Need understanding this math. each will have vertices a, b and c with a point d lying on the line segment ab. 1. if ac = 15, cb = 20, angle acb = 90◦ and angle adc = 90◦ , what is cd? 2. if ac = 15, cb = 20, ab = 25 and cd = 12, what is ad? what is db?

1. C is the right angle so AB is the hypotenuse and AD is the altitude to the hypotenuse.

The hypotenuse is

The area calculations must match. Let h=CD

12

2. This is the same triangle as above. We seek x=AD and DB=25-x

AD=9 and DB=25-9=16

AD=9, DB=16

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: