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 = \( \sqrt{a} \) = \( \sqrt{64} \) = 8

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 = 8² + 8²
c² = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

4a⁴ - 5a⁴ = -1a⁴

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(9 + 4)(4)
a = ½(13)(4)
a = ½(52) = \( \frac{52}{2} \)
a = 26

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 equal sign and the answer on the other.

-8a + 1 = \( \frac{a}{-7} \)
-7 x (-8a + 1) = a
(-7 x -8a) + (-7 x 1) = a
56a - 7 = a
56a - 7 - a = 0
56a - a = 7
55a = 7
a = \( \frac{7}{55} \)
a = \(\frac{7}{55}\)

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.

(5a)(9ab) + (8a²)(5b)
(5 x 9)(a x a x b) + (8 x 5)(a² x b)
(45)(a¹⁺¹ x b) + (40)(a²b)
45a²b + 40a²b
85a²b