What is the length of the hypotenuse of the right angle defined by the points (-3,-,-1),and (1,2)? a)square root of 3 b)square root of 3 c) 2 timessquare root of 3 d)5

To find the length of the triangle first find the two coordinates with a common x coordinate, (1,-1) and (1,2). Now find the difference between their y coordinates, -1 and 2. This means that the length of the triangle is 3.
To find the width of the triangle first find the two coordinates with a common y coordinate, (-3,-1) and (1,-1). Now find the difference between their x coordinates, -3 and 1. This means that the width of the triangle is 4. 
By Pythagoras' theorem, we know that . Inserting our newfound values into this equation, we an find thelength of the hypotenuse:

Therefore, your answer is D0 5. To visualise this question better, you can plot the points on a graph. 

Answer

1 number

explanation

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.