I answer to the question is C
Y = sallys grocerys
x = how much sally paid
y - (.05) = x
Answer:
![|\alpha| = 2](https://tex.z-dn.net/?f=%7C%5Calpha%7C%20%3D%202)
Step-by-step explanation:
Since
and
are complex conjugates, let's define them as follows:
![\alpha = a+bi](https://tex.z-dn.net/?f=%5Calpha%20%3D%20a%2Bbi)
![\beta = a-bi](https://tex.z-dn.net/?f=%5Cbeta%20%3D%20a-bi)
![\frac{\alpha}{\beta^2}=\frac{a+bi}{a^2-b^2-2abi} =\frac{(a+bi)*(a^2-b^2+2abi)}{(a^2-b^2-2abi)*(a^2-b^2+2abi)} =\frac{a^3-3ab^2+(3a^2b-b^3)i}{a^4+2a^2b^2+b^4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Calpha%7D%7B%5Cbeta%5E2%7D%3D%5Cfrac%7Ba%2Bbi%7D%7Ba%5E2-b%5E2-2abi%7D%20%3D%5Cfrac%7B%28a%2Bbi%29%2A%28a%5E2-b%5E2%2B2abi%29%7D%7B%28a%5E2-b%5E2-2abi%29%2A%28a%5E2-b%5E2%2B2abi%29%7D%20%3D%5Cfrac%7Ba%5E3-3ab%5E2%2B%283a%5E2b-b%5E3%29i%7D%7Ba%5E4%2B2a%5E2b%5E2%2Bb%5E4%7D)
Since
is a real number, complex part of above result must be zero.
![3a^2b-b^3=0](https://tex.z-dn.net/?f=3a%5E2b-b%5E3%3D0)
From to hold above equality,
or
.
However, since
, ![b\neq 0](https://tex.z-dn.net/?f=b%5Cneq%200)
So,
or ![b =-\sqrt 3 a](https://tex.z-dn.net/?f=b%20%3D-%5Csqrt%203%20a)
And since
and
are complex conjugates, taking plus or minus sign as found above will not affect the result, so let's write the last version of
and
as follows:
![\alpha = a+\sqrt 3 ai](https://tex.z-dn.net/?f=%5Calpha%20%3D%20a%2B%5Csqrt%203%20ai)
![\beta = a-\sqrt 3 ai](https://tex.z-dn.net/?f=%5Cbeta%20%3D%20a-%5Csqrt%203%20ai)
Since ![|\alpha-\beta|=2\sqrt 3](https://tex.z-dn.net/?f=%7C%5Calpha-%5Cbeta%7C%3D2%5Csqrt%203)
⇒ ![a = 1](https://tex.z-dn.net/?f=a%20%3D%201)
Finally,
⇒ ![|\alpha| = \sqrt{(1^2+\sqrt 3^2)}=2](https://tex.z-dn.net/?f=%7C%5Calpha%7C%20%3D%20%5Csqrt%7B%281%5E2%2B%5Csqrt%203%5E2%29%7D%3D2)
Answer:
About 5
Step-by-step explanation:
2/3 times 7 is 4.66666666667
Round that up to 5