Answer:
it must also have the root : - 6i
Step-by-step explanation:
If a polynomial is expressed with real coefficients (which must be the case if it is a function f(x) in the Real coordinate system), then if it has a complex root "a+bi", it must also have for root the conjugate of that complex root.
This is because in order to render a polynomial with Real coefficients, the binomial factor (x - (a+bi)) originated using the complex root would be able to eliminate the imaginary unit, only when multiplied by the binomial factor generated by its conjugate: (x - (a-bi)). This is shown below:
![(x-(a+bi))*(x-(a-bi))=\\(x-a-bi)*(x-a+bi)=\\([x-a]-bi)*([x-a]+bi)=\\(x-a)^2-(bi)^2=\\(x-a)^2-b^2(-1)=\\(x-a)^2+b^2](https://tex.z-dn.net/?f=%28x-%28a%2Bbi%29%29%2A%28x-%28a-bi%29%29%3D%5C%5C%28x-a-bi%29%2A%28x-a%2Bbi%29%3D%5C%5C%28%5Bx-a%5D-bi%29%2A%28%5Bx-a%5D%2Bbi%29%3D%5C%5C%28x-a%29%5E2-%28bi%29%5E2%3D%5C%5C%28x-a%29%5E2-b%5E2%28-1%29%3D%5C%5C%28x-a%29%5E2%2Bb%5E2)
where the imaginary unit has disappeared, making the expression real.
So in our case, a+bi is -6i (real part a=0, and imaginary part b=-6)
Then, the conjugate of this root would be: +6i, giving us the other complex root that also may be present in the real polynomial we are dealing with.
Answer is given below :
Step-by-step explanation:
- Histograms are used in group frequency parameters. Furthermore, it is useless as a given set of five parameters or data and only results in a bar graph and, basically, the vertical graph mentioned above is the correct choice to display the numbers.
- It is used to expand on the definition of the histogram when the frequency is grouped. For example, data sets 1–5, 6–10, 11–15 and 16–20 can now be used to describe histograms due to the given number and size of data.
X= -1 t= 7
4(3x-1)=3+8x-11
12x-4=3+8x-11
12x-8x=4+3-11
4x= -4
\4. \4
x= -1
2t+4+5t=6t+11
2t-6t+5t=-4+11
1t=7
\1. \1
t=7
The total value of the uniform Aileen sold is x= 2260 on monthly Commission sells.
Given,
Let us assume the all little League uniform = x
Aileen first commission 10% of 2000$ in sales.
Aileen Second Commission 12% of (x-2000)$
Total Commission Aileen Earner = 10% ×2000 + 12% × (x-2000)
231.2 = 0.1× 2000 + 0.12× (x-2000)
231.2 = 200 + (0.12x - 240 )
231.2 = 200 + 0.12x - 240
After Transformation, we get
0.12x = 231.2 - 200 +240
0.12x = 271.2
x = 271.2/.12
x = 2260
Aileen Sell the total value of Lopez Sporting Goods Uniform is 2260.
So the final Answer is x = 2260$.
Learn more about the Commission here.
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Euler's formula for Vertices, Edges and faces is V-E+F = 2
Replace the letters with the given information and solve for the missing one.
From the problem V ( Vertices) = 11 and F (faces) = 15.
11 - E + 15 = 2
11 + 15 = 26
26 - E = 2
E = 26-2
E = 24
The answer is b. 24
