Required potynomial = (x -5)(x - 3 - 2i)(x - 3 + 2i) = (x - 5)(x^2 - 6x + 13) = x^3 - 6x^2 + 13x - 5x^2 + 30x - 65 = x^3 - 11x^2 + 43x - 65
Answer:
![=4.+2.](https://tex.z-dn.net/?f=%3C8%2C26%2C-10%3E%3D4.%3C4%2C5%2C-4%3E%2B2.%3C-4%2C3%2C3%3E)
Step-by-step explanation:
<u>Linear Combination Of Vectors
</u>
One vector
is a linear combination of
and
if there are two scalars
such as
![\vec b=x_1\vec a_1+x_2\vec a_2](https://tex.z-dn.net/?f=%5Cvec%20b%3Dx_1%5Cvec%20a_1%2Bx_2%5Cvec%20a_2)
In our case, all the vectors are given in
but there are only two possible components for the linear combination. This indicates that only two conditions can be used to determine both scalars, and the other condition must be satisfied once the scalars are found.
We have
![\vec a_1=,\ \vec a2=,\ \vec b=](https://tex.z-dn.net/?f=%5Cvec%20a_1%3D%3C4%2C5%2C-4%3E%2C%5C%20%5Cvec%20a2%3D%3C-4%2C3%2C3%3E%2C%5C%20%5Cvec%20b%3D%3C8%2C26%2C-10%3E)
We set the equation
![=x_1.+x_2.](https://tex.z-dn.net/?f=%3C8%2C26%2C-10%3E%3Dx_1.%3C4%2C5%2C-4%3E%2Bx_2.%3C-4%2C3%2C3%3E)
Multiplying both scalars by the vectors
![=+](https://tex.z-dn.net/?f=%3C8%2C26%2C-10%3E%3D%3C4x_1%2C5x_1%2C-4x_1%3E%2B%3C-4x_2%2C3x_2%2C3x_2%3E)
Equating each coordinate, we get
![4x_1-4x_2=8](https://tex.z-dn.net/?f=4x_1-4x_2%3D8)
![5x_1+3x_2=26](https://tex.z-dn.net/?f=5x_1%2B3x_2%3D26)
![-4x_1+3x_2=-10](https://tex.z-dn.net/?f=-4x_1%2B3x_2%3D-10)
Adding the first and the third equations:
![-x_2=-2](https://tex.z-dn.net/?f=-x_2%3D-2)
![x_2=2](https://tex.z-dn.net/?f=x_2%3D2)
Replacing in the first equation
![4x_1-4(2)=8](https://tex.z-dn.net/?f=4x_1-4%282%29%3D8)
![4x_1=8+8](https://tex.z-dn.net/?f=4x_1%3D8%2B8)
![x_1=4](https://tex.z-dn.net/?f=x_1%3D4)
We must test if those values make the second equation become an identity
![5(4)+3(2)=20+6=26](https://tex.z-dn.net/?f=5%284%29%2B3%282%29%3D20%2B6%3D26)
The second equation complies with the values of
and
, so the solution is
![=4.+2.](https://tex.z-dn.net/?f=%3C8%2C26%2C-10%3E%3D4.%3C4%2C5%2C-4%3E%2B2.%3C-4%2C3%2C3%3E)
Answer:
32 red
28 white
20 blue
Step-by-step explanation:
.40 x 80 = 32 red
.35 x 80 = 28 white
.25 x 80 = 20 blue
The totals have to equal the total number of strands.