bear in mind that one can always get the common ratio by simply dividing any of the terms by the one before it namely, say 18÷12 or 27÷18.
![\bf 12~~,~~\stackrel{12\cdot \frac{3}{2}}{18}~~,~~\stackrel{18\cdot \frac{3}{2}}{27}\qquad \qquad \stackrel{\textit{common ratio}}{r = \cfrac{3}{2}} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%2012~~%2C~~%5Cstackrel%7B12%5Ccdot%20%5Cfrac%7B3%7D%7B2%7D%7D%7B18%7D~~%2C~~%5Cstackrel%7B18%5Ccdot%20%5Cfrac%7B3%7D%7B2%7D%7D%7B27%7D%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bcommon%20ratio%7D%7D%7Br%20%3D%20%5Ccfrac%7B3%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf S_8=12\left( \cfrac{1-\left( \frac{3}{2} \right)^8}{1-\frac{3}{2}} \right)\implies S_8=12\cdot \cfrac{\frac{-6305}{256}}{-\frac{1}{2}}\implies S_8=12\cdot \cfrac{6305}{128} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill S_8=\cfrac{18915}{32}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20S_8%3D12%5Cleft%28%20%5Ccfrac%7B1-%5Cleft%28%20%5Cfrac%7B3%7D%7B2%7D%20%5Cright%29%5E8%7D%7B1-%5Cfrac%7B3%7D%7B2%7D%7D%20%5Cright%29%5Cimplies%20S_8%3D12%5Ccdot%20%5Ccfrac%7B%5Cfrac%7B-6305%7D%7B256%7D%7D%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20S_8%3D12%5Ccdot%20%5Ccfrac%7B6305%7D%7B128%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20S_8%3D%5Ccfrac%7B18915%7D%7B32%7D~%5Chfill)
Answer:
6 (3x+5) GCF= 6
Step-by-step explanation:
Answer:
x = 7
Step-by-step explanation:
3x - 4 = 2x + 3
3x - 2x = 3 + 4
x = 7.
The answer is 5 books.
1 book per 20 books, since its 100 books you do 100/20.
Getting 5 times 20 went into those books, and because per stack of 20 you got 1 you end up with 5 books.
Hope this helps :P
Answer:
The graph has been moved 7 units to the left and 8 units down.
Step-by-step explanation:
When numbers are added directly to the "x" value, the graph shifts to the left. If negative numbers are added directly to the "x" value, the grap shifts to the right. Therefore, if there is a +7 directly altering the "x" value, the function shifts 7 units to the left.
When a number is added to the overall function, it shifts upwards. If this number is negative, the entire function shifts downwards. Therefore, if there is a -8 outside altering the function, then it has been shifted 8 units down.
