Algebra
2x + 5 = 17
What does x equal?
x is equal to 6.
What's the chance of getting 1, 2, 3, and 4 in that order from 4 dice rolls?
The chance of rolling these values in order is 1/1296 (1/6^4).
What is the smallest positive integer that is divisible by 2, 3, and 5?
The smallest positive integer divisible by 2, 3, and 5 is 30.
What is the area of a rectangle with a length of 6m and a width of 5m?
The area of this rectangle is 30m^2.
What is 91 × 109?
The answer is 9919.
The absolute value of a number (denoted as |x|) is always positive. That is, |3| = 3, but |-3| = 3.
What are all possible values of x if |x + 2| = 7?
The possible values of x are 5 and -9.
How many ways are there to pick 2 books from a set of 5 books? (order does not matter)
How many factors does the number 24 have?
The number 24 has 8 factors.
What is the volume of a cone with a base circumference of 10pi cm and a height of 5cm?
The cone has a volume of 125pi/3 cm^3.
Let i be the square root of -1. What is i^6?
i^6 is -1.
What is the value of c such that x^2 + 4x + c = 0 has exactly one root?
c must be equal to 4 for there to be exactly one root.
If you roll 3 dice, what’s the chance of you landing 6 at least once?
The chance of landing 6 at least once is 91/216.
What is the smallest positive integer that, when divided by 6, gives a remainder of 5, and when divided by 7, gives a remainder of 6?
The smallest integer that satisfies these conditions is 41.
A triangle has angle measures of 30°, 60° and 90°. If the hypotenuse is 17 meters long, what is the length of the shortest side of the triangle?
The length of the shortest side of the triangle is 8.5 meters.
Binary, or base 2, is a counting system where the only numbers are 1 and 0, and numbers increase by powers of 2.
An example is the number 1011₂, which is (1 × 2^3 + 0 × 2^2 + 1 × 2^1 + 1 × 2^0) = 11
What is 1001₂ × 1101₂, expressed in base 10?
1001₂ × 1101₂ in base 10 is 117.
What is the sum of all (not necessarily real) roots of
5x^2 + 27x - 3
The sum of all roots of this equation is -27/5.
What is the chance of getting exactly 3 heads and 7 tails from 10 fair coin flips?
The chance of getting exactly 3 heads and 7 tails out of 10 fair coin flips is 120/1024.
Why are there infinite prime numbers?
This is because if you multiply all known primes and subtract one, the resulting number must either be prime or have a smaller prime factor that divides it
A cube of side length 4cm is cut into 8 identical pieces. What is the surface area of the 8 pieces?
The cube 192cm^2
Bob lives on a series of islands: Alcatraz Island, Bethesda Island, Cataclysm Island, Double Dip Island, and Epipen Island.
There are 8 bridges, each connecting:
Alcatraz Island to Bethesda Island
Alcatraz Island to Cataclysm Island
Alcatraz Island to Double Dip Island
Alcatraz Island to Epipen Island
Bethesda Island to Cataclysm Island
Cataclysm Island to Double Dip Island
Cataclysm Island to Epipen Island
Double Dip Island to Epipen Island
Bob likes the view of his bridges, and wants to go to each bridge exactly once. Which islands can Bob start and end on to accomplish this goal?
Bob can start on Double Dip Island or Epipen Island, and he will end on the opposite island.
As x becomes extremely large, what is the value of (2x^3+5x-1)/(3x^2-3) in relation to x? (an example is ⅜x)
As x becomes extremely large, this value tends towards ⅔x.
An ant travels from the bottom left corner of a grid (at 0, 0). If it can only travel to the right and up (no diagonal, down, or left movement) how many ways are there for it to reach the point (5, 3)?
There are 56 ways to reach the point (5, 3).
The factorial of a number is the number that results from multiplying that number by every number before it, and is expressed as x!.
For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
Find how many zeroes are at the end of 100!.
There are 24 zeroes at the end of 100!.
What is the maximum number of pieces of pizza (pieces do not have to be of equal size or triangle-shaped) that you can make with 25 cuts?
The maximum number of pizza pieces you can make with 25 cuts is 326.
In a magic square, all the rows, columns, and diagonals are the same number. Determine the value of x in this magic square.
|_____| x + 3 |_____|
|_____|_____|_____|
|x + 2 | x - 5 | x |
The value of x is 11.