A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.

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:

z² + 17z + 33 = 5z - 2
z² + 17z + 33 + 2 = 5z
z² + 17z - 5z + 35 = 0
z² + 12z + 35 = 0

Next, factor the quadratic equation:

z² + 12z + 35 = 0
(z + 5)(z + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 5) or (z + 7) must equal zero:

If (z + 5) = 0, z must equal -5
If (z + 7) = 0, z must equal -7

So the solution is that z = -5 or -7

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(9 + 5)(5)
a = ½(14)(5)
a = ½(70) = \( \frac{70}{2} \)
a = 35

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 -72 as well and sum (Inside, Outside) to equal 1. For this problem, those two numbers are -8 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + y - 72
y² + (-8 + 9)y + (-8 x 9)
(y - 8)(y + 9)

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 10cm + 7cm + 10cm = 27cm