First we need to find the slope.
slope = (y2 - y1) / (x2 - x1)
slope = (-5 - 2) / (5 - -3)
slope = (-7) / (5 + 3)
slope = -7/8
.
Point-slope form:
y - y1 = m(x - x1)
y - 2 = (-7/8)(x - -3)
y - 2 = (-7/8)(x + 3)
y - 2 = (-7/8)x - 21/8
y = (-7/8)x - 21/8 + 2
y = (-7/8)x - 21/8 + 16/8
y = (-7/8)x - 5/8
Answer: Choice A) 12x^2 - 48x + 21; all real numbers
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Work Shown:
(f * g)(x) = f(x) * g(x)
(f * g)(x) = ( f(x) ) * ( g(x) )
(f * g)(x) = ( -2x+7 ) * ( -6x+3 )
(f * g)(x) = -2x*( -6x+3 ) + 7*( -6x+3 )
(f * g)(x) = -2x*(-6x) - 2x*(3) + 7*(-6x) + 7*(3)
(f * g)(x) = 12x^2 - 6x - 42x + 21
(f * g)(x) = 12x^2 - 48x + 21
The domain is the set of all real numbers because we can plug in any number in for x, to get some output for y. There are no issues to worry about such as division by zero errors, square root of a negative number, etc.
Jack was planting a tree. He was to dig a hole that was 3 feet deep for every 5 feet of tree height. How deep should he dig the hole for a tree that is 17feet high.
Calculations 
Cross multiplication
=
5x = 2 x 13
Divide by 5 to isolate x
=
x = 10.2
Answer = 10.2
