To solve the equation |x-6|= 0.5x, kiana graphed the functions f(x) = |x-6|
and g(x) = 0.5x on the same set of coordinate axes. she then found that the
graphs intersected at the points (4, 2) and (12, 6). finally, she concluded that
the solutions of the equation |x-6|= 0.5x are x = 4 and x = 12. which of the
following reasons best justifies kiana's conclusion?

F(4) = G(4) and F(12) = G(12) ⇒ answer B

Step-by-step explanation:

* Lets explain the meaning of the common solutions of two equation

- If two equations intersect at one point, (x , y) where x and y have the

 same values for both equations

- The point (x , y) belongs to the two graphs

- Ex: If (2 , 3) is a common solution of f(x) and g(x) , then the graphs of

 f(x) and g(x) meet each other at the point (2 , 3) that means f(2) = 3

 and g(2) = 3

- So f(2) = g(2)

* Lets solve the problem

∵ F(x) = Ix - 6I

∵ G(x) = 0.5 x

∵ The two graphs intersected at points (4 , 2) and (12 , 6)

- That means the two points (4 , 2) and (2 , 6) on the two graphs

∴ F(4) = 2 and G(4) = 2

∴ F(12) = 6 and G(12) = 6

- That means the two points are common solutions for both equations

∴ The solutions of the equation |x - 6|= 0.5 x are x = 4 and x = 12

∴ F(4) = G(4) and F(12) = G(12)

∴ The  best reasons which justifies Kiana's conclusion is;

   F(4) = G(4) and F(12) = G(12)

- Look to the attached graph to more understanding

- The red graph is F(x)

- The blue graph is G(x)

b. 10=9.1+0.2x

step-by-step explanation:

that's it

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)