Answer:
(1)7 (2)9 (3)6
Step-by-step explanation:
![\left|\begin{array}{c|cc}X&f(X)=X^2+7\\--&-----\\2&11\\3&16\\4&23\\5&32\\6&43\end{array}\right|](https://tex.z-dn.net/?f=%5Cleft%7C%5Cbegin%7Barray%7D%7Bc%7Ccc%7DX%26f%28X%29%3DX%5E2%2B7%5C%5C--%26-----%5C%5C2%2611%5C%5C3%2616%5C%5C4%2623%5C%5C5%2632%5C%5C6%2643%5Cend%7Barray%7D%5Cright%7C)
(1)The average rate of change between x=2 and x=5
![\dfrac{dy}{dx} =\dfrac{f(5)-f(2)}{5-2} =\dfrac{32-11}{3} =\dfrac{21}{3} =7](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%5Cdfrac%7Bf%285%29-f%282%29%7D%7B5-2%7D%20%3D%5Cdfrac%7B32-11%7D%7B3%7D%20%3D%5Cdfrac%7B21%7D%7B3%7D%20%3D7)
(2)The average rate of change between x=3 and x=6
![\dfrac{dy}{dx} =\dfrac{f(6)-f(3)}{6-3} =\dfrac{43-16}{3} =\dfrac{27}{3} =9](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%5Cdfrac%7Bf%286%29-f%283%29%7D%7B6-3%7D%20%3D%5Cdfrac%7B43-16%7D%7B3%7D%20%3D%5Cdfrac%7B27%7D%7B3%7D%20%3D9)
(3)The average rate of change between x=2 and x=4
![\dfrac{dy}{dx} =\dfrac{f(4)-f(2)}{4-2} =\dfrac{23-11}{2} =\dfrac{12}{2} =6](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%5Cdfrac%7Bf%284%29-f%282%29%7D%7B4-2%7D%20%3D%5Cdfrac%7B23-11%7D%7B2%7D%20%3D%5Cdfrac%7B12%7D%7B2%7D%20%3D6)
The answer would be de = 14x but i’m not fully confident in the answer
Answer:
Problem:
Solve x+y=7;x+2y=11
Steps:
I will try to solve your system of equations.
x+y=7;x+2y=11
Step: Solvex+y=7for x:
x+y+−y=7+−y(Add -y to both sides)
x=−y+7
Step: Substitute−y+7forxinx+2y=11:
x+2y=11
−y+7+2y=11
y+7=11(Simplify both sides of the equation)
y+7+−7=11+−7(Add -7 to both sides)
y=4
Step: Substitute4foryinx=−y+7:
x=−y+7
x=−4+7
x=3(Simplify both sides of the equation)
Answer:
x=3 and y=4
Answer:
256,781
Step-by-step explanation:
Answer:
<em>P=log(2)+log(3)+4.log(x)</em>
Step-by-step explanation:
To solve the problem, we need to recall the following properties of the logarithms:
![log(x.y)=log(x)+log(y)](https://tex.z-dn.net/?f=log%28x.y%29%3Dlog%28x%29%2Blog%28y%29)
![log(x^y)=y.log(x)](https://tex.z-dn.net/?f=log%28x%5Ey%29%3Dy.log%28x%29)
We have the expression:
![P=log(6x^4)](https://tex.z-dn.net/?f=P%3Dlog%286x%5E4%29)
Factor 6=2*3:
![P=log(2\cdot 3x^4)](https://tex.z-dn.net/?f=P%3Dlog%282%5Ccdot%203x%5E4%29)
Apply the property of the product:
![P=log(2)+log(3)+log(x^4)](https://tex.z-dn.net/?f=P%3Dlog%282%29%2Blog%283%29%2Blog%28x%5E4%29)
Now apply the property of the exponent:
P=log(2)+log(3)+4.log(x)