8.7x
- Cy=8.7+0.8x
- Dy=8.7-0.8x
D
8
3x-2y=-18
For the given equation, which table gives three values of x and their corresponding values of y?
- A
- B
- C
- D
A
9
A chemist combines water and isopropanol to make a mixture with a volume of 41 milliliters (mL). The volume of isopropanol in the mixture is 10 mL. What is the volume of water, in mL, in the mixture? (Assume that the volume of the mixture is the sum of the volumes of water and isopropanol before they were mixed.)
31
10
A clothing store buys shirts at a wholesale price of 4.00 dollars each and resells them each at a retail price that is 280% of the wholesale price. At the end of the season, any remaining shirts are marked at a discounted price that is 80% off the retail price. What is the discounted price of each remaining shirt, in dollars?
2.24
11
y=-1/4x
y=1/6x
The solution to the given system of equations is (x, y). What is the value of x?
- A-4
- B0
- C2
- D6
B
12
PC=N(18-C)
The given equation relates the variables P, N, and C. Which expression represents the value of C for distinct positive values of P and N?
- A(C(N+P))/N
- BPC/(18-C)
- C18N/(N+P)
- D18N/(P+1)
C
13
A company has a customer loyalty program. In January 2018, there were 200 customers enrolled in the loyalty program. For the next 24 months after January 2018, the total number of customers enrolled in the loyalty program each month was 4% greater than the total number enrolled the previous month. Which equation gives the total number of customers, c, enrolled in the company's loyalty program m months after January 2018, where m≤24 ?
- Ac=200(0.04)^m
- Bc=200(1.04)^m
- Cc=200(1.4)^m
- Dc=200(4)^m
B
14
The function f(t)=8,000(2)^(t/300) gives the number of bacteria in a population t minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?
300
15
y=2/9x+8
One of two equations in a system of linear equations is given. The system has infinitely many solutions. What is the slope of the graph of the second equation?
- A-9/2
- B-2/9
- C2/9
- D9/2
C
16
If 3x^2-6x-30=0,what is the value ofx^2-2x?
- A10
- B3
- C2
- D0
A
17
The function f is defined by f(x)=(x-4)(x-11)(x+k) , where k is a constant. In the xy-plane, the graph of y=f(x) passes through the point(-2,0) . What is the value of f (0) ?
- A-156
- B-2
- C13
- D88
D
18
Line k is shown in the xy-plane. Line j (not shown) is perpendicular to line k and passes through the point (-15,-28) . Which equation defines line j?
- Ay=4/3x-8
- By=4/3x-48
- Cy=3/4x-8
- Dy=3/4x-48
A
19
In right triangle ABC, angles A and B are acute, side AC has a length of 23.2, andTanB=1/7 . What is the length of side BC, rounded to the nearest tenth?
- A538.2
- B162.4
- C4.8
- D3.3
B
20
A rectangular banner has an area of 3,500 square inches. A copy of the banner is made in which the length and width of the original banner are each increased by 40%. What is the area of the copy, in square inches?
- A6,860
- B4,900
- C3,580
- D3,540
A
21
f(x)=(x-1)^2+7
What is the minimum value of the given function?
- A1
- B6
- C7
- D8
C
22
Point F lies on a unit circle in the xy-plane and has coordinates (1,0) . Point G is the center of the circle and has coordinates (0,0). Point H also lies on the circle and has coordinates(-1,y) , where y is a constant. Which of the following could be the positive measure of angle FGH, in radians?
- A13π/2
- B15π/2
- C10π
- D11π
D
Module 2 (Advanced)
1
An object's average acceleration, in meters per second squared, is the change in the object's speed, in meters per second, divided by the time during which the change occurred, in seconds. A certain object's speed changes by 45 meters per second in 6 seconds. What is this object's average acceleration, in meters per second squared, during this time period?
- A0.13
- B7.5
- C39
- D51
B
2
x+26=y
(x+26)^2=y
A solution to the given system of equations is (x, y). What is a possible value of x?
- A-25
- B0
- C1
- D26
A
3
Lao walks at a speed of 2 miles per hour and runs at a speed of 6 miles per hour. He walksfor w hours and runs for r hours for a combined total of 10 miles. Which equation represents this situation?
- A2w+6r=10
- B1/2w+1/6r=10
- C2w+6r=80
- D1/2w+1/6r=80
A
4
f(x)=50x+12
The given function f estimates the distance a train has traveled, in kilometers, from a station in a certain city x hours after crossing the city border. What is the best interpretation of 12 in this context?
- ABetween the station and the city border, the train traveled an estimated total distance of 12 kilometers.
- BAfter crossing the city border the train traveled at an estimated speed of 12 kilometers per hour.
- CAfter crossing the city border the train traveled an estimated total distance of 12 kilometers.
- DBetween the station and the city border, the train traveled at an estimated speed of 12 kilometers per hour.
A
5
1/3(x+7)-1/2(x+7)=-8
What value of x is the solution to the given equation?
