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

c² = a² + b²
c² = 5² + 4²
c² = 25 + 16
c² = 41
c = \( \sqrt{41} \)

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

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 + 7)(4)
a = ½(16)(4)
a = ½(64) = \( \frac{64}{2} \)
a = 32

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 solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

-7a - 8z = 2a - 7z + 3
-7a = 2a - 7z + 3 + 8z
-7a - 2a = -7z + 3 + 8z
-9a = z + 3
a = \( \frac{z + 3}{-9} \)
a = \( \frac{z}{-9} \) + \( \frac{3}{-9} \)
a = -\(\frac{1}{9}\)z - \(\frac{1}{3}\)