The function f(x) = 5x² + 40x is a parabola. Then the vertex of the parabola will be at (–4, –80).
<h3>What is the parabola?</h3>
It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
The function f(x) = 5x² + 40x
Then add and subtract 80, then we have
f(x) = 5x² + 40x + 80 – 80
f(x) = 5(x² + 8x + 16) – 80
f(x) = 5(x + 4)² – 80
The vertex of the parabola will be at (–4, –80).
More about the parabola link is given below.
brainly.com/question/8495504
a. 
has an average value on [5, 11] of
b. The mean value theorem guarantees the existence of 
such that 
. This happens for
5*(n-2) = 29
5n-10=29 (distributive property)
5n-10+10=29+10 (do operations to both sides to isolate variable)
5n/5 = 39/5 (further isolate)
n = 7.8 (answer)
Your number is 7.8.
