Algebra
Find the mean of all solutions for x when x^3 + 3x^2 - 10x = 0.
-1
Compute sin(510°).
1/2
Compute the remainder as 85x46 is divided by 7
What is 4?
In a game of split or steal, contestants Ronald and Jacob are equally likely to split as they are to steal. If both participants split the money, they each get half the money. If one steals, and the other splits, the stealer gets all the money. If they both steal, neither get the money. This is the probability Jacob runs home with at least half the money
How many pairs of perfect squares between 1 and 100 inclusive differ by a prime number?
7
An equilateral triangle has two vertices at (0,5) and (8,5). If the third vertex is in the first quadrant, what is the y-coordinate? Express your answer in simplest radical form.
5 + 4√3
What’s the sum of all the factors/divisors of 128
255
If I have 6 indistinguishable balls of yarn, I can distribute them in 3 distinguishable boxes in this number of ways.
What are 28 ways?
What is the greatest possible value of a in the system of equations 5a + 2b = 0 and ab = -10?
2
A rhombus has an area of 108 square units. The lengths of its diagonals have a ratio of 3 to 2. What is the length of the longest diagonal, in units?
18
While conquering Europe, Napoleon’s general Davout has a division consisting of a number of cavalry around 1000. When these horses are lined up into rows of 7, there will be 2 horses remaining. When these horses are lined up in rows. When these horses are lined up in rows of 9, there would be 3 remaining. When these horses are lined up in rows of 5, there are 3 remaining. This is the exact number of cavalry.
What are 1038 horses?
Aaron, Benjamin, Calvin, Danny and Sora run a race. Aaron has a magical device that makes him always ahead of Benjamin (dirty cheater). This is the number of ways the gold, silver, and bronze metals can be distributed.
What are 12 ways?
What is the sum of the coefficients of (x+1)(x2+1)(x-1) when written in expanded form?
0
ABC is triangle with AC = 28 and BC = 56. Let point X be on AB such that CX is the angle bisector of angle ACB. Find the value of AX.
50/3
The number of positive integer pair solutions to the equation:
(1+2a)(2+2b)(2a+b)=32ab
Haha none
The number of unique 6- lettered sequences consisting of only letters A,B, and C such that the sequence utilizes all letters at least once.
What is 540?