8. find the values for x and y (2 points)

In a tra pezoid, the sum of angles on one leg is 180 °.

Therefore:

        use distributive property

       combine like terms

     subtract 45 from both sides

     divide both sides by 9

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.