Answer:
The correct option is O B'
Step-by-step explanation:
We have a quadrilateral with vertices A, B, C and D. A line of reflection is drawn so that A is 6 units away from the line, B is 4 units away from the line, C is 7 units away from the line and D is 9 units away from the line.
Now we perform the reflection and we obtain a new quadrilateral A'B'C'D'.
In order to apply the reflection to the original quadrilateral ABCD, we perform the reflection to all of its points, particularly to its vertices.
Wherever we have a point X and a line of reflection L and we perform the reflection, the new point X' will keep its original distance from the line of reflection (this is an important concept in order to understand the exercise).
I will attach a drawing with an example.
Finally, we only have to look at the vertices and its original distances to answer the question.
The vertice that is closest to the line of reflection is B (the distance is 4 units). We answer O B'
Answer:
y +2 = 2(x +3)
Step-by-step explanation:
The equation in point-slope form for a line with slope m through point (h, k) is ...
y -k = m(x -h)
The slope of your given line is the coefficient of x, -1/2. The slope of a perpendicular line will be the negative reciprocal of that: -1/(-1/2) = 2. So, you have m = 2, (h, k) = (-3, -2), and your desired equation is ...
y -(-2) = 2(x -(-3)) . . . . . . which can be simplified to ...
y +2 = 2(x +3)
Answer:
![\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4](https://tex.z-dn.net/?f=%5Cfrac%7B125x%5E3%20-%208%7D%7B5x%20-%202%7D%20%3D%2025x%5E2%20%2B%2010x%20%2B4)
Step-by-step explanation:
Given
![Dividend = 125x^3 - 8](https://tex.z-dn.net/?f=Dividend%20%3D%20125x%5E3%20-%208)
![Divisor = 5x - 2](https://tex.z-dn.net/?f=Divisor%20%3D%205x%20-%202)
Required
Determine the quotient
See attachment for complete process.
First, divide 125x^3 by 5x
![\frac{125x^3}{5x} =25x^2](https://tex.z-dn.net/?f=%5Cfrac%7B125x%5E3%7D%7B5x%7D%20%3D25x%5E2)
Write
at the top
Multiply
by ![25x^2](https://tex.z-dn.net/?f=25x%5E2)
![= 125x^3 - 50x^2](https://tex.z-dn.net/?f=%3D%20125x%5E3%20-%2050x%5E2)
Subtract from 125x^3 - 8
i.e.
![125x^3 - 8 - (125x^3 - 50x^2) = 50x^2 - 8](https://tex.z-dn.net/?f=125x%5E3%20-%208%20-%20%28125x%5E3%20-%2050x%5E2%29%20%3D%2050x%5E2%20-%208)
Step 2:
Divide 50x^2 by 5x
![\frac{50x^2}{5x} = 10x](https://tex.z-dn.net/?f=%5Cfrac%7B50x%5E2%7D%7B5x%7D%20%3D%2010x)
Write
at the top
Multiply
by ![10x](https://tex.z-dn.net/?f=10x)
![= 50x^2 - 20x](https://tex.z-dn.net/?f=%3D%2050x%5E2%20-%2020x)
Subtract from 50x^2 - 8
i.e.
![50x^2 - 8 - (50x^2 - 20x) = 20x - 8](https://tex.z-dn.net/?f=50x%5E2%20-%208%20-%20%2850x%5E2%20-%2020x%29%20%3D%2020x%20-%208)
Step 3:
Divide 20x by 5x
![\frac{20x}{5x} = 4](https://tex.z-dn.net/?f=%5Cfrac%7B20x%7D%7B5x%7D%20%3D%204)
Write
at the top
Multiply
by ![4](https://tex.z-dn.net/?f=4)
![= 20x - 8](https://tex.z-dn.net/?f=%3D%2020x%20-%208)
Subtract from 20x - 8
i.e.
![20x - 8 - (20x - 8) = 0](https://tex.z-dn.net/?f=20x%20-%208%20-%20%2820x%20-%208%29%20%3D%200)
Hence:
![\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4](https://tex.z-dn.net/?f=%5Cfrac%7B125x%5E3%20-%208%7D%7B5x%20-%202%7D%20%3D%2025x%5E2%20%2B%2010x%20%2B4)
70/2 = 35
The car gets 35 miles per gallons.
You can also find that out by looking at the slope of the equation. y = 35x. 35 is the slope here.
For your graph, plot the points:
(0,0)
(1,35)
(2,70)
(3,105)
(4,140)
(5,175)
(6,210)
(7,245)
(8,280)
And then draw a line through the points.