![\dfrac{12^3}{12^7}=\dfrac{12^3}{12^3\cdot 12^4}=\dfrac{12^3}{12^3}\cdot \dfrac{1}{12^4}\\\\=\dfrac{1}{12^4}](https://tex.z-dn.net/?f=%5Cdfrac%7B12%5E3%7D%7B12%5E7%7D%3D%5Cdfrac%7B12%5E3%7D%7B12%5E3%5Ccdot%2012%5E4%7D%3D%5Cdfrac%7B12%5E3%7D%7B12%5E3%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B12%5E4%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B12%5E4%7D)
The 2nd choice is appropriate.
Answer:
![\dfrac{19}{840}](https://tex.z-dn.net/?f=%5Cdfrac%7B19%7D%7B840%7D)
Step-by-step explanation:
The given fraction is:
![\dfrac{1}{168}+\dfrac{3}{180}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B168%7D%2B%5Cdfrac%7B3%7D%7B180%7D)
We need to solve it.
The LCM of 168 and 180 is 2520.
So,
![\dfrac{1}{168}+\dfrac{3}{180}=\dfrac{15+3\cdot14}{2520}\\\\=\dfrac{19}{840}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B168%7D%2B%5Cdfrac%7B3%7D%7B180%7D%3D%5Cdfrac%7B15%2B3%5Ccdot14%7D%7B2520%7D%5C%5C%5C%5C%3D%5Cdfrac%7B19%7D%7B840%7D)
So, the required answer is equal to
.
Answer:
infinitely many solutions.
Step-by-step explanation:
y=4x
y-4=4 (x-1)
Lets substitute the first equation into the second equation.
4x -4 = 4(x-1)
Distribute
4x-4 = 4x-4
Subtract 4x from each side
4x-4x-4 =4x-4x-4
-4=-4
This is always true. X can be anything. We have infinite solutions
I believe it's the last one, but it's a matrix not a vector as the question asks
Answer:
60
Step-by-step explanation: