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

-9b + 7z = -2b + 7z + 3
-9b = -2b + 7z + 3 - 7z
-9b + 2b = 7z + 3 - 7z
-7b = + 3
b = \( \frac{ + 3}{-7} \)
b = \( \frac{}{-7} \) + \( \frac{3}{-7} \)
b = z - \(\frac{3}{7}\)

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.)

8b(b - y)
8(3)(3 + 9)
8(3)(12)
(24)(12)
288

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.

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 = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

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 = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.