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.

-3a - 9z = a - 6z - 6
-3a = a - 6z - 6 + 9z
-3a - a = -6z - 6 + 9z
-4a = 3z - 6
a = \( \frac{3z - 6}{-4} \)
a = \( \frac{3z}{-4} \) + \( \frac{-6}{-4} \)
a = -\(\frac{3}{4}\)z + 1\(\frac{1}{2}\)

When solving an equation with two variables, 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.)

A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides.

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.

(3a)(5ab) - (9a²)(4b)
(3 x 5)(a x a x b) - (9 x 4)(a² x b)
(15)(a¹⁺¹ x b) - (36)(a²b)
15a²b - 36a²b
-21a²b

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\( \sqrt{2} \)