Answer:
answer = 21
Step-by-step explanation:
2n - 2 = 40
2n - 2 + 2 = 40 + 2
2n = 42
2n/2 = 42/2
n = 21
So basically you're dividing 12 by 3 times x which is 12 over 3x. 12/3x
Answer:
8/5
Step-by-step explanation:
You can rewrite the equation to 2/5 * 12/3
Which is equal to 2/5*4
So 2 times 4 is 8
So the answer is 8/5
Hope this helps!
Answer:
226.2 feet
Step-by-step explanation:
The fence around the dog's house is a circle, with a radius of 12 meters.
To calculate the distance the dog runs, we need to find the circumference of that circle, which is given by the formula:
C = 2 π r, since we know r, the calculation is easy:
C = 2 π 12 = 24 π = 75.4 feet.
The dog makes three laps around the circle before calming down... so he runs 3 times 75.4 feet.
Dogs run = 3 x 75.4 ft = 226.2 feet
Answer:
The length of the resulting segment is 500.
Step-by-step explanation:
Vectorially speaking, the dilation is defined by following operation:
![P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]](https://tex.z-dn.net/?f=P%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2B%20k%5Ccdot%20%5BP%28x%2Cy%29-O%28x%2Cy%29%5D)
(1)
Where:
- Center of dilation.
- Original point.
- Scale factor.
- Dilated point.
First, we proceed to determine the coordinates of the dilated segment:
(
, 
, 
, 
)
![P(x,y) = (0,0) +5\cdot [(10,40)-(0,0)]](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B5%5Ccdot%20%5B%2810%2C40%29-%280%2C0%29%5D)
![Q'(x,y) = O(x,y) + k\cdot [Q(x,y)-O(x,y)]](https://tex.z-dn.net/?f=Q%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2B%20k%5Ccdot%20%5BQ%28x%2Cy%29-O%28x%2Cy%29%5D)
![Q' (x,y) = (0,0) +5\cdot [(70,120)-(0,0)]](https://tex.z-dn.net/?f=Q%27%20%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B5%5Ccdot%20%5B%2870%2C120%29-%280%2C0%29%5D)
Then, the length of the resulting segment is determined by following Pythagorean identity:
The length of the resulting segment is 500.
