Help please? Does anyone understand this?

15

Step-by-step explanation:

TU is parallel to IJ.  So ∠I and ∠T are corresponding angles, and ∠U and ∠J are corresponding angles.

By AA similarity, ΔHTU and ΔHIJ are similar.

Write a proportion:

HT / HI = HU / HJ

Plug in values:

4 / 10 = x / (x + 9)

Cross multiply:

4 (x + 9) = 10x

4x + 36 = 10x

36 = 6x

x = 6

So HU = 6, and HJ = 6 + 9 = 15.

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: