Nataliya's Responses in WyzAnt Answers

a^m · aⁿ = a^m+n
(-x)²(-x)⁵ = (-x)²⁺⁵ = (-x)⁷

(x - 8) ≤ 40/(x + 4) - 90/(x + 5) 
important condition: x + 4 ≠ 0 ---> x ≠ -4     and                    x + 5 ≠ 0 ---> x ≠ -5
1. Let's assume (x + 5) > 0 and (x + 4) > 0 ---> x is from (-4, ∞)
    or                (x + 5) < 0 and (x + 4) < 0 ---> x is from (-∞. -5)
(x - 8)(x + 4)(x + 5) ≤ 40(x + 5) - 90(x + 4)
After open parentheses and combine like terms:
x³ + x² - 2x ≤ 0
x(x - 1)(x + 2) ≤ 0 ---> x is from (-∞, -5)
2. Let's assume that (x + 5)(x + 4) < 0 ---> x is from (-5, -4)
x(x - 1)(x + 2) ≥ 0 does not have solution without conflict with (1.)
The final answer is (-∞, -5)

ANOTHER WAY TO SOLVE THIS INEQUALITY:
Divide the numeric line onto intervals (-∞, -5), (-5, -4), (-4, 8) and (8, +∞) then pickup any number from each interval plug it into original inequality, simplify and look at gotten inequality, is it true or false.

2. 14^x + 1 = 36
14^x = 35

log₁₄ 35 = x
x ≈ 1.3572

Value of "x" is any real number except 0.

y = ax² + bx + c
"c" is the y-intercept
y = a(x - h)² + k
(h,k) are coordinate of the vertex
x-coordinate of vertex: -b / (2a)
~~~~~~~~~~~~
c = 5
Let's use (-2, -1) :
1. a(-2)² + b(-2) + 5 = 1
4a - 2b = - 4
2. -b / (2a) = -2 ---> b = 4a
Now, let's solve system of equation:
4a - 2b = - 4
b = 4a
4a - 2(4a) = - 4
a = 1
b = 4
c = 5
y = x² + 4x + 5   <---- final answer