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

sa = 2πr² + 2πrh
sa = 2π(1²) + 2π(1 x 3)
sa = 2π(1) + 2π(3)
sa = (2 x 1)π + (2 x 3)π
sa = 2π + 6π
sa = 8π

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(4 + 5)(3)
a = ½(9)(3)
a = ½(27) = \( \frac{27}{2} \)
a = 13\(\frac{1}{2}\)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 41° - 30° = 109°

So, d° = 30° + 109° = 139°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 41° = 139°

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

z² + 14z + 48 = 0
(z + 6)(z + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 6) or (z + 8) must equal zero:

If (z + 6) = 0, z must equal -6
If (z + 8) = 0, z must equal -8

So the solution is that z = -6 or -8