To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

8c(c - y)
8(-2)(-2 + 2)
8(-2)(0)
(-16)(0)
0

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

-b - 8 < \( \frac{b}{4} \)
4 x (-b - 8) < b
(4 x -b) + (4 x -8) < b
-4b - 32 < b
-4b - 32 - b < 0
-4b - b < 32
-5b < 32
b < \( \frac{32}{-5} \)
b < -6\(\frac{2}{5}\)

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 1² + 4²
c² = 1 + 16
c² = 17
c = \( \sqrt{17} \)

A trapezoid is a quadrilateral with one set of parallel sides.