Domain is x’s and range is y’s.
For a, the domain is -2<=x<1
For a, the range is 1<=y<2
For b, the domain is 1<=x<=2
For b, the range is -2<=y<=2
(The <= is the ones with a line under, meaning equal to, if that makes sense. So write with a line under rather than equal sign)
Hope this helps!
Answer:
5. Inequality form: n ≥ 3
Interval notation: [3, ∞)
6. Inequality form: x < 4
Interval notation: (- ∞, 4)
11. Inequality form: x > 50
Interval notation: (50, ∞)
12. Inequality form: y
8
Interval notation: [8, ∞)
15. Inequality form: z < 8
Interval notation: (- ∞, 8)
16. Inequality form: y
4
Interval notation: [4, ∞)
Step-by-step explanation:
I tried to graph them as best as I could, I hope this helps!
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where:
m: It's the slope
b: It is the cut-off point with the y axis
On the other hand we have that if two lines are perpendicular, then the product of their slopes is -1. So:
![m_ {1} * m_ {2} = - 1](https://tex.z-dn.net/?f=m_%20%7B1%7D%20%2A%20m_%20%7B2%7D%20%3D%20-%201)
The given line is:
![5x-2y = -6\\-2y = -6-5x\\2y = 5x + 6\\y = \frac {5} {2} x + \frac {6} {2}\\y = \frac {5} {2} x + 3](https://tex.z-dn.net/?f=5x-2y%20%3D%20-6%5C%5C-2y%20%3D%20-6-5x%5C%5C2y%20%3D%205x%20%2B%206%5C%5Cy%20%3D%20%5Cfrac%20%7B5%7D%20%7B2%7D%20x%20%2B%20%5Cfrac%20%7B6%7D%20%7B2%7D%5C%5Cy%20%3D%20%5Cfrac%20%7B5%7D%20%7B2%7D%20x%20%2B%203)
So we have:
![m_ {1} = \frac {5} {2}](https://tex.z-dn.net/?f=m_%20%7B1%7D%20%3D%20%5Cfrac%20%7B5%7D%20%7B2%7D)
We find ![m_ {2}:](https://tex.z-dn.net/?f=m_%20%7B2%7D%3A)
![m_ {2} = \frac {-1} {\frac {5} {2}}\\m = - \frac {2} {5}](https://tex.z-dn.net/?f=m_%20%7B2%7D%20%3D%20%5Cfrac%20%7B-1%7D%20%7B%5Cfrac%20%7B5%7D%20%7B2%7D%7D%5C%5Cm%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D)
So, a line perpendicular to the one given is of the form:
![y = - \frac {2} {5} x + b](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D%20x%20%2B%20b)
We substitute the given point to find "b":
![-4 = - \frac {2} {5} (5) + b\\-4 = -2 + b\\-4 + 2 = b\\b = -2](https://tex.z-dn.net/?f=-4%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D%20%285%29%20%2B%20b%5C%5C-4%20%3D%20-2%20%2B%20b%5C%5C-4%20%2B%202%20%3D%20b%5C%5Cb%20%3D%20-2)
Finally we have:
![y = - \frac {2} {5} x-2](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D%20x-2)
In point-slope form we have:
![y - (- 4) = - \frac {2} {5} (x-5)\\y + 4 = - \frac {2} {5} (x-5)](https://tex.z-dn.net/?f=y%20-%20%28-%204%29%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D%20%28x-5%29%5C%5Cy%20%2B%204%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D%20%28x-5%29)
ANswer:
![y = - \frac {2} {5} x-2\\y + 4 = - \frac {2} {5} (x-5)](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D%20x-2%5C%5Cy%20%2B%204%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D%20%28x-5%29)
Answer:
(a, a)
Step-by-step explanation:
actually there are two cases, don't have intersection and have. if have intersection, then they intersect at line y = x or point (a, a) by definition of inverse function.
Well the answer i got was
![a^{8}x](https://tex.z-dn.net/?f=%20a%5E%7B8%7Dx%20)
when i multiplied
the answer i got when i added was