For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with z° = 30, the value of w° is 30.

The volume of a cylinder is πr²h:

v = πr²h
v = π(8² x 7)
v = 448π

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.

-4x - 7 > \( \frac{x}{4} \)
4 x (-4x - 7) > x
(4 x -4x) + (4 x -7) > x
-16x - 28 > x
-16x - 28 - x > 0
-16x - x > 28
-17x > 28
x > \( \frac{28}{-17} \)
x > -1\(\frac{11}{17}\)

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 + 22y + 67 = 5y - 5
y² + 22y + 67 + 5 = 5y
y² + 22y - 5y + 72 = 0
y² + 17y + 72 = 0

Next, factor the quadratic equation:

y² + 17y + 72 = 0
(y + 8)(y + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 8) or (y + 9) must equal zero:

If (y + 8) = 0, y must equal -8
If (y + 9) = 0, y must equal -9

So the solution is that y = -8 or -9

An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.