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 -63 as well and sum (Inside, Outside) to equal -2. For this problem, those two numbers are -9 and 7. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 2y - 63
y² + (-9 + 7)y + (-9 x 7)
(y - 9)(y + 7)

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

-a + x = 3
x = 3 + a

then substitute the result (3 - -1a) into the second equation:

-6a - 4(3 + a) = -8
-6a + (-4 x 3) + (-4 x a) = -8
-6a - 12 - 4a = -8
-6a - 4a = -8 + 12
-10a = 4
a = \( \frac{4}{-10} \)
a = -\(\frac{2}{5}\)

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

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.

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.

3x + 5 < 8 - 2x
3x < 8 - 2x - 5
3x + 2x < 8 - 5
5x < 3
x < \( \frac{3}{5} \)
x < \(\frac{3}{5}\)