Find the value of x.
AS
7
х
D
3
B
'c
X=
V[?]
Enter

9514 1404 393

  x = √70

Step-by-step explanation:

The triangles shown are all similar, so corresponding sides are proportional.

  hypotenuse/long side = x/7 = (7+3)/x

Cross-multiplying gives ...

  x^2 = 7(10)

  x = √70

You will note that the value of x (the long side) is the geometric mean of the long segment and the whole hypotenuse.

A similar "geometric mean" relation holds for the short side:

  BC = √(CD·CA)

There is yet another "geometric mean" relation that holds for the altitude:

  BD = √(CD·AD)

You may see these again.

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.