The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

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 42 as well and sum (Inside, Outside) to equal 13. For this problem, those two numbers are 6 and 7. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 13y + 42
y² + (6 + 7)y + (6 x 7)
(y + 6)(y + 7)

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 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, 0) so the slope becomes:

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 8² + 7²
c² = 64 + 49
c² = 113
c = \( \sqrt{113} \)