It is given in the question that
![2(2x-1)>6 \ or \ x+3 \leq -6](https://tex.z-dn.net/?f=2%282x-1%29%3E6%20%5C%20or%20%5C%20x%2B3%20%5Cleq%20-6)
For th first inequality, we divide both sides by 2, and for second, we subtract 3 to both sides, that is
![2x-1>3 \ or \ x \leq -6-3 \\ 2x>4 \ or \ x \leq -9 \\ x>2 \ or \ x \leq -9](https://tex.z-dn.net/?f=2x-1%3E3%20%5C%20or%20%5C%20x%20%5Cleq%20-6-3%0A%5C%5C%0A2x%3E4%20%5C%20or%20%5C%20x%20%5Cleq%20-9%0A%5C%5C%0Ax%3E2%20%5C%20or%20%5C%20x%20%5Cleq%20-9)
So the required inequality is
![(- \infty, -9] U (2, \infty)](https://tex.z-dn.net/?f=%28-%20%5Cinfty%2C%20-9%5D%20U%20%282%2C%20%5Cinfty%29)
Correct option is B
Answer:
Step-by-step explanation:
let n be the number
n+9
Answer:
Look below
Step-by-step explanation:
First you multiply the top and bottom
5/12 x 6/7
5x6 and 12x7
you get your new fraction of 30/84
then you simplify it by 6 to get 5/14
hope this helps
Answer:
There are two choices for angle Y:
for
,
for
.
Step-by-step explanation:
There are mistakes in the statement, correct form is now described:
<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>
The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:
(1)
If we know that
,
and
, then we have the following second order polynomial:
![14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}](https://tex.z-dn.net/?f=14%5E%7B2%7D%20%3D%20XZ%5E%7B2%7D%20%2B%2018%5E%7B2%7D%20-%202%5Ccdot%20%2818%29%5Ccdot%20XZ%5Ccdot%20%5Ccos%2049%5E%7B%5Ccirc%7D)
(2)
By the Quadratic Formula we have the following result:
![XZ \approx 15.193\,\lor\,XZ \approx 8.424](https://tex.z-dn.net/?f=XZ%20%5Capprox%2015.193%5C%2C%5Clor%5C%2CXZ%20%5Capprox%208.424)
There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:
![XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y](https://tex.z-dn.net/?f=XZ%5E%7B2%7D%20%3D%20XY%5E%7B2%7D%20%2B%20YZ%5E%7B2%7D%20-%202%5Ccdot%20XY%20%5Ccdot%20YZ%20%5Ccdot%20%5Ccos%20Y)
![\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}](https://tex.z-dn.net/?f=%5Ccos%20Y%20%3D%20%5Cfrac%7BXY%5E%7B2%7D%2BYZ%5E%7B2%7D-XZ%5E%7B2%7D%7D%7B2%5Ccdot%20XY%5Ccdot%20YZ%7D)
![Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)](https://tex.z-dn.net/?f=Y%20%3D%20%5Ccos%20%5E%7B-1%7D%5Cleft%28%5Cfrac%7BXY%5E%7B2%7D%2BYZ%5E%7B2%7D-XZ%5E%7B2%7D%7D%7B2%5Ccdot%20XY%5Ccdot%20YZ%7D%20%5Cright%29)
1) ![XZ \approx 15.193](https://tex.z-dn.net/?f=XZ%20%5Capprox%2015.193)
![Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]](https://tex.z-dn.net/?f=Y%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B18%5E%7B2%7D%2B14%5E%7B2%7D-15.193%5E%7B2%7D%7D%7B2%5Ccdot%20%2818%29%5Ccdot%20%2814%29%7D%20%5Cright%5D)
![Y \approx 54.987^{\circ}](https://tex.z-dn.net/?f=Y%20%5Capprox%2054.987%5E%7B%5Ccirc%7D)
2) ![XZ \approx 8.424](https://tex.z-dn.net/?f=XZ%20%5Capprox%208.424)
![Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]](https://tex.z-dn.net/?f=Y%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B18%5E%7B2%7D%2B14%5E%7B2%7D-8.424%5E%7B2%7D%7D%7B2%5Ccdot%20%2818%29%5Ccdot%20%2814%29%7D%20%5Cright%5D)
![Y \approx 27.008^{\circ}](https://tex.z-dn.net/?f=Y%20%5Capprox%2027.008%5E%7B%5Ccirc%7D)
There are two choices for angle Y:
for
,
for
.