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, 3) and (2, -1) so the slope becomes:

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(3²) + 2π(3 x 4)
sa = 2π(9) + 2π(12)
sa = (2 x 9)π + (2 x 12)π
sa = 18π + 24π
sa = 42π

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\( \sqrt{2} \)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-7a - 2 = -4 + 3a
-7a = -4 + 3a + 2
-7a - 3a = -4 + 2
-10a = -2
a = \( \frac{-2}{-10} \)
a = \(\frac{1}{5}\)

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)