![\csc\Theta=\frac{1}{\sin\Theta}](https://tex.z-dn.net/?f=%5Ccsc%5CTheta%3D%5Cfrac%7B1%7D%7B%5Csin%5CTheta%7D)
Since the function
![\csc\Theta](https://tex.z-dn.net/?f=%5Ccsc%5CTheta)
is literally defined as the reciprocal of
![\sin\Theta](https://tex.z-dn.net/?f=%5Csin%5CTheta)
, any value of
![\Theta](https://tex.z-dn.net/?f=%5CTheta)
will satisfy this equation.
A. All real numbers
2x - 2 < -12
2x < -12 + 2 add 2 to each side
2x < -10 perform the addition on the right side
x < -10 / 2 divide each side by 2
x < -5 perform the division on the right side
2x + 3 > 7
2x > 7 - 3 subtract 3 from each side
2x > 4 perform the subtraction on the right side
x > 4 / 2 divide each side by 2
x > 2 perform the division on the right side
These are just like equations, except the you have to change the direction of the sign when you multiply or divide by a negative number
(C) x < -5 or x > 2
Given:
The slope of the line joining points (3,2) and (0,a) is -1.
To find:
The value of a.
Solution:
If a line passes through two points
and
, the slope of a line is:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
The slope of the line joining points (3,2) and (0,a) is -1. So,
![\dfrac{a-2}{0-3}=-1](https://tex.z-dn.net/?f=%5Cdfrac%7Ba-2%7D%7B0-3%7D%3D-1)
![\dfrac{a-2}{-3}=-1](https://tex.z-dn.net/?f=%5Cdfrac%7Ba-2%7D%7B-3%7D%3D-1)
Multiply both sides by -3.
![a-2=-1(-3)](https://tex.z-dn.net/?f=a-2%3D-1%28-3%29)
![a-2=3](https://tex.z-dn.net/?f=a-2%3D3)
![a=3+2](https://tex.z-dn.net/?f=a%3D3%2B2)
![a=5](https://tex.z-dn.net/?f=a%3D5)
Therefore, the value of a is 5.
I believe the answer is c
This is quite simple, you can see that the x-axis stays the same so then you know that it is a vertical line. You can tell because any point on this line will be (2,x). So to graph it, you draw a vertical line where x=2