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 formula for circumference is circle diameter x π. Circle diameter is 2 x radius:

c = πd
c = π(2 * r)
c = π(2 * 6)
c = 12π

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

sa = 2πr² + 2πrh
sa = 2π(6²) + 2π(6 x 4)
sa = 2π(36) + 2π(24)
sa = (2 x 36)π + (2 x 24)π
sa = 72π + 48π
sa = 120π

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 < sign and the answer on the other.

-5z + 7 < -2 - z
-5z < -2 - z - 7
-5z + z < -2 - 7
-4z < -9
z < \( \frac{-9}{-4} \)
z < 2\(\frac{1}{4}\)

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, \(c = \sqrt{a + b}\)