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.
<h2>
Answer:</h2>
∠LMN is a right angle
<h2>
Step-by-step explanation:</h2>
If we want to prove that two right triangles are congruent by knowing that the corresponding hypotenuses and one leg are congruent, we begin as follows:
- Since two legs are congruent and we know this by the hash marks, then the triangle ΔLKN is isosceles.
- By definition LN ≅ NK
- If ∠LMN is a right angle, then MN is the altitude of triangle ΔLKN
- Also MN is the bisector of LK, so KM ≅ ML
- So we have two right triangles ΔLMN and ΔKM having the same lengths of corresponding sides
- In conclusion, ΔLMN ≅ ΔKMN
The confidence interval is from 0.2191 to 0.2649, given by
.
The z-score we need is found by first subtracting the confidence level from 1:
1 - 0.95 = 0.05
Divide that by 2:
0.05/2 = 0.025
Subtract that from 1:
1 - 0.025 = 0.975
Look this up in the middle of a z-table (http://www.z-table.com) and we see that the z-score is 1.96.
Now our confidence interval is given by
Whenever we have a negative exponent, that means that the function should be in the denomenator. then the exponent will be positive.
Example
16^-4 = 1/(16^4)
Answer:
Idk what u mean by fraction but 80% of 15 is 12
Step-by-step explanation:
