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 w° = 40, the value of c° is 40.

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.

8a⁹ + 3a⁹ = 11a⁹

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.

(6a)(7ab) - (6a²)(9b)
(6 x 7)(a x a x b) - (6 x 9)(a² x b)
(42)(a¹⁺¹ x b) - (54)(a²b)
42a²b - 54a²b
-12a²b

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.

-8c + 1 > \( \frac{c}{-8} \)
-8 x (-8c + 1) > c
(-8 x -8c) + (-8 x 1) > c
64c - 8 > c
64c - 8 - c > 0
64c - c > 8
63c > 8
c > \( \frac{8}{63} \)
c > \(\frac{8}{63}\)

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

c² = a² + b²
c² = 3² + 1²
c² = 9 + 1
c² = 10
c = \( \sqrt{10} \)