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° = 150, the value of d° is 150.

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:

y² + 4y + 17 = -4y + 1
y² + 4y + 17 - 1 = -4y
y² + 4y + 4y + 16 = 0
y² + 8y + 16 = 0

Next, factor the quadratic equation:

y² + 8y + 16 = 0
(y + 4)(y + 4) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, (y + 4) must equal zero:

If (y + 4) = 0, y must equal -4

So the solution is that y = -4

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

v = h x l x w
v = 9 x 8 x 8
v = 576

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.

(9a)(8ab) - (8a²)(4b)
(9 x 8)(a x a x b) - (8 x 4)(a² x b)
(72)(a¹⁺¹ x b) - (32)(a²b)
72a²b - 32a²b
40a²b

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{9} \) = 3

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 3² + 3²
c² = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)