The range is: B. {12, 4, -6}
Step-by-step explanation:
Given
12x + 6y = 24
Here x is the input and y is the output
So,
Replacing y with f(x)
![12x +6f(x) = 24\\6f(x) = 24 - 12x\\\frac{6f(x)}{6} = \frac{24-12x}{6}\\f(x) = \frac{24-12x}{6}](https://tex.z-dn.net/?f=12x%20%2B6f%28x%29%20%3D%2024%5C%5C6f%28x%29%20%3D%2024%20-%2012x%5C%5C%5Cfrac%7B6f%28x%29%7D%7B6%7D%20%3D%20%5Cfrac%7B24-12x%7D%7B6%7D%5C%5Cf%28x%29%20%3D%20%5Cfrac%7B24-12x%7D%7B6%7D)
Domain = {-4, 0, 5},
We will put the elements of domain, one by one, to find range
![f(-4) = \frac{24-12(-4)}{6}\\=\frac{24+48}{6}\\= \frac{72}{6}\\=12\\\\f(0) = \frac{24-12(0)}{6}\\=\frac{24}{6}\\= 4\\\\f(5) = \frac{24-12(5)}{6}\\=\frac{24-60}{6}\\=\frac{-36}{6}\\=-6](https://tex.z-dn.net/?f=f%28-4%29%20%3D%20%5Cfrac%7B24-12%28-4%29%7D%7B6%7D%5C%5C%3D%5Cfrac%7B24%2B48%7D%7B6%7D%5C%5C%3D%20%5Cfrac%7B72%7D%7B6%7D%5C%5C%3D12%5C%5C%5C%5Cf%280%29%20%3D%20%5Cfrac%7B24-12%280%29%7D%7B6%7D%5C%5C%3D%5Cfrac%7B24%7D%7B6%7D%5C%5C%3D%204%5C%5C%5C%5Cf%285%29%20%3D%20%5Cfrac%7B24-12%285%29%7D%7B6%7D%5C%5C%3D%5Cfrac%7B24-60%7D%7B6%7D%5C%5C%3D%5Cfrac%7B-36%7D%7B6%7D%5C%5C%3D-6)
Hence,
The range is: B. {12, 4, -6}
Keywords: Range, Domain, functions
Learn more about functions at:
#LearnwithBrainly
Answer:
260 minutes > 4.25 hours
Step-by-step explanation:
1h=60 min.
0.25 h=¼h=¼*60min=15min.
4.25h=4h+0.25h=60*4+15min=240+15=255min
260>255
To answer this equation, firs you must assign the g(x) to the value of f(x) to make the function answerable and able to find the value of x. So its gonna be f(g(x)) = 4(4x)-32. So x = 2 and f(x) = -24 and g(x) = 8
Answer:
![\large\boxed{\dfrac{3x+6}{x-4}\div\dfrac{2x^2+9x+10}{x^2+4x}=\dfrac{3x(x+4)}{(x-4)(2x+5)}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Cdfrac%7B3x%2B6%7D%7Bx-4%7D%5Cdiv%5Cdfrac%7B2x%5E2%2B9x%2B10%7D%7Bx%5E2%2B4x%7D%3D%5Cdfrac%7B3x%28x%2B4%29%7D%7B%28x-4%29%282x%2B5%29%7D%7D)
Step-by-step explanation:
Just like that
![\dfrac{3x+6}{x-4}\div\dfrac{2x^2+9x+10}{x^2+4x}=\dfrac{3x+6}{x-4}\cdot\dfrac{x^2+4x}{2x^2+9x+10}\\\\=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{2x^2+4x+5x+10}=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{2x(x+2)+5(x+2)}\\\\=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{(x+2)(2x+5)}\qquad\text{cancel}\ (x+2)\\\\=\dfrac{3x(x+4)}{(x-4)(2x+5)}](https://tex.z-dn.net/?f=%5Cdfrac%7B3x%2B6%7D%7Bx-4%7D%5Cdiv%5Cdfrac%7B2x%5E2%2B9x%2B10%7D%7Bx%5E2%2B4x%7D%3D%5Cdfrac%7B3x%2B6%7D%7Bx-4%7D%5Ccdot%5Cdfrac%7Bx%5E2%2B4x%7D%7B2x%5E2%2B9x%2B10%7D%5C%5C%5C%5C%3D%5Cdfrac%7B3%28x%2B2%29%7D%7B%28x-4%29%7D%5Ccdot%5Cdfrac%7Bx%28x%2B4%29%7D%7B2x%5E2%2B4x%2B5x%2B10%7D%3D%5Cdfrac%7B3%28x%2B2%29%7D%7B%28x-4%29%7D%5Ccdot%5Cdfrac%7Bx%28x%2B4%29%7D%7B2x%28x%2B2%29%2B5%28x%2B2%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7B3%28x%2B2%29%7D%7B%28x-4%29%7D%5Ccdot%5Cdfrac%7Bx%28x%2B4%29%7D%7B%28x%2B2%29%282x%2B5%29%7D%5Cqquad%5Ctext%7Bcancel%7D%5C%20%28x%2B2%29%5C%5C%5C%5C%3D%5Cdfrac%7B3x%28x%2B4%29%7D%7B%28x-4%29%282x%2B5%29%7D)
Answer:
24
Step-by-step explanation:
5 th grade ixl