Algebra
Find a quadratic polynomial with roots 2 and 3.
y=(x-2)(x-3)
or
y=x2-5x+6
Find the dimensions of the rectangle with the largest possible area if the perimeter is 24 units.
6 x 6
This specific angle is formed by the line of sight looking upward from the horizontal when observing an object above you.
Angle of elevation
Find three distinct non-negative integers whose sum is 9, and where exactly all numbers are multiples of 3.
0, 3, and 6
Amy has 3 shirts, 4 bottoms, and 2 pairs of shoes in a box. If an outfit consists of a shirt, a bottom, and a pair of shoes, how many different outfits can Amy make using clothes from the box?
??
Find a cubic polynomial with roots 2, 3, and 4.
y=(x-2)(x-3)(x-4)
or
y=x3-9x2+26x-24
Find the perimeter of an equilateral triangle with area β3.
Perimeter = 6
In a right triangle, if one leg is 5 and the adjacent angle theta has a tangent of 12/5, the length of the opposite leg is this value.
12
Express as a rational number in lowest terms 2 1/3 divided by 4 1/5
5/9
Find the probability that a roll of two dice gives a total greater than 9.
1/6 or 16.67%
Write the equation of the line perpendicular to y=-2x+4 that passes through the point (4, 1).
y=1/2x-1
or
y=1/2(x-4)+1
What is the area of the figure inside the x-axis, the line
y = 2x, the line y = x + 1, and the line y = 3?
Area = 5/4 or 1.25
Say βABC is a right triangle with right angle A. If tan(C) = 12/5, find cos(A).
0
A= (1+2(3-4))(5+6) and B=1+2*3-4*5+6
Find A-B
-4
Two hours from now, it will be half as long until midnight as it will be one hour from now. What time is it now? Express your answer in the form of hours:minutes.
9:00 pm
If (x2y-12)4*(xy)3/(x5y2)-3 is expressed xmyn, what is the value of m+n?
-13
A sphere is inscribed in a cube. If the surface area of the cube is 216 square units, what is the volume of the sphere?
36pi cubic units
From the top of a fire tower, a forest ranger sees a partner on the ground at an angle of depression of 40 degrees. If the tower is 45 feet high, how far is the partner from the base of the tower (rounded to the nearest tenth)?
53.7 feet
The sum of the digits of a two-digit number is 9. When the digits are reversed, the number increases by 63. Find the number.
18
The price of a pair of shoes is reduced by 20%, and the new price is later reduced by 25%. If the final price is $36, what was the original price of the shoes?
$60
A quadratic polynomial π(π₯) satisfies π(0) = 3, π(1) = 5, and π(2) = 8. Find the value of π(5).
23
Find the equation of a circle that has a center at (3,-3) and has both the x-axis and y-axis as tangent lines.
(x-3)2+(y+3)2=9
A Ferris wheel with a radius of 15 meters turns at a constant speed, completing one full rotation every 40 seconds. A passenger boards from a platform 2 meters above the ground and time t = 0. Write the height of the passenger off the ground as a function of t.
h(t)=-15cos(pi/20t)+17
The sum of a perfect square and a positive perfect cube is 241. What is the value of their product?
5400
What is the smallest positive integer whose digits consist only of 6s and 7s that is divisible by both 6 and 7?
76776