Areas of trapezoids, rhombuses and kites?

Rhombus has perpendicular diagonals that bisects each other. On diagonal has half lenght 12 in (the whole diagonal will have length 24 in). Let second diagonal has length 2x in, then half of this diagonal has length x in.

Consider right triangle, formed by two halves of diagonals (legs) and one rhombus side (hypotenuse). By the Pythagorean theorem,

.

Substitude given values:

.

Then the length of whole diagonal is 18 in. The area of the rhombus is

.

Substitute values:

sq. in.

sq. in.

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify

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.