Algebra
Solve for x:
2(x - 3) + 4 = 3(2x + 1)
x = -5/4
A rectangular room is 5 meters long, 3 meters wide, and 2.5 meters high. What is the volume of the room in cubic meters?
37.5 m3
Factor completely:
3x2 - 12x
3x(x - 4)
In a right triangle, the length of the hypotenuse is 10 units, and one of the acute angles is 30 degrees. What is the length of the shorter leg?
5 units
A bag contains 5 red marbles, 8 blue marbles, and 7 green marbles. If one marble is drawn randomly, what is the probability that it will be blue?
2/5 or 40%
Simplify the expression:
3(2x - 4) - 2(3x + 1)
-14
The average of five numbers is 25. If one of the numbers is removed from the group, the average becomes 30. What is the value of the removed number?
5
Simplify:
√(9x2)
3x
A cylindrical tank with a radius of 5 meters is filled with water to a height of 8 meters. What is the volume of the water in the tank?
200π m3 or about 628.32 m3
The area of a rectangular garden is 96 square feet. Its length is 4 feet longer than its width. Find the dimensions of the garden.
Width = 8ft, Length = 12ft
The equation y = 2x - 3 represents a linear function. What does the coefficient 2 represent in the context of this function?
The slope of the line
A company's sales increased by 15% each year for three consecutive years. If their sales were $1,000,000 at the end of the third year, what were their initial sales at the beginning of year one?
Expand and simplify the expression:
(2x + 3)2
4x2 + 12x + 9
A regular hexagon is inscribed in a circle with a radius of 6 inches. what is the perimeter of the hexagon?
36 inches
John can wash a car in 30 minutes. Sarah can wash the same car in 20 minutes. If they work together, how long will it take them to wash the car?
12 minutes
Solve the system of equations:
x - 7y = -11
5x + 2y = -18
(-4, 1)
A car travels at a constant speed for the first 3 hours at 60 miles per hour. It then travels at another constant speed for the next 2 hours at 40 miles per hour. What is the car's average speed for the entire journey?
52 mph
Solve for x:
x2 + 5x + 6 = 0
x = -3 and x = -2
Find the area of a trapezoid with a height of 8 units, a base of 10 units, and a shorter parallel side of 4 units.
60 square units
The sum of three consecutive integers is less than 150. Find the largest possible value of the smallest integer.
48
If 4x - 2y = 10 and 2x + 5y = 1, what is the value of y?
y = -2/3
A survey of 300 people found that 40% prefer tea, 30% prefer coffee, and the rest had no preference. If 90 people had no preference, how many people prefer coffee?
90 people
What is the maximum area of a garden with a perimeter of 40 meters?
100 m2
If sin(θ) = 3/5, what is the value of cos(θ)?
4/5
You invest $5000 in a savings account with a 3% annual interest rate, compounded yearly. How much money will you have in the account after 5 years?
Approximately $5796.37