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 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 -64 as well and sum (Inside, Outside) to equal 0. For this problem, those two numbers are -8 and 8. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 64
y² + (-8 + 8)y + (-8 x 8)
(y - 8)(y + 8)

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

The volume of a cube is height x length x width:

v = h x l x w
v = 9 x 8 x 8
v = 576

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -4. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -8) and (2, 0) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = 2x - 4