Answer:
A .1458333333 B 1.02081 C terminating because it does not repeat
Step-by-step explanation:
Divide by 3
then mutiply .14583 by 7
Answer:
![\large \boxed{\sf \ \ k=1 \ \ }](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5Csf%20%5C%20%5C%20k%3D1%20%5C%20%5C%20%7D)
Step-by-step explanation:
Hello,
First of all, let's notice that even if we do not know the zeros of P(x) we can say that
![(1) \ \alpha + \beta =\dfrac{5}{6} \\ \\ (2) \ \alpha * \beta =\dfrac{k}{6}](https://tex.z-dn.net/?f=%281%29%20%5C%20%5Calpha%20%2B%20%5Cbeta%20%3D%5Cdfrac%7B5%7D%7B6%7D%20%5C%5C%20%5C%5C%20%282%29%20%5C%20%5Calpha%20%2A%20%5Cbeta%20%3D%5Cdfrac%7Bk%7D%7B6%7D)
<u>But, why !?</u>
As they are the zeros of P(x), we can write:
![P(x)=6(x^2-\boxed{\dfrac{5}{6}}x+\boxed{\dfrac{k}{6}})=6(x-\alpha)(x-\beta)=6(x^2-\boxed{(\alpha +\beta)}x+ \boxed{\alpha *\beta} )](https://tex.z-dn.net/?f=P%28x%29%3D6%28x%5E2-%5Cboxed%7B%5Cdfrac%7B5%7D%7B6%7D%7Dx%2B%5Cboxed%7B%5Cdfrac%7Bk%7D%7B6%7D%7D%29%3D6%28x-%5Calpha%29%28x-%5Cbeta%29%3D6%28x%5E2-%5Cboxed%7B%28%5Calpha%20%2B%5Cbeta%29%7Dx%2B%20%5Cboxed%7B%5Calpha%20%2A%5Cbeta%7D%20%29)
And then we can identify the coefficients of the like terms to find the equations (1) and (2).
Now, we have <u>one more equation</u> which is:
![(3) \ \alpha -\beta =\dfrac{1}{6}](https://tex.z-dn.net/?f=%283%29%20%5C%20%5Calpha%20-%5Cbeta%20%3D%5Cdfrac%7B1%7D%7B6%7D)
(1)+(3) gives:
![\alpha + \beta +\alpha -\beta =\dfrac{5}{6}+\dfrac{1}{6}=\dfrac{6}{6}=1 \\ \\ 2\alpha =1 \ \text{ divide by 2 } \\ \\ \alpha =\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Calpha%20%2B%20%5Cbeta%20%2B%5Calpha%20-%5Cbeta%20%3D%5Cdfrac%7B5%7D%7B6%7D%2B%5Cdfrac%7B1%7D%7B6%7D%3D%5Cdfrac%7B6%7D%7B6%7D%3D1%20%5C%5C%20%5C%5C%3C%3D%3E%202%5Calpha%20%3D1%20%5C%20%5Ctext%7B%20divide%20by%202%20%7D%20%5C%5C%20%5C%5C%20%3C%3D%3E%20%5Calpha%20%3D%5Cdfrac%7B1%7D%7B2%7D)
And we replace in (3) to get the value of the second zero.
![\beta = \dfrac{1}{2}-\dfrac{1}{6}=\dfrac{3-1}{6}=\dfrac{2}{6}=\dfrac{1}{3}](https://tex.z-dn.net/?f=%5Cbeta%20%3D%20%5Cdfrac%7B1%7D%7B2%7D-%5Cdfrac%7B1%7D%7B6%7D%3D%5Cdfrac%7B3-1%7D%7B6%7D%3D%5Cdfrac%7B2%7D%7B6%7D%3D%5Cdfrac%7B1%7D%7B3%7D)
And, finally, from (2), it comes:
![k=6*\alpha *\beta =6*\dfrac{1}{2}*\dfrac{1}{3}=\dfrac{6}{6}=1](https://tex.z-dn.net/?f=k%3D6%2A%5Calpha%20%2A%5Cbeta%20%3D6%2A%5Cdfrac%7B1%7D%7B2%7D%2A%5Cdfrac%7B1%7D%7B3%7D%3D%5Cdfrac%7B6%7D%7B6%7D%3D1)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
y=1/2x +4
Step-by-step explanation:
Parallel lines have the same slope 1/2
and passes through (-4,2)
first we should use the equation form y-2=1/2(x-(-4))
y-2=1/2x +2 y=1/2x+4
Answer:
Hello!
answer: 13
Step-by-step explanation:
The mode is simply just the number that is shown the most in the data set so as you can see 13 is shown the most so 13 is our mode Hope that helps!
Hello,
The answer is
<span>B. Y-intercept of (0, −1), starts down on the left, gets closer to y = −3 on the right
Hope this helps</span>