Heart of Algebra
x/4 + 6 = 14
What is the value of x in the expression above?
x = 32
A train travels at a speed of 431 kilometers per hour. Approximately what is the train's speed in miles per hour?
(1 mile ≈ 1.61 kilometer)
268 miles per hour
What are the solution(s) to the equation
72 = 2x2 ?
A cube has a side length of 3 cm. What is its volume in cm3?
27 cm3
If 3 = √(x - 1), what is the value of x?
What is the slope of the line represented by
3x + 4y = 7 ?
If 12 people made up 40% of the workforce at a company, how many people work at the company?
30 people
If b3∙(b4)2 = bx, what is the value of x?
x = 11
If i = √ -1, what is the sum of 3+i and 5+4i ?
8+5i
A survey conducted about the number of cars owned in a household had the following responses:
0 cars: 6 people
1 cars: 15 people
2 cars: 4 people
According to the survey, what is the mean number of cars per household?
0.92 cars per household
In the system of equations:
3x - 4y = 10
2x - 4y = 6
what is the value of y?
y = 1/2
A study of 120,000 randomly selected photos posted to a photography site determined that 4% were pictures of dogs. If the percent of dog pictures is consistent throughout the rest of the photos on the site, and there are 20 billion photos, how many billions of photos on the site are of dogs?
0.8 billion
If f(x) = 3x - 1, and g(x) = x2 + 1, what is the value of g(f(3))?
g(f(3)) = 65
A circle has an area of 36π. It has a sector with a central angle of 48 degrees. What is the area of the sector?
24π/5
If x2 + 11x + 24 = 0, what are the value(s) of x?
x = -3 and -8
A piece of glass with an initial temperature of 99℃ is cooled at a rate of 3℃ per minute. At the same time, a piece of copper with an initial temperature of 0℃ is heated at a rate of 2.5℃ per minute. After how many minutes will the piece of glass and piece of copper be at the same temperature?
18 minutes
A geneticist conducts a study to investigate the prevalence of a certain genetic marker in a particular population of United States (US) adults. During the study, the geneticist observes the genetic code of 1,000 randomly selected US adults in that population and finds that 350 of those adults have the genetic marker. According to the results of the study, what is the ratio of observed adults with the genetic marker to observed adults without the genetic marker?
7 : 13
Let a = 125/b + 50c.
What is c expressed in terms of a and b?
c = a/50 + 5/(2b)
What is the value of 135 degrees in radians? (no calculator!)
3π/4 radians
Stacy wants to build a pen out of fence in the shape of a right triangle. If the hypotenuse is 1830 feet long, and one side is 605 feet long, how many feet of fence does she need for the third side?
1727 feet
Let f(x) = (1/3)x + 1. If the graph of the line g(x) is perpendicular to the line of f(x), and g(x) goes through the point (1, -5), what is the value of g(-2)?
g(-2) = 4
Erika plans to purchase seed to plant grass in a large field. She has a map of the region, and calculates the area on the piece of paper to be 180 cm2. The scale on the map shows that 1 cm = 20 ft. If Erika plans to cover every 800 ft2 with 3 pounds of seed, approximately how many pounds of seed will she need to cover the entire field?
270 pounds of seed
y = 2x2 + 13x - 3
y + 3 = 2(x + 3)
If (x,y) is a solution to the system of equations above, and x>0, what is the value of xy?
xy = 2
A circle on the xy-plane has a diameter of 6. If points (2,3) and (-1, 6) lie on the circle, and its center is in Quadrant II, what is the equation of the circle?
(x + 1)2 + (y - 3)2 = 9
243 cubic centimeters