Algebra
Ele's car is x years old, and Kat's car is y years old. Kat's car is 3 times as old as Ele's car. If Kat's car is also 6 years older than Ele's car, which of the following systems of equations best models this situation?
y = 3x
y - x = 6
-20x2 + 25x2y - 40x = -5x (4x - 5xy + c)
In this given equation, c is a positive constant. What is the value of c?
8
Which of the following percent values is equivalent to 42 out of 50?
84%
Which of the following radian measures is equal to 540°?
(The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2π.
3π radians
Rob is crocheting scarves for a craft fair. He will give away the first 2 scarves and will sell the rest for $8 each. Rob's goal is to earn at least $75. If n represents the number of scarves which Rob needs to crochet to meet his goal, which of the following inequalities best models the situation described above?
8(n - 2) ≥ 75
The equation s = (t + 3)2(t + 2)(t + 1)(t)(t - 1) is graphed on the st‑plane. What is the product of the unique t‑intercepts of the graph?
0
Elsie was a solo performer for 4 of the 15 years she was a professional musician. What is the ratio of the number of years Elsie was a solo performer to the number of years she was a professional musician?
4:15
If x° is equal to 7π radians, what is the value of x ?
(The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2π.)
1,260
Each year, one hectare of Moso bamboo in China absorbs 5.1 tons of carbon dioxide, which can compensate for the annual CO2 emissions of 3 people. Which of the following equations best models the number of hectares, h, of Moso bamboo that must be planted to compensate for the annual CO2 emissions of 100 people in China?
100 = 3h
The equation (x3+y) * x5 = x20 is true for all values of x. What is the value of y?
12
A research article Omari was reading showed that middle school students with more nutrition knowledge tend to eat more fruits and vegetables, and middle school students with less nutrition knowledge tend to eat fewer fruits and vegetables. Based on the results of the study, which of the following is a valid conclusion?
a) Eating fruits and vegetables gives middle school students more nutrition knowledge.
b) There is a positive association between nutrition knowledge and fruit and vegetable consumption.
c) There is no association between nutrition knowledge and fruit and vegetable consumption.
d) A student who has a lot of nutrition knowledge must eat a lot of fruits and vegetables.
There is a positive association between nutrition knowledge and fruit and vegetable consumption.
Which of the following radian measures is equal to 315°
7π/4
The quantitative theory of money states that given M dollars in circulation in a year, a monetary velocity of V, a price level of P, and a real output of Q dollars, the given equation is correct. An economist considers the case where the dollars in circulation and the real output are known constants. Which of the following expressions is the change in monetary velocity as the price level increases by 1?
Q/M
x-5√ x+6=0
What are the possible values of x that solve the given equation?
a) 1 and 4
b) 4 and 9
c) 9 and 16
d) 9 and 25
4 and 9
A food reporter conducted a survey to determine whether people in a certain city like the new dessert created by Chef Domenica. The reporter asked 87 people who were waiting in line outside of Chef Domenica's bakery on a Tuesday, and 9 people refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about whether people in the city like Chef Domenica's new dessert?
a) Sample size
b) Population size
c) Where the survey was given
d) The number of of people who refused to respond
Where the survey was given
A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches (in). The volume of the dictionary will be 216 in3. What must be the area of the front cover, a face perpendicular to the thickness, in square inches?
72
4 - 3y= 6y + 4 - 9y
Which of the following best describes the solution set to the equation shown?
The equation has infinitely many solutions.
(x2+9x+20)/(x2+3x-10)
Which expression is equivalent to the given expression for all x>0?
(x+4)/(x-2)
Based on random samples of river heights, oceanographers estimate that 4,800 cubic kilometers (km3) of freshwater is discharged into the Arctic Ocean annually. The estimate has a margin of error of 240km3 at the 90% confidence level. Which of the following is the most reasonable claim about the volume of freshwater discharged annually into the Arctic Ocean?
It is between 4,560 and 5,040 km3.
A circle in the xy-plane has its center on the line y=1. If the point (2,-3) lies on the circle and the radius is 4, which of the following could be the center of the circle?
a) (2,-3)
b) (4,1)
c) (2,1)
d) (-4,1)
(2,1)