Use what you know about operations and their properties to write three expressions equivalent to the expression shown. 10(2+3)−8⋅3

1) Simplify 2 + 3 to 5.

10 * 5 - 8 * 3

2) Simplify 10 * 5 to 50.

50 - 8 * 3

3) Simplify 8 * 3 to 24.

50 - 24

4) Simplify.

24

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.