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 = \( \sqrt{a} \) = \( \sqrt{16} \) = 4

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 = 4² + 4²
c² = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)

You need to find the value of c so solve the first equation in terms of z:

-6c + z = 3
z = 3 + 6c

then substitute the result (3 - -6c) into the second equation:

8c + 6(3 + 6c) = 9
8c + (6 x 3) + (6 x 6c) = 9
8c + 18 + 36c = 9
8c + 36c = 9 - 18
44c = -9
c = \( \frac{-9}{44} \)
c = -\(\frac{9}{44}\)

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

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 24 as well and sum (Inside, Outside) to equal 11. For this problem, those two numbers are 3 and 8. Then, plug these into a set of binomials using the square root of the First variable (y²):

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

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, 4) and (2, -8) so the slope becomes: