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.

-z + 2 = 4 + 8z
-z = 4 + 8z - 2
-z - 8z = 4 - 2
-9z = 2
z = \( \frac{2}{-9} \)
z = -\(\frac{2}{9}\)

An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.

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 = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

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 = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(3²) + 2π(3 x 8)
sa = 2π(9) + 2π(24)
sa = (2 x 9)π + (2 x 24)π
sa = 18π + 48π
sa = 66π

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.)