In rectangle abcd, ac = -x + 21, bp = -9x + 19, and dp = -y + 5. find the value of y.

y=-5

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The diagonals of a rectangle are equal and bisect each other

so

step 1

Find the value of x

substitute the given values

solve for x

Multiply by 2 both sides

step 2

Find the value of y

we have

substitute

substitute the value of x

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.