Work out the value of
x
.

The diagram is not drawn to scale

12.41

Step-by-step explanation:

4x + 10 + 3x - 10 + 5x + 10 +6x + 36 + 6x + 26 = 360

360 is sum of exterior angles

24x + 62= 360

x = 12.41

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.