- A-15
- B-7
- C41
- D132
C
6
The function g is defined byg(x)=4/9x-24. What is the x-coordinate of the x-intercept of the graph of y=g(x) in the xy-plane?
54
7
Two students are playing a game. In the first round, Player 1 answers 49 questions. If an answer is correct, Player 1 earns 1 point. If an answer is incorrect, Player 2 will earn 1 point instead. The graph shows y=f(x) , where y is the number of points Player 2 will earn when x is the number of points Player 1 earns. Which of the following is the best interpretation of the point (49, 0) in this context?
- AWhen Player 1 earns 49 points, Player 2 will earn 49 points.
- BWhen Player 1 earns 49 points, Player 2 will earn 0 points.
- CWhen Player 1 earns 0 points, Player 2 will earn 49 points.
- DWhen Player 1 earns0 points, Player 2 will earn 0 points.
B
8
Which expression is a factor of 3x^2-5x+6x-10?
- Ax-2
- Bx+5
- C3x-5
- D3x+2
C
9
The graph shows the momentum y, in newton-seconds, of an object x seconds after the object started moving, for0≤x≤8. What is the average rate of change, in newton-seconds per second, in the momentum of the object from x=2 tox=6 ?
1.25,5/4
10
(x+64)^2=-100
How many distinct real solutions does the given equation have?
- AExactly one
- BExactly two
- CInfinitely many
- DZero
D
11
|x-8| =11
What is the sum of the solutions to the given equation?
- A0
- B16
- C19
- D22
B
12
The manager of a gym selected a sample of 159 members at random to estimate the percentage of the gym's members that would continue to pay for a membership if the price increased. From the survey, the manager estimates that 88% of the gym's members would continue to pay for a membership if the price increased, with an associated margin of error of 5.05%. If the survey is repeated with a random sample of 318 members and the results are calculated in the same way, which of the following will be the most likely effect of using the larger random sample compared to the smaller random sample?
- AThe margin of error will be lower.
- BThe margin of error will be higher.
- CThe estimate of the percentage of the gym's members that would continue to pay for a membership if the price increased will be lower.
- DThe estimate of the percentage of the gym's members that would continue to pay for a membership if the price increased will be higher.
A
The maximum temperature on April 1. in degrees Fahrenheit (°F), was recorded each year at a certain weather station for 11 years. The histogram summarizes the recorded data set.
13
The temperature of 76.2 °F is removed from this data set to create a new data set of 10 temperatures. Which of the following statements must be true?
I.The mean of the new data set is less than the mean of the original data set.
II.The median of the new data set is less than the median of the original data set.
- AI only
- BII only
- CI and II
- DNeither I nor II
A
14
For the positive quantities h, j, and k, 44% of h is equivalent to 62% of j, and j is equivalent to 22% of k. What percentage of k is h? (Disregard the % sign when entering your answer. For example, if your answer is 39%, enter 39)
31
15
The graph shows the relationship between the number of shares of stock from Company A, x , and the number of shares of stock from Company B, y, that Sayen can purchase. Which equation could represent this relationship?
- Ay=10x+18
- B10x+18y=900
- Cy=18x+10
- D18x+10y=900
B
16
For the exponential function f , the value of f(1) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?
- Af(x)=35(1.2)^(x+1)
- Bf(x)=42(1.2)^x
- Cf(x)=50.4(1.2)^(x-1)
- Df(x)=60.48(1.2)^(x-2)
C
17
In triangle PQR, the measure of angle P is(4x+9)°, the measure of angle Q is(5x+4)°,and the measure of angle R is(5y+4)°. If side QR is extended through point R to point S, and the measure of angle PRS is (x+y)° , what is the value of x+y?
31
18
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of 5 and 9, which inequality represents the possible lengths, x, of the third side of the triangle?
- Ax<14
- Bx>14
- C4<x<14
- Dx<4 orx>14
C
19
A right circular cone has a volume of 34,496π cubic centimeters and the area of its base is 3,136π square centimeters. What is the slant height, in centimeters, of this cone?
- A11
- B33
- C56
- D65
D
20
A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object was launched. According to the model, the object was launched from a height of 0 feet and reached its maximum height of 400 feet 5 seconds after it was launched. Based on the model, what was the height. in feet, of the object 9 seconds after it was launched?
144
21
The cost of renting a power washer is $56 for the first day and $28 for each additional day. Which of the following functions gives the cost C(d), in dollars, of renting the power washer for d days, where d is a positive integer?
- AC(d)=28d+28
- BC(d)=28d+56
- CC(d)=56d-28
- DC(d)=56d+84
A
22
The function ff is defined byf(x)=ax^2+bx+c , where a, b, and c are constants. The graph of y=f(x) in the xy-plane passes through the points (8,0) and(-5,0). If a is an integer greater than 1, which of the following could be the value of a+b?
- A4
- B3
- C-2
- D-4
D