Simplify.

a - {4b - [a - (5b - c) + 3c - (a - b - 9c)]}

a)-a - 8b + 13c
b) a - 8b + 13c
c) a - 2b + 13c
d)-a - 2b + 13c

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

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.