Find the value of x. Round your answer to the nearest tenth.

+4√5

Step-by-step explanation:

Note that this is a right triangle.  Therefore, the lengths of the three sides are related through the Pythagorean Theorem:  a^2 + b^2 = c^2, where c is the length of the hypotenuse.  

Thus, x^2 + 19^2 = 21^2, or, after solving this for x^2,

x^2 = 441 - 361 = 80

x is therefore +√80, or +4√5.

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.