Answer:
The predicted calories would be 403 calories.
Step-by-step explanation:
We have a linear regression model relating y: calories with x: carbohydrates, which has a slope of 4.0 and a y-intercept of 3.0.
Then, the model equation is:
![y=4.0x+3.0](https://tex.z-dn.net/?f=y%3D4.0x%2B3.0)
With these model we can predict the calories values for any amount of carbohydrates, within the interval within which this model is valid.
If a new food is tested, and the number of carbohydrates (x) is 100, the predicted value will be:
![y(100)=4.0(100)+3.0=400+3=403](https://tex.z-dn.net/?f=y%28100%29%3D4.0%28100%29%2B3.0%3D400%2B3%3D403)
The predicted calories would be 403 calories.
- <em>The graph of f is a polynomial function</em>
- <em>There are two turning points, namely, x = 0 and x = -2</em>
<h2>
Explanation:</h2>
A polynomial function in one variable is given by the form:
![f(x)=a_{n}x^n+a_{n-1}x^{n-1}+\cdots +a_{2}x^2+a_{1}x+a_{0}](https://tex.z-dn.net/?f=f%28x%29%3Da_%7Bn%7Dx%5En%2Ba_%7Bn-1%7Dx%5E%7Bn-1%7D%2B%5Ccdots%20%2Ba_%7B2%7Dx%5E2%2Ba_%7B1%7Dx%2Ba_%7B0%7D)
Since you haven't provided any expression, I'll choose the following function:
![f(x)=x^{3}+3x^{2}+3](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B3%7D%2B3x%5E%7B2%7D%2B3)
So this is indeed a polynomial function. A turning point is an x-value where we have either a local maximum or local minimum. So we need to take the derivative of this functions:
![f'(x)=3x^2+6x \\ \\ Finding \ turning \ points: \\ \\ 3x^2+6x=0 \\ \\ x(3x+6)=0 \\ \\ \\ So: \\ \\ x=0 \\ \\ and \\ \\ \ 3x+6=0 \therefore \ \boxed{x=-2}](https://tex.z-dn.net/?f=f%27%28x%29%3D3x%5E2%2B6x%20%5C%5C%20%5C%5C%20Finding%20%5C%20turning%20%5C%20points%3A%20%5C%5C%20%5C%5C%203x%5E2%2B6x%3D0%20%5C%5C%20%5C%5C%20x%283x%2B6%29%3D0%20%5C%5C%20%5C%5C%20%5C%5C%20So%3A%20%5C%5C%20%5C%5C%20x%3D0%20%5C%5C%20%5C%5C%20%20and%20%5C%5C%20%5C%5C%20%5C%203x%2B6%3D0%20%5Ctherefore%20%5C%20%5Cboxed%7Bx%3D-2%7D)
Conclusion:
- <em>The graph of f is a polynomial function</em>
- <em>There are two turning points, namely, x = 0 and x = -2</em>
<em />
<h2>
Learn more:</h2>
Polynomial function: brainly.com/question/13729121
#LearnWithBrainly
Answer:
The original area would be multiplied by the scale factor of 2² to get the new area.
Step-by-step explanation:
If you double the radius lets so lets do an example
(a=πr²) so
if x is the radius the area would be x²π
double the radius so 2x then the area would be
(2x)²π so 4x²π
4x²π/x²π= 4 so its 4 times greater or
D the last answer or The original area would be multiplied by the scale factor of 2² to get the new area.
C
Step-by-step explanation:
Graphs are simple I would know trust me man