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 - 11y + 17 = -4y + 5
y² - 11y + 17 - 5 = -4y
y² - 11y + 4y + 12 = 0
y² - 7y + 12 = 0

Next, factor the quadratic equation:

y² - 7y + 12 = 0
(y - 3)(y - 4) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 3) or (y - 4) must equal zero:

If (y - 3) = 0, y must equal 3
If (y - 4) = 0, y must equal 4

So the solution is that y = 3 or 4

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.

a + 1 > \( \frac{a}{-4} \)
-4 x (a + 1) > a
(-4 x a) + (-4 x 1) > a
-4a - 4 > a
-4a - 4 - a > 0
-4a - a > 4
-5a > 4
a > \( \frac{4}{-5} \)
a > -\(\frac{4}{5}\)

The volume of a cylinder is πr²h:

v = πr²h
v = π(5² x 8)
v = 200π

A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.

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° - 31° - 67° = 82°

So, d° = 67° + 82° = 149°

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° - 31° = 149°