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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.

to solve the equation x905x kiana graphed the functions fxx9 and gx05x on the same set of coordinate axes She then found that the graphs intersected at the poin class=

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calculista

Answer:

The answer is the option D

[tex]f(6)=g(6)[/tex] and [tex]f(18)=g(18)[/tex]

Step-by-step explanation:

we have

[tex]f\left(x\right)=\left|x-9\right|[/tex]

[tex]g(x)=0.5x[/tex]

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 [tex](6,3)[/tex] and [tex](18,9)[/tex]

therefore

The solution of the equation [tex]\left|x-9\right|=0.5x[/tex] are

[tex]x=6, x=18[/tex]

so

For [tex]x=6[/tex]

[tex]f\left(6\right)=\left|6-9\right|=3[/tex]

[tex]g(6)=0.5(6)=3[/tex]

[tex]f(6)=g(6)[/tex]

For [tex]x=18[/tex]

[tex]f\left(18\right)=\left|18-9\right|=9[/tex]

[tex]g(18)=0.5(18)=9[/tex]

[tex]f(18)=g(18)[/tex]

therefore

[tex]f(6)=g(6)[/tex] and [tex]f(18)=g(18)[/tex] because the intersection points are common points for both graphs

Ver imagen calculista

Answer:

Option: D is the correct answer.

  F(6)=G(6)     and   F(18)=G(18)

Step-by-step explanation:

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)

Ver imagen virtuematane

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