D. f(x)=2X
This is your answer
The constant in an algebraic expression is the only term that cannot be changed.
Terms with variables are not constants as their values can changed as the variables change.
Our equation is 3m+7
M is a variable. Therefore the term '3m' is not the constant.
This leaves us with the term '7'. There is no variable present in this term.
'7' is the constant in this equation.
Answer:
![m=8x-5-4\Delta x](https://tex.z-dn.net/?f=m%3D8x-5-4%5CDelta%20x)
Step-by-step explanation:
We have the function:
![f(x)=4x^2-5x-1](https://tex.z-dn.net/?f=f%28x%29%3D4x%5E2-5x-1)
And we want to use the difference quotient:
![m=\frac{f(x+\Delta x)-f(x)}{\Delta x}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bf%28x%2B%5CDelta%20x%29-f%28x%29%7D%7B%5CDelta%20x%7D)
To find the slope function.
So, let's substitute
for our function. This yields:
![m=\frac{(4(x+\Delta x)^2-5(x+\Delta x)-1)-(4x^2-5x-1))}{\Delta x}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%284%28x%2B%5CDelta%20x%29%5E2-5%28x%2B%5CDelta%20x%29-1%29-%284x%5E2-5x-1%29%29%7D%7B%5CDelta%20x%7D)
Let's square. Use the perfect square trinomial pattern. This yields:
![m=\frac{(4(x^2+2x\Delta x-\Delta x^2)-5(x+\Delta x)-1)-(4x^2-5x-1))}{\Delta x}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%284%28x%5E2%2B2x%5CDelta%20x-%5CDelta%20x%5E2%29-5%28x%2B%5CDelta%20x%29-1%29-%284x%5E2-5x-1%29%29%7D%7B%5CDelta%20x%7D)
Distribute:
![m=\frac{(4x^2+8x\Delta x-4\Delta x^2-5x-5\Delta x-1)-(4x^2-5x-1)}{\Delta x}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%284x%5E2%2B8x%5CDelta%20x-4%5CDelta%20x%5E2-5x-5%5CDelta%20x-1%29-%284x%5E2-5x-1%29%7D%7B%5CDelta%20x%7D)
Distribute the right:
![m=\frac{(4x^2+8x\Delta x-4\Delta x^2-5x-5\Delta x-1)+(-4x^2+5x+1)}{\Delta x}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%284x%5E2%2B8x%5CDelta%20x-4%5CDelta%20x%5E2-5x-5%5CDelta%20x-1%29%2B%28-4x%5E2%2B5x%2B1%29%7D%7B%5CDelta%20x%7D)
Combine like terms:
![m=\frac{(4x^2-4x^2)+(-5x+5x)+(1-1)+(8x\Delta x-4\Delta x^2-5\Delta x)}{\Delta x}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%284x%5E2-4x%5E2%29%2B%28-5x%2B5x%29%2B%281-1%29%2B%288x%5CDelta%20x-4%5CDelta%20x%5E2-5%5CDelta%20x%29%7D%7B%5CDelta%20x%7D)
The first three terms will cancel. This leaves us with:
![m=\frac{8x\Delta x-4\Delta x^2-5\Delta x}{\Delta x}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B8x%5CDelta%20x-4%5CDelta%20x%5E2-5%5CDelta%20x%7D%7B%5CDelta%20x%7D)
We can factor out a Δx from the numerator:
![m=\frac{\Delta x(8x-4\Delta x-5)}{\Delta x}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%5CDelta%20x%288x-4%5CDelta%20x-5%29%7D%7B%5CDelta%20x%7D)
The Δx will cancel. So, our slope function is:
![m=8x-5-4\Delta x](https://tex.z-dn.net/?f=m%3D8x-5-4%5CDelta%20x)
And we're done!
Answer:
18/50
Step-by-step explanation:
The spinner was spun 50 times and both 2 and 4 are even numbers which was landed on 8 and 10 time so therefore 18/50
I believe it should be 216