You need to find the value of a so solve the first equation in terms of z:

-5a + z = -6
z = -6 + 5a

then substitute the result (-6 - -5a) into the second equation:

-a + 4(-6 + 5a) = -2
-a + (4 x -6) + (4 x 5a) = -2
-a - 24 + 20a = -2
-a + 20a = -2 + 24
19a = 22
a = \( \frac{22}{19} \)
a = 1\(\frac{3}{19}\)

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 d° = 147, the value of a° is 33.

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 2. 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 + 2y - 48
y² + (-6 + 8)y + (-6 x 8)
(y - 6)(y + 8)

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

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.

5x + 5 > \( \frac{x}{6} \)
6 x (5x + 5) > x
(6 x 5x) + (6 x 5) > x
30x + 30 > x
30x + 30 - x > 0
30x - x > -30
29x > -30
x > \( \frac{-30}{29} \)
x > -1\(\frac{1}{29}\)