The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

The formula for area is πr²:

a = πr²
a = π(2²)
a = 4π

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 7 x 9) + (2 x 9 x 2) + (2 x 7 x 2)
sa = (126) + (36) + (28)
sa = 190

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 8 as well and sum (Inside, Outside) to equal -6. For this problem, those two numbers are -4 and -2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 6y + 8
y² + (-4 - 2)y + (-4 x -2)
(y - 4)(y - 2)

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 = \( \sqrt{a} \) = \( \sqrt{1} \) = 1

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 = 1² + 1²
c² = 2
c = \( \sqrt{2} \)