64p=-16+8p-40p^2 solve by factoring.

Solution set = {(-1,-2/5)]

Step-by-step explanation:

64p=-16+8p-40p²

64p-8p=-16-40p²

56p+16+40p²=0

40p²+56p+16=0

8(5p² +7p+2)=0

5p²+5p+2p+2=0

5p(p+1) +2(p+1)=0

(p+1)(5p+2)=0

p+1=0;   5p+2=0

p=-1;      p=-2/5

50- 250 is correct i did that one too

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.