According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 8² + 9²
c² = 64 + 81
c² = 145
c = \( \sqrt{145} \)

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(8a)(7ab) - (2a²)(3b)
(8 x 7)(a x a x b) - (2 x 3)(a² x b)
(56)(a¹⁺¹ x b) - (6)(a²b)
56a²b - 6a²b
50a²b

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 2. 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, -4) and (2, 8) so the slope becomes:

m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(8.0) - (-4.0)}{(2) - (-2)} \) = \( \frac{12}{4} \)
m = 3

Plugging these values into the slope-intercept equation:

y = 3x + 2

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.

5a + 7a = 12a

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° = 158, the value of c° is 22.