The volume of a cube is height x length x width:

v = h x l x w
v = 7 x 3 x 6
v = 126

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 48 as well and sum (Inside, Outside) to equal 14. For this problem, those two numbers are 6 and 8. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 14y + 48
y² + (6 + 8)y + (6 x 8)
(y + 6)(y + 8)

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

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 - 3z - 25 = -4z - 5
z² - 3z - 25 + 5 = -4z
z² - 3z + 4z - 20 = 0
z² + z - 20 = 0

Next, factor the quadratic equation:

z² + z - 20 = 0
(z - 4)(z + 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 4) or (z + 5) must equal zero:

If (z - 4) = 0, z must equal 4
If (z + 5) = 0, z must equal -5

So the solution is that z = 4 or -5

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 a° = 34, the value of b° is 146.