Given:
A figure of dilation and the center of dilation is O.
To find:
The value of y.
Solution:
The distance between center and vertex of image (d') is proportional to the distance between center and the corresponding vertex of original figure (d).
![d'\propto d](https://tex.z-dn.net/?f=d%27%5Cpropto%20d)
![d'=kd](https://tex.z-dn.net/?f=d%27%3Dkd)
![\dfrac{d'}{d}=k](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%27%7D%7Bd%7D%3Dk)
Where, k is the scale factor or constant of proportionality.
So, the scale factor for the given dilation is
![k=\dfrac{OB'}{OB}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7BOB%27%7D%7BOB%7D)
![k=\dfrac{36}{16}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B36%7D%7B16%7D)
![k=\dfrac{9}{4}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B9%7D%7B4%7D)
We know that,
![k=\dfrac{\text{Side length of image}}{\text{Corresponding side length of original figure}}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B%5Ctext%7BSide%20length%20of%20image%7D%7D%7B%5Ctext%7BCorresponding%20side%20length%20of%20original%20figure%7D%7D)
![\dfrac{9}{4}=\dfrac{A'C'}{AC}](https://tex.z-dn.net/?f=%5Cdfrac%7B9%7D%7B4%7D%3D%5Cdfrac%7BA%27C%27%7D%7BAC%7D)
![\dfrac{9}{4}=\dfrac{27}{y}](https://tex.z-dn.net/?f=%5Cdfrac%7B9%7D%7B4%7D%3D%5Cdfrac%7B27%7D%7By%7D)
![9\times y=27\times 4](https://tex.z-dn.net/?f=9%5Ctimes%20y%3D27%5Ctimes%204)
Divide both sides by 9.
![y=\dfrac{27\times 4}{9}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B27%5Ctimes%204%7D%7B9%7D)
![y=3\times 4](https://tex.z-dn.net/?f=y%3D3%5Ctimes%204)
![y=12](https://tex.z-dn.net/?f=y%3D12)
Therefore, the value of y is 12.
Answer:
The hurricane traveled 260 miles per hour.
Step-by-step explanation:
Given,
Distance covered by hurricane = 130 miles
Then time =
hours=
hour
Distance=Speed*Time
Speed=![\frac{Distance}{Time}](https://tex.z-dn.net/?f=%5Cfrac%7BDistance%7D%7BTime%7D)
Speed=![\frac{130}{0.5}](https://tex.z-dn.net/?f=%5Cfrac%7B130%7D%7B0.5%7D)
Speed=260 miles per hour
So, the hurricane traveled 260 miles per hour
Answer:
The point slope formula states (y-y1)=m(x-x1)
Where m is the slope and (x1 y1) is a point the line passes through
Substituting the point and slope from the problem give
(y-5)=-2(x-3) ~answer
Answer:
B=9
Step-by-step explanation:
X=-3 Plus c = b
C= 27
|x plus b| also = c
B=27 divided by 3
It is correct if you're trying to add 0 for the first one
1 for the second one
and so on