The answer is 828 apples. There are 828 apples in each of the five boxes.
The correct answer choice is D
Answer:
![c = 5](https://tex.z-dn.net/?f=c%20%3D%205)
Step-by-step explanation:
Given
![f(c) = M](https://tex.z-dn.net/?f=f%28c%29%20%3D%20M)
![f(x) = x^2 - x + 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20-%20x%20%2B%201)
![Interval: [1,8]](https://tex.z-dn.net/?f=Interval%3A%20%5B1%2C8%5D)
![M = 21](https://tex.z-dn.net/?f=M%20%3D%2021)
Required
Find c using Intermediate Value theorem
First, check if the value of M is within the given range:
![f(x) = x^2 - x + 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20-%20x%20%2B%201)
![f(1) = 1^2 - 1 + 1](https://tex.z-dn.net/?f=f%281%29%20%3D%201%5E2%20-%201%20%2B%201)
![f(1) = 1](https://tex.z-dn.net/?f=f%281%29%20%3D%201)
![f(x) = 8^2 - 8 + 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%208%5E2%20-%208%20%2B%201)
![f(x) = 57](https://tex.z-dn.net/?f=f%28x%29%20%3D%2057)
![1 \le M \le 57](https://tex.z-dn.net/?f=1%20%5Cle%20M%20%5Cle%2057)
![1 \le 21 \le 57](https://tex.z-dn.net/?f=1%20%5Cle%2021%20%5Cle%2057)
M is within range.
Solving further:
We have:
![f(c) = f(x) = M](https://tex.z-dn.net/?f=f%28c%29%20%3D%20f%28x%29%20%3D%20M)
![f(x) = 21](https://tex.z-dn.net/?f=f%28x%29%20%3D%2021)
Substitute 21 for f(x) in ![f(x) = x^2 - x + 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20-%20x%20%2B%201)
![21 = x^2 - x + 1](https://tex.z-dn.net/?f=21%20%3D%20x%5E2%20-%20x%20%2B%201)
Express as quadratic function
![x^2 - x + 1 - 21 = 0](https://tex.z-dn.net/?f=x%5E2%20-%20x%20%2B%201%20-%2021%20%20%3D%200)
![x^2 - x - 20 = 0](https://tex.z-dn.net/?f=x%5E2%20-%20x%20-%2020%20%20%3D%200)
Expand
![x^2 + 4x - 5x - 20](https://tex.z-dn.net/?f=x%5E2%20%2B%204x%20-%205x%20-%2020)
![x(x+4)-5(x+4)=0](https://tex.z-dn.net/?f=x%28x%2B4%29-5%28x%2B4%29%3D0)
![(x - 5)(x+4) = 0](https://tex.z-dn.net/?f=%28x%20-%205%29%28x%2B4%29%20%3D%200)
or ![x + 4= 0](https://tex.z-dn.net/?f=x%20%2B%204%3D%200)
or ![x = -4](https://tex.z-dn.net/?f=x%20%3D%20-4)
The value of
is outside the ![Interval: [1,8]](https://tex.z-dn.net/?f=Interval%3A%20%5B1%2C8%5D)
So:
![x = 5](https://tex.z-dn.net/?f=x%20%3D%205)
![f(c) = f(x) = M](https://tex.z-dn.net/?f=f%28c%29%20%3D%20f%28x%29%20%3D%20M)
![f(c) = f(5) = 21](https://tex.z-dn.net/?f=f%28c%29%20%3D%20f%285%29%20%3D%2021)
By comparison:
![c = 5](https://tex.z-dn.net/?f=c%20%3D%205)
The number for x after the equals should be a 4
Answer:
The correct answer is B. b=3a + 2
Step-by-step explanation:
Plug in the values from column A into each equation and find which one works. In this case, the only option that works is B.