R^2+15r+56=0
Quadratics factoring

Step-by-step explanation:

Find the product, sum and factors which are P=56, S=15 and F=8,7 respectively.

r²+15r+56=0

replacing with the factors in the equation

=> r²+8r+7r+56=0

r(r+8)+7(r+8)=0

(r+8)(r+7)=0

=> r= –8 and –7

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.