Answer:
third option: log_2 1/3
Step-by-step explanation:
change of base formula:
log_b a= (log_x a)/(log_x b)
(log 1/3)/(log 2)
apply reverse change of base formula
2 from log 2 becomes new base, and 1/3 becomes the other number
=log_2 1/3
Answer:
The length of the resulting segment is 500.
Step-by-step explanation:
Vectorially speaking, the dilation is defined by following operation:
(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) = 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)
![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.
Answer:
Step-by-step explanation:
Another way to solve would be to distribute first:
22 = 2(x + 6)
22 = 2x + 12
Subtract 12:
22 - 12 = 2x - 12
10 = 2x
Divide by 2:
10 / 2 = 2x / 2
5 = x