Answer:
The first one is right the rest of them is not right correct
Step-by-step explanation:
Answer:
2x+7
Step-by-step explanation:
To Simplify an Expression , we combine Like-Terms
So for our Question , we have Terms with x and Constant Term
Combine Terms with x : 5x-2x-x=2x
Constant Term : 7
Then 5x-2x+7-x = 2x+7
Answer:
The other pairs are:
and ![(-2, \frac{23\pi}{6})](https://tex.z-dn.net/?f=%28-2%2C%20%5Cfrac%7B23%5Cpi%7D%7B6%7D%29)
and ![(-1, \frac{7\pi}{3})](https://tex.z-dn.net/?f=%28-1%2C%20%5Cfrac%7B7%5Cpi%7D%7B3%7D%29)
and ![(1, \frac{7\pi}{4})](https://tex.z-dn.net/?f=%281%2C%20%5Cfrac%7B7%5Cpi%7D%7B4%7D%29)
See attachment for plots
Step-by-step explanation:
Given
![(a)\ (2, \frac{5\pi}{6})](https://tex.z-dn.net/?f=%28a%29%5C%20%282%2C%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%29)
![(b)\ (1, -\frac{2\pi}{3})](https://tex.z-dn.net/?f=%28b%29%5C%20%281%2C%20-%5Cfrac%7B2%5Cpi%7D%7B3%7D%29)
![(c)\ (-1, \frac{5\pi}{4})](https://tex.z-dn.net/?f=%28c%29%5C%20%28-1%2C%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%29)
Solving (a): Plot a, b and c
See attachment for plots
Solving (b): Find other pairs for
and ![r < 0](https://tex.z-dn.net/?f=r%20%3C%200)
The general rule is that:
The other points can be derived using
and
Let
---- You can assume any value of n
So, we have:
![(r, \theta) = (r, \theta + 2*1*\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28r%2C%20%5Ctheta%20%2B%202%2A1%2A%5Cpi%29)
![(r, \theta) = (r, \theta + 2\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28r%2C%20%5Ctheta%20%2B%202%5Cpi%29)
![(r, \theta) = (-r, \theta + (2n + 1)\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28-r%2C%20%5Ctheta%20%2B%20%282n%20%2B%201%29%5Cpi%29)
![(r, \theta) = (-r, \theta + (2*1 + 1)\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28-r%2C%20%5Ctheta%20%2B%20%282%2A1%20%2B%201%29%5Cpi%29)
![(r, \theta) = (-r, \theta + (2 + 1)\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28-r%2C%20%5Ctheta%20%2B%20%282%20%2B%201%29%5Cpi%29)
![(r, \theta) = (-r, \theta + 3\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28-r%2C%20%5Ctheta%20%2B%203%5Cpi%29)
![(a)\ (2, \frac{5\pi}{6})](https://tex.z-dn.net/?f=%28a%29%5C%20%282%2C%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%29)
So, the pairs are:
![(r, \theta) = (r, \theta + 2\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28r%2C%20%5Ctheta%20%2B%202%5Cpi%29)
![(2, \frac{5\pi}{6}) = (2, \frac{5\pi}{6} + 2\pi)](https://tex.z-dn.net/?f=%282%2C%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%29%20%3D%20%282%2C%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%20%2B%202%5Cpi%29)
Take LCM
![(2, \frac{5\pi}{6}) = (2, \frac{5\pi+12\pi}{6})](https://tex.z-dn.net/?f=%282%2C%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%29%20%3D%20%282%2C%20%5Cfrac%7B5%5Cpi%2B12%5Cpi%7D%7B6%7D%29)
![(2, \frac{5\pi}{6}) = (2, \frac{17\pi}{6})](https://tex.z-dn.net/?f=%282%2C%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%29%20%3D%20%282%2C%20%5Cfrac%7B17%5Cpi%7D%7B6%7D%29)
And
![(r, \theta) = (-r, \theta + 3\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28-r%2C%20%5Ctheta%20%2B%203%5Cpi%29)
![(2, \frac{5\pi}{6}) = (-2, \frac{5\pi}{6} + 3\pi)](https://tex.z-dn.net/?f=%282%2C%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%29%20%3D%20%28-2%2C%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%20%2B%203%5Cpi%29)
Take LCM
![(2, \frac{5\pi}{6}) = (-2, \frac{5\pi+18\pi}{6})](https://tex.z-dn.net/?f=%282%2C%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%29%20%3D%20%28-2%2C%20%5Cfrac%7B5%5Cpi%2B18%5Cpi%7D%7B6%7D%29)
![(2, \frac{5\pi}{6}) = (-2, \frac{23\pi}{6})](https://tex.z-dn.net/?f=%282%2C%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%29%20%3D%20%28-2%2C%20%5Cfrac%7B23%5Cpi%7D%7B6%7D%29)
The other pairs are:
and ![(-2, \frac{23\pi}{6})](https://tex.z-dn.net/?f=%28-2%2C%20%5Cfrac%7B23%5Cpi%7D%7B6%7D%29)
![(b)\ (1, -\frac{2\pi}{3})](https://tex.z-dn.net/?f=%28b%29%5C%20%281%2C%20-%5Cfrac%7B2%5Cpi%7D%7B3%7D%29)
So, the pairs are:
![(r, \theta) = (r, \theta + 2\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28r%2C%20%5Ctheta%20%2B%202%5Cpi%29)
![(1, -\frac{2\pi}{3}) = (1, -\frac{2\pi}{3} + 2\pi)](https://tex.z-dn.net/?f=%281%2C%20-%5Cfrac%7B2%5Cpi%7D%7B3%7D%29%20%3D%20%281%2C%20-%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%2B%202%5Cpi%29)
Take LCM
![(1, -\frac{2\pi}{3}) = (1, \frac{-2\pi+6\pi}{3})](https://tex.z-dn.net/?f=%281%2C%20-%5Cfrac%7B2%5Cpi%7D%7B3%7D%29%20%3D%20%281%2C%20%5Cfrac%7B-2%5Cpi%2B6%5Cpi%7D%7B3%7D%29)
![(1, -\frac{2\pi}{3}) = (1, \frac{4\pi}{3})](https://tex.z-dn.net/?f=%281%2C%20-%5Cfrac%7B2%5Cpi%7D%7B3%7D%29%20%3D%20%281%2C%20%5Cfrac%7B4%5Cpi%7D%7B3%7D%29)
And
![(r, \theta) = (-r, \theta + 3\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28-r%2C%20%5Ctheta%20%2B%203%5Cpi%29)
![(1, -\frac{2\pi}{3}) = (-1, -\frac{2\pi}{3} + 3\pi)](https://tex.z-dn.net/?f=%281%2C%20-%5Cfrac%7B2%5Cpi%7D%7B3%7D%29%20%3D%20%28-1%2C%20-%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%2B%203%5Cpi%29)
Take LCM
![(1, -\frac{2\pi}{3}) = (-1, \frac{-2\pi+9\pi}{3})](https://tex.z-dn.net/?f=%281%2C%20-%5Cfrac%7B2%5Cpi%7D%7B3%7D%29%20%3D%20%28-1%2C%20%5Cfrac%7B-2%5Cpi%2B9%5Cpi%7D%7B3%7D%29)
![(1, -\frac{2\pi}{3}) = (-1, \frac{7\pi}{3})](https://tex.z-dn.net/?f=%281%2C%20-%5Cfrac%7B2%5Cpi%7D%7B3%7D%29%20%3D%20%28-1%2C%20%5Cfrac%7B7%5Cpi%7D%7B3%7D%29)
The other pairs are:
and ![(-1, \frac{7\pi}{3})](https://tex.z-dn.net/?f=%28-1%2C%20%5Cfrac%7B7%5Cpi%7D%7B3%7D%29)
![(c)\ (-1, \frac{5\pi}{4})](https://tex.z-dn.net/?f=%28c%29%5C%20%28-1%2C%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%29)
![r = -1 \ \ \ \ \theta = \frac{-5\pi}{4}](https://tex.z-dn.net/?f=r%20%3D%20-1%20%5C%20%5C%20%5C%20%5C%20%5Ctheta%20%3D%20%5Cfrac%7B-5%5Cpi%7D%7B4%7D)
So, the pairs are
![(r, \theta) = (r, \theta + 2\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28r%2C%20%5Ctheta%20%2B%202%5Cpi%29)
![(-1, \frac{-5\pi}{4}) = (-1, \frac{-5\pi}{4} + 2\pi)](https://tex.z-dn.net/?f=%28-1%2C%20%5Cfrac%7B-5%5Cpi%7D%7B4%7D%29%20%3D%20%28-1%2C%20%5Cfrac%7B-5%5Cpi%7D%7B4%7D%20%2B%202%5Cpi%29)
Take LCM
![(-1, \frac{-5\pi}{4}) = (-1, \frac{-5\pi+8\pi}{4} )](https://tex.z-dn.net/?f=%28-1%2C%20%5Cfrac%7B-5%5Cpi%7D%7B4%7D%29%20%3D%20%28-1%2C%20%5Cfrac%7B-5%5Cpi%2B8%5Cpi%7D%7B4%7D%20%29)
![(-1, \frac{-5\pi}{4}) = (-1, \frac{3\pi}{4} )](https://tex.z-dn.net/?f=%28-1%2C%20%5Cfrac%7B-5%5Cpi%7D%7B4%7D%29%20%3D%20%28-1%2C%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%20%29)
And
![(r, \theta) = (-r, \theta + 3\pi)](https://tex.z-dn.net/?f=%28r%2C%20%5Ctheta%29%20%3D%20%28-r%2C%20%5Ctheta%20%2B%203%5Cpi%29)
![(-1, \frac{-5\pi}{4}) = (-(-1), \frac{-5\pi}{4}+ 3\pi)](https://tex.z-dn.net/?f=%28-1%2C%20%5Cfrac%7B-5%5Cpi%7D%7B4%7D%29%20%3D%20%28-%28-1%29%2C%20%5Cfrac%7B-5%5Cpi%7D%7B4%7D%2B%203%5Cpi%29)
Take LCM
![(-1, \frac{-5\pi}{4}) = (1, \frac{-5\pi+12\pi}{4})](https://tex.z-dn.net/?f=%28-1%2C%20%5Cfrac%7B-5%5Cpi%7D%7B4%7D%29%20%3D%20%281%2C%20%5Cfrac%7B-5%5Cpi%2B12%5Cpi%7D%7B4%7D%29)
![(-1, \frac{-5\pi}{4}) = (1, \frac{7\pi}{4})](https://tex.z-dn.net/?f=%28-1%2C%20%5Cfrac%7B-5%5Cpi%7D%7B4%7D%29%20%3D%20%281%2C%20%5Cfrac%7B7%5Cpi%7D%7B4%7D%29)
So, the other pairs are:
and ![(1, \frac{7\pi}{4})](https://tex.z-dn.net/?f=%281%2C%20%5Cfrac%7B7%5Cpi%7D%7B4%7D%29)
Answer:
7.5
Step-by-step explanation:
You have to divide the miles by the hours drived and then divide 60 per the miles per hour
I believe it would be -28. Withdrawing means to take money out of your account. That means you are subtracting 28 which will turn it to a negative. So, the answer is -28. Hope this helps if you have any questions please comment.