Answer:
-0.2
Step-by-step explanation:
Gradient/slope = ![\frac{7-5}{15-25} = \frac{2}{-10} = -0.2](https://tex.z-dn.net/?f=%5Cfrac%7B7-5%7D%7B15-25%7D%20%20%3D%20%5Cfrac%7B2%7D%7B-10%7D%20%3D%20-0.2)
Answer:
X = -3. non-extraneous
Step-by-step explanation:
The given equation is ![\frac{6}{x-3} =\frac{x}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7Bx-3%7D%20%3D%5Cfrac%7Bx%7D%7B3%7D)
We cross multiply to get:
![6*3=x(x-3)](https://tex.z-dn.net/?f=6%2A3%3Dx%28x-3%29)
Expand and multiply.
![18=x^2-3x](https://tex.z-dn.net/?f=18%3Dx%5E2-3x)
![x^2-3x-18=0](https://tex.z-dn.net/?f=x%5E2-3x-18%3D0)
We factor to obtain:
![(x-6)(x+3)=0](https://tex.z-dn.net/?f=%28x-6%29%28x%2B3%29%3D0)
![x=-3,x=6](https://tex.z-dn.net/?f=x%3D-3%2Cx%3D6)
Checking for extraneous solutions
Substitute x=-3 ![\frac{6}{-3-3} =\frac{-3}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B-3-3%7D%20%3D%5Cfrac%7B-3%7D%7B3%7D)
![\frac{6}{-6} =\frac{-3}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B-6%7D%20%3D%5Cfrac%7B-3%7D%7B3%7D)
![-1=-1](https://tex.z-dn.net/?f=-1%3D-1)
.....Non-extraneous
Checking for x=6
![\frac{6}{6-3} =\frac{6}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B6-3%7D%20%3D%5Cfrac%7B6%7D%7B3%7D)
![\frac{6}{3} =\frac{6}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B3%7D%20%3D%5Cfrac%7B6%7D%7B3%7D)
....Non-extraneous
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The best and most correct answer among the choices provided by the question is <span>C. x over 520 = 5 over 13</span>.<span>
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Hope my answer would be a great help for you.</span>