The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 1 x 7) + (2 x 7 x 2) + (2 x 1 x 2)
sa = (14) + (28) + (4)
sa = 46

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y - 8)(y - 3)
(y x y) + (y x -3) + (-8 x y) + (-8 x -3)
y² - 3y - 8y + 24
y² - 11y + 24

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).

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 = \( \sqrt{a} \) = \( \sqrt{9} \) = 3

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 = 3² + 3²
c² = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)

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.

8a + 3x = 2a - 2x + 1
8a = 2a - 2x + 1 - 3x
8a - 2a = -2x + 1 - 3x
6a = -5x + 1
a = \( \frac{-5x + 1}{6} \)
a = \( \frac{-5x}{6} \) + \( \frac{1}{6} \)
a = -\(\frac{5}{6}\)x + \(\frac{1}{6}\)