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 30 as well and sum (Inside, Outside) to equal -11. For this problem, those two numbers are -6 and -5. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 11y + 30
y² + (-6 - 5)y + (-6 x -5)
(y - 6)(y - 5)

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

6a + z = 1
z = 1 - 6a

then substitute the result (1 - 6a) into the second equation:

7a + 7(1 - 6a) = 5
7a + (7 x 1) + (7 x -6a) = 5
7a + 7 - 42a = 5
7a - 42a = 5 - 7
-35a = -2
a = \( \frac{-2}{-35} \)
a = \(\frac{2}{35}\)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 51° - 47° = 82°

So, d° = 47° + 82° = 129°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 51° = 129°

A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.