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:

y² - 3y + 9 = 2y + 5
y² - 3y + 9 - 5 = 2y
y² - 3y - 2y + 4 = 0
y² - 5y + 4 = 0

Next, factor the quadratic equation:

y² - 5y + 4 = 0
(y - 1)(y - 4) = 0

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

If (y - 1) = 0, y must equal 1
If (y - 4) = 0, y must equal 4

So the solution is that y = 1 or 4

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(7 + 4)(4)
a = ½(11)(4)
a = ½(44) = \( \frac{44}{2} \)
a = 22

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

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 volume of a cylinder is πr²h:

v = πr²h
v = π(8² x 1)
v = 64π