The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

The formula for circumference is circle diameter x π:

c = πd
c = 8π

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 8 x 3) + (2 x 3 x 4) + (2 x 8 x 4)
sa = (48) + (24) + (64)
sa = 136

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

z² - 2z - 29 = -z + 1
z² - 2z - 29 - 1 = -z
z² - 2z + z - 30 = 0
z² - z - 30 = 0

Next, factor the quadratic equation:

z² - z - 30 = 0
(z + 5)(z - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 5) or (z - 6) must equal zero:

If (z + 5) = 0, z must equal -5
If (z - 6) = 0, z must equal 6

So the solution is that z = -5 or 6

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.