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

c² = a² + b²
c² = 4² + 1²
c² = 16 + 1
c² = 17
c = \( \sqrt{17} \)

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.

8a + 8a = 16a

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 c° = 13, the value of y° is 167.

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -72 as well and sum (Inside, Outside) to equal 1. For this problem, those two numbers are -8 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + y - 72
y² + (-8 + 9)y + (-8 x 9)
(y - 8)(y + 9)

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 8 x 9) + (2 x 9 x 2) + (2 x 8 x 2)
sa = (144) + (36) + (32)
sa = 212