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 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 1 x 1) + (2 x 1 x 7) + (2 x 1 x 7)
sa = (2) + (14) + (14)
sa = 30

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

x² + 4x + 3 = 0
(x + 1)(x + 3) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 1) or (x + 3) must equal zero:

If (x + 1) = 0, x must equal -1
If (x + 3) = 0, x must equal -3

So the solution is that x = -1 or -3

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(8a)(7ab) + (4a²)(5b)
(8 x 7)(a x a x b) + (4 x 5)(a² x b)
(56)(a¹⁺¹ x b) + (20)(a²b)
56a²b + 20a²b
76a²b

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(3 + 8)(5)
a = ½(11)(5)
a = ½(55) = \( \frac{55}{2} \)
a = 27\(\frac{1}{2}\)