19. a silver statue of pooja is leaning against a wall. the top of her head
touches the wall at 40 feet. if the base of the statue is 9 feet away from the
wall, how tall is pooja’s statue, in feet?

Step-by-step explanation:

You need to draw a right triangle.

Observe the right triangle attached, where "x" is the height in feet of Pooja’s statue.

You need to use the Pythagorean Theorem. This is:

Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.

In this case you can identify that:

Therefore, you can substitute values into :

Finally, you must solve for "x" in order to find its value.

You get that this is:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: