The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 6 and 9. what is the length of the altitude?

Hence the length of the altitude is:

Step-by-step explanation:

Right Triangle Altitude Theorem Part a: The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.

In terms of our triangle i.e. figure attached to the answer, this theorem simply states :

Here in our question we are given:

CD=6 and DB=9

Hence the length of the altitude is:

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step-by-step explanation:

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.