To solve the equation |x-9|=0.5x, kiana graphed the functions f(x)=|x-9| and g(x)=0.5x on the same set of coordinate axes. she then found that the graphs intersected at the points (6,3) and (18,9). finally, she concluded that the solutions of the equation |x-9|=0.5x are x=6 amd x=18. which of the following reasons best justifies kiana's conclusion.

The answer is the option D

and

Step-by-step explanation:

we have

we know that

The solution of the system of equations is the intersection point both graphs

Using a graphing tool

see the attached figure

The solution are the points and

therefore

The solution of the equation are

so

For

For

therefore

and because the intersection points are common points for both graphs

Option: D is the correct answer.

  F(6)=G(6)     and   F(18)=G(18)

We know that the point of intersection of the graph of two function f(x) and g(x) is the set of possible x values at which both the function have the same output values.

i.e. if the graph of two functions intersect at x=a than that means:

                                 f(a)=g(a)

Hence, here the graph of F(x)=|x-9| and G(x)=0.5x intersect at x=6 and x=18 ,

this means that:

                F(6)=G(6)

      and    F(18)=G(18)