To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a - 4a = 3a

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 y° = 147, the value of b° is 147.

The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -1) and (2, -7) so the slope becomes:

A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

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 - 22z + 75 = -5z + 3
z² - 22z + 75 - 3 = -5z
z² - 22z + 5z + 72 = 0
z² - 17z + 72 = 0

Next, factor the quadratic equation:

z² - 17z + 72 = 0
(z - 8)(z - 9) = 0

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

If (z - 8) = 0, z must equal 8
If (z - 9) = 0, z must equal 9

So the solution is that z = 8 or 9