I need help with #1 and #2 how do I do this?

The answer to your question is below

Step-by-step explanation:

Data

1) AB = 6   BC = 4   AE = 9  ED = ?

Use proportions to solve this problem

              AB / AE = 6/9    (AB + BC) / (AE + ED) = (6 + 4) / (9 + ED)

-Equal both proportions

                              6/9 = 10 / (9 + ED)

-Solve for ED

                             9 + ED = 10(9)/ 6

-Simplification

                             9 + ED = 90/6

                             9 + ED = 15

                                   ED = 15 - 9

-Result

                                   ED = 6

2.-   AB = 12   AC = 16  ED = 5  AE = ?

Use proportions to solve this problem

             AE / AB = AE / 12          AD/AC = (AE + 5) / 16

-Equal both proportions

                          AE/12 = (AE + 5 ) / 16

-Solve for AE

                         16AE = 12(AE + 5)

                         16AE = 12AE + 60

                         16AE -12AE = 60

                                     4AE = 60

                                       AE = 60/4

-Result

                                      AE = 15                          

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.