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 = \( \sqrt{a} \) = \( \sqrt{64} \) = 8

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 = 8² + 8²
c² = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

x² + 4x + 3 = -x - 1
x² + 4x + 3 + 1 = -x
x² + 4x + x + 4 = 0
x² + 5x + 4 = 0

Next, factor the quadratic equation:

x² + 5x + 4 = 0
(x + 1)(x + 4) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 1) or (x + 4) must equal zero:

If (x + 1) = 0, x must equal -1
If (x + 4) = 0, x must equal -4

So the solution is that x = -1 or -4

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 0. 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, -6) and (2, 6) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = 3x + 0