Answer:
y=6x+12
Step-by-step explanation:
Hope this helps!
Answer:
It is correct
Step-by-step explanation:
Gr8 job
Answer:
8 Liters
Step-by-step explanation:
Percentage of Alcohol in water= 2L X 0 =0
Percentage of Alcohol to be added = xL X 0.9 =0.9x
- New Volume =(x+2) Liters
- Desired Concentration = 0.72%
Therefore:
0+0.9x=0.72(x+2)
0.9x=0.72x+1.44
Collect like terms
0.9x-0.72x=1.44
0.18x=1.44
Divide both sides by 1.44
x=8 Liters
Therefore, Shanice must add 8 Liters of 90% alcohol solution to create the desired mixture
Answer:
![m = 12](https://tex.z-dn.net/?f=m%20%3D%2012)
![n =3](https://tex.z-dn.net/?f=n%20%3D3)
Step-by-step explanation:
Given
![P(x) = x^3 + mx^2 - nx - 10](https://tex.z-dn.net/?f=P%28x%29%20%3D%20x%5E3%20%2B%20mx%5E2%20-%20nx%20-%2010)
Required
The values of m and n
For x - 1;
we have:
![x - 1 = 0](https://tex.z-dn.net/?f=x%20-%201%20%3D%200)
![x=1](https://tex.z-dn.net/?f=x%3D1)
So:
![P(1) = (1)^3 + m*(1)^2 - n*(1) - 10](https://tex.z-dn.net/?f=P%281%29%20%3D%20%281%29%5E3%20%2B%20m%2A%281%29%5E2%20-%20n%2A%281%29%20-%2010)
![P(1) = 1 + m*1 - n*1 - 10](https://tex.z-dn.net/?f=P%281%29%20%3D%201%20%2B%20m%2A1%20-%20n%2A1%20-%2010)
![P(1) = 1 + m - n - 10](https://tex.z-dn.net/?f=P%281%29%20%3D%201%20%2B%20m%20-%20n%20-%2010)
Collect like terms
![P(1) = m - n + 1 - 10](https://tex.z-dn.net/?f=P%281%29%20%3D%20m%20-%20n%20%2B%201%20-%2010)
![P(1) = m - n -9](https://tex.z-dn.net/?f=P%281%29%20%3D%20m%20-%20n%20-9)
Because x - 1 divides the polynomial, then P(1) = 0;
So, we have:
![m - n -9 = 0](https://tex.z-dn.net/?f=m%20-%20n%20-9%20%3D%200)
Add 9 to both sides
--- (1)
For x + 2;
we have:
![x + 2 = 0](https://tex.z-dn.net/?f=x%20%2B%202%20%3D%200)
![x = -2](https://tex.z-dn.net/?f=x%20%3D%20-2)
So:
![P(-2) = (-2)^3 + m*(-2)^2 - n*(-2) - 10](https://tex.z-dn.net/?f=P%28-2%29%20%3D%20%28-2%29%5E3%20%2B%20m%2A%28-2%29%5E2%20-%20n%2A%28-2%29%20-%2010)
![P(-2) = -8 + 4m + 2n - 10](https://tex.z-dn.net/?f=P%28-2%29%20%3D%20-8%20%2B%204m%20%2B%202n%20-%2010)
Collect like terms
![P(-2) = 4m + 2n - 10 - 8](https://tex.z-dn.net/?f=P%28-2%29%20%3D%204m%20%2B%202n%20-%2010%20-%208)
![P(-2) = 4m + 2n - 18](https://tex.z-dn.net/?f=P%28-2%29%20%3D%204m%20%2B%202n%20-%2018)
x + 2 leaves a remainder of 36, means that P(-2) = 36;
So, we have:
![4m + 2n - 18 = 36](https://tex.z-dn.net/?f=4m%20%2B%202n%20-%2018%20%3D%2036)
Collect like terms
![4m + 2n = 36+18](https://tex.z-dn.net/?f=4m%20%2B%202n%20%3D%2036%2B18)
![4m + 2n = 54](https://tex.z-dn.net/?f=4m%20%2B%202n%20%3D%2054)
Divide through by 2
--- (2)
Add (1) and (2)
![m + 2m - n + n = 9 +27](https://tex.z-dn.net/?f=m%20%2B%202m%20-%20n%20%2B%20n%20%3D%209%20%2B27)
![3m =36](https://tex.z-dn.net/?f=3m%20%3D36)
Divide by 3
![m = 12](https://tex.z-dn.net/?f=m%20%3D%2012)
Substitute
in (1)
![m - n =9](https://tex.z-dn.net/?f=m%20-%20n%20%3D9)
Make n the subject
![n = m - 9](https://tex.z-dn.net/?f=n%20%3D%20m%20-%209)
![n = 12 - 9](https://tex.z-dn.net/?f=n%20%3D%2012%20-%209)
![n =3](https://tex.z-dn.net/?f=n%20%3D3)