Random Math Set Builder

A square has sides of length \(10\), and a circle centered at one of its vertices has radius \(10\). What is the area of the union of the regions enclosed by the square and the circle?

A square and an equilateral triangle have equal perimeters. The area of the triangle is \(9\sqrt{3}\) square inches. Expressed in inches the diagonal of the square is?

For what base, \(b,\) is \(14_b+24_b=41_b\) true?

Determine \(k\) so that the roots of \(x^2 + 2kx − 1 = 2k\) will be equal.

Compute the sum of all the roots of \((2x + 3)(x − 4) + (2x + 3)(x − 6) = 0.\)

In triangle \(ABC\), points \(D, E,\) and \(F\) are chosen on \(AB , BC,\) and \(AC\) respectively so that \(DE\) and \(DF\) are parallel to \(AC\) and \(BC\), respectively. If \(BE\) is \(5\) units and \(EC\) is \(3\) units, what is the ratio of the area of triangle \(AFD\) to the area of parallelogram \(DFCE\)?

A regular \(n\)-gon has interior angles of \(171º\). What is the value of \(n\)?

If three people are selected at random from a group of seven men and three women, what is the probability that at least one woman is selected?

Abigail, Brandon, George, Danielle, and Ernie are waiting in line at the movie theater. In how many different ways can they queue up if Danielle must be in front of Brandon?

Real numbers \(x\) and \(y\) satisfy the equation \(x^2 + y^2 = 10x - 6y - 34\). What is \(x + y\) ?

The first four terms of an arithmetic sequence are \(a\), \(x\), \(b\), \(2x\). Find the ratio of \(a\) to \(b\).

For some positive integer n, the number \(110n^3\) has \(110\) positive integer divisors, including \(1\) and the number \(110n^3\). How many positive integer divisors does the number \(81n^4\) have?

The ten-digit number \(363355116K\) is divisible by both \(9\) and \(11\). What is the digit \(K\)?