Since the triangles are similar, all sides are proportional by the same scale factor.
The relationship between the bases 32 and 8 is 4 (32/8 = 4). This means that the smaller triangle need to be multiplied by a scale factor 4 to result in the bigger triangle.
This means that 4x + 12 is 4 times greater than 15.
The equation to solve for x can be written as:
4x + 12 = 4*15
Now just solve for x as u normally would
4x + 12 = 60
(Subtract twelve from both sides)
4x = 48
(Divide both sides by 4 to isolate x)
x = 12
I hope this somewhat helped :)
Was my explanation clear enough?
Please use " ^ " to denote exponentiation:
<span>f(x) = –(x + 8)^2 – 1
Find the first derivative: f '(x) = -2(x+8)(1)
Set this = to 0: -2(x+8) = 0
solve for x: x = -8
Divide the number line into subintervals based upon x=-8:
(-inf, -8) and (-8, inf)
Choose a test value for x from each interval, e. g., -10 from the first interval and 20 from the second.
Subst. this test value into the derivative, shown above.
If the result is + the function is incr on that interval; if - the fn. is decr.
Questions welcome!</span>