Answer:
She spent 2 and a half hours doing extra work.
Answer:
37.5
Step-by-step explanation:
if it decreases by 1/2 every 8 hours;
( 3×8= 24)
the first 8 hours 1/2×300 =150 gram
the second 8 hours(16 hours) = 1/2×150=75 gram
the third 8 hours(24 hours) = 1/2×75= 37.5gram
Answer:
Simply: It makes sure you get the correct answer
Step-by-step explanation:
Using order of operations (pemdas) ensures you do the correct operations in the correct order. If not, then everyone could get loads of different answers for the same question. It provides order in the math world.
Hope this helps!
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.
The only ratio there equal to 6:3 is 54:27
Both 54 and 27 are divisible by 9.
54/9 = 6
27/9= 3
Therefore, 54:27=6:3
