<h2>
Answer:</h2>
The linear function is given by:
![y=\dfrac{3}{2}x-\dfrac{7}{2}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B3%7D%7B2%7Dx-%5Cdfrac%7B7%7D%7B2%7D)
<h2>
Step-by-step explanation:</h2>
It is given that the rate of change of the linear function is equal to the average rate of change of function f on the interval [-1, 1].
The slope(m) or average rate of change of the linear function will be:
![m=\dfrac{f(1)-f(-1)}{1-(-1)}\\\\\\m=\dfrac{-2-(-5)}{1+1}\\\\\\m=\dfrac{-2+5}{2}\\\\\\m=\dfrac{3}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7Bf%281%29-f%28-1%29%7D%7B1-%28-1%29%7D%5C%5C%5C%5C%5C%5Cm%3D%5Cdfrac%7B-2-%28-5%29%7D%7B1%2B1%7D%5C%5C%5C%5C%5C%5Cm%3D%5Cdfrac%7B-2%2B5%7D%7B2%7D%5C%5C%5C%5C%5C%5Cm%3D%5Cdfrac%7B3%7D%7B2%7D)
and the linear function pass through (1,-2)
We know that the equation of a line with given slope m and passing through point (a,b) is given by:
Here (a,b)=(1,-2)
and ![m=\dfrac{3}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B3%7D%7B2%7D)
Hence, the equation of linear function is:
![y-(-2)=\dfrac{3}{2}\times (x-1)\\\\\\y+2=\dfrac{3}{2}x-\dfrac{3}{2}\\\\\\y=\dfrac{3}{2}x-\dfrac{3}{2}-2\\\\\\y=\dfrac{3}{2}x-\dfrac{7}{2}](https://tex.z-dn.net/?f=y-%28-2%29%3D%5Cdfrac%7B3%7D%7B2%7D%5Ctimes%20%28x-1%29%5C%5C%5C%5C%5C%5Cy%2B2%3D%5Cdfrac%7B3%7D%7B2%7Dx-%5Cdfrac%7B3%7D%7B2%7D%5C%5C%5C%5C%5C%5Cy%3D%5Cdfrac%7B3%7D%7B2%7Dx-%5Cdfrac%7B3%7D%7B2%7D-2%5C%5C%5C%5C%5C%5Cy%3D%5Cdfrac%7B3%7D%7B2%7Dx-%5Cdfrac%7B7%7D%7B2%7D)
Answer:
C. the circumference of a circle
Step-by-step explanation:
The perimeter of a square is the length of the outside, which is found by adding all the side lengths. The circumference of a circle is similar because it is also the length of the outside of the shape.
Answer:
8 cups of white paint, 8 cups of red paint, and 20 cups of lilac
Step-by-step explanation:
20% of the paint is blue In the mixture(4 cups of blue paint were used)
20%= 4 cups of blue paint
Therefore 40% of white paint equals 8 cups of white paint same applies to the rest of the red paint
The rest of the red paint equals 40% because if you add 20% + 40%=60%
100% of the total of the mixture -60% of the blue paint and white equals 40% left of the rest of the red paint.
Answer:
9
Explanation :
check out my attached work
Hope it helps, let me know if you have any questions !
Have a nice rest of your day :)
Answer:
2(x-2y)/(4x-y) = dy/dx
Step-by-step explanation:
2x^2+y^2=8xy
Take the derivative of each term, remembering that we take the 8xy as derivative by parts)
2 * 2x dx + *2y dy = 8 ( x dy + dx *y)
4x dx +2y dy = 8x dy + 8y dx
Subtract 2y dy from each side
4x dx +2y dy -4y dy = 8x dy - 2y dy + 8y dx
4x dx = 8x dy - 2y dy + 8y dx
Subtract 8y dx from each side
4x dx -8y dx = 8x dy - 2y dy + 8y dx-8y dx
4x dx -8y dx = 8x dy - 2y dy
(4x-8y) dx = (8x-2y) dy
Factor out a 4 from the left side and a 2 from the right side
4(x-2y) dx = 2( 4x-y) dy
Cancel a 2
2(x-2y) dx = ( 4x-y) dy
Divide each side by (4x-y)
2(x-2y)/(4x-y) dx = ( 4x-y)/(4x-y) dy
2(x-2y)/(4x-y) dx = dy
Divide by dx
2(x-2y)/(4x-y) dx/dx = dy/dx
2(x-2y)/(4x-y) = dy/dx