1369. If this is what you are trying to find, hope this helps.
Answer:c
Step-by-step explanation:
Answer:
Step-by-step explanation:
a coordinate point is (x, y) so for point W (4, -1), 4 is the x-coordinate and -1 is the y-coordinate.
Start at the origin (O). Go 4 units to the right (along the x-axis in a positive direction) and then 1 unit down (in the y plane in a negative direction).
Question:
Find numbers a and k so that x-2 is a factor of
![f(x)=x^4-2ax^3+ax^2- x+k](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4-2ax%5E3%2Bax%5E2-%20x%2Bk)
and
![f(-1)=3](https://tex.z-dn.net/?f=f%28-1%29%3D3)
Answer:
and ![a=1](https://tex.z-dn.net/?f=a%3D1)
Step-by-step explanation:
Given
![f(x)=x^4-2ax^3+ax^2- x+k](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4-2ax%5E3%2Bax%5E2-%20x%2Bk)
![Factor:\ x - 4](https://tex.z-dn.net/?f=Factor%3A%5C%20x%20-%204)
![f(-1)=3](https://tex.z-dn.net/?f=f%28-1%29%3D3)
Required
Find a and k
For ![f(-1)=3](https://tex.z-dn.net/?f=f%28-1%29%3D3)
Substitute -1 for x
![f(x)=x^4-2ax^3+ax^2- x+k](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4-2ax%5E3%2Bax%5E2-%20x%2Bk)
![f(-1) = (-1)^4 - 2a *(-1)^3 + a*(-1)^2 - (-1) + k](https://tex.z-dn.net/?f=f%28-1%29%20%3D%20%28-1%29%5E4%20-%202a%20%2A%28-1%29%5E3%20%2B%20a%2A%28-1%29%5E2%20-%20%28-1%29%20%2B%20k)
![f(-1) = 1 - 2a *-1 + a*1 +1 + k](https://tex.z-dn.net/?f=f%28-1%29%20%3D%201%20-%202a%20%2A-1%20%2B%20a%2A1%20%2B1%20%2B%20k)
![f(-1) = 1 +2a + a +1 + k](https://tex.z-dn.net/?f=f%28-1%29%20%3D%201%20%2B2a%20%2B%20a%20%2B1%20%2B%20k)
![f(-1) = 2 +3a + k](https://tex.z-dn.net/?f=f%28-1%29%20%3D%202%20%2B3a%20%2B%20k)
Substitute 3 for f(-1)
![3 = 2 +3a + k](https://tex.z-dn.net/?f=3%20%3D%202%20%2B3a%20%2B%20k)
Collect Like Terms
![3 - 2 = 3a + k](https://tex.z-dn.net/?f=3%20-%202%20%3D%203a%20%2B%20k)
![1 = 3a + k](https://tex.z-dn.net/?f=1%20%3D%203a%20%2B%20k)
Also:
If
is a factor, then
![f(2) = 0](https://tex.z-dn.net/?f=f%282%29%20%3D%200)
Substitute 2 for x and 0 for f(x)
![f(x)=x^4-2ax^3+ax^2- x+k](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4-2ax%5E3%2Bax%5E2-%20x%2Bk)
![0 = 2^4 - 2a * 2^3 + a * 2^2 - 2 + k](https://tex.z-dn.net/?f=0%20%3D%202%5E4%20-%202a%20%2A%202%5E3%20%2B%20a%20%2A%202%5E2%20-%202%20%2B%20k)
![0 = 16 - 2a * 8 + a * 4 - 2 + k](https://tex.z-dn.net/?f=0%20%3D%2016%20-%202a%20%2A%208%20%2B%20a%20%2A%204%20-%202%20%2B%20k)
![0 = 16 - 16a + 4a - 2 + k](https://tex.z-dn.net/?f=0%20%3D%2016%20-%2016a%20%2B%204a%20-%202%20%2B%20k)
![0 = 16 - 12a - 2 + k](https://tex.z-dn.net/?f=0%20%3D%2016%20-%2012a%20-%202%20%2B%20k)
Collect Like Terms
![2 - 16 = - 12a + k](https://tex.z-dn.net/?f=2%20-%2016%20%3D%20-%2012a%20%2B%20k)
![-14 = k - 12a](https://tex.z-dn.net/?f=-14%20%3D%20k%20-%2012a)
![k = 12a - 14](https://tex.z-dn.net/?f=k%20%3D%2012a%20-%2014)
Substitute 12a - 14 for k in ![1 = 3a + k](https://tex.z-dn.net/?f=1%20%3D%203a%20%2B%20k)
![1 = 3a + 12a - 14](https://tex.z-dn.net/?f=1%20%3D%203a%20%2B%2012a%20-%2014)
![1 = 15a - 14](https://tex.z-dn.net/?f=1%20%3D%2015a%20-%2014)
Collect Like Terms
![15a = 1 + 14](https://tex.z-dn.net/?f=15a%20%3D%201%20%2B%2014)
![15a = 15](https://tex.z-dn.net/?f=15a%20%3D%2015)
Solve for a
![a = \frac{15}{15}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B15%7D%7B15%7D)
![a=1](https://tex.z-dn.net/?f=a%3D1)
Substitute 1 for a in ![k = 12a - 14](https://tex.z-dn.net/?f=k%20%3D%2012a%20-%2014)
![k = 12 * 1 - 14](https://tex.z-dn.net/?f=k%20%3D%2012%20%2A%201%20-%2014)
![k = 12 - 14](https://tex.z-dn.net/?f=k%20%3D%2012%20-%2014)
![k = -2](https://tex.z-dn.net/?f=k%20%3D%20-2)
Answer:
1 bag of apples would cost $5.92.
Step-by-step explanation:
All you have to do is take the 41.44 and divide it by 7 to see how much one bag would cost. I used a calculator and got $5.92.
Hope this helps!