Answer:
Step-by-step explanation:
11:1
11*2 : 1*2 = 22 : 2
11*3 : 1 *3 = 33 : 3
11*4 : 1 * 4 = 44 : 4
To find equivalent fractions multiply with the same number
let's firstly convert the mixed fractions to improper fractions and then add them up, bearing in mind that the LCD from 12 and 6 will just be 12.
![\bf \stackrel{mixed}{14\frac{11}{12}}\implies \cfrac{14\cdot 12+11}{12}\implies \stackrel{improper}{\cfrac{179}{12}}~\hfill \stackrel{mixed}{3\frac{1}{6}}\implies \cfrac{3\cdot 6+1}{6}\stackrel{improper}{\cfrac{19}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{179}{12}+\cfrac{19}{6}\implies \stackrel{\textit{using the LCD of 12}}{\cfrac{(1)179~~+~~(2)19}{12}}\implies \cfrac{179+38}{12}\implies \cfrac{217}{12}\implies 18\frac{1}{12}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B14%5Cfrac%7B11%7D%7B12%7D%7D%5Cimplies%20%5Ccfrac%7B14%5Ccdot%2012%2B11%7D%7B12%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B179%7D%7B12%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B6%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%206%2B1%7D%7B6%7D%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B19%7D%7B6%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B179%7D%7B12%7D%2B%5Ccfrac%7B19%7D%7B6%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20LCD%20of%2012%7D%7D%7B%5Ccfrac%7B%281%29179~~%2B~~%282%2919%7D%7B12%7D%7D%5Cimplies%20%5Ccfrac%7B179%2B38%7D%7B12%7D%5Cimplies%20%5Ccfrac%7B217%7D%7B12%7D%5Cimplies%2018%5Cfrac%7B1%7D%7B12%7D)
Answer:
hence triangle can be formed with sides 5, 6,10
Step-by-step explanation:
it is fundamental principle of elementary geometry that sum of ant two sides of a triangle must be greater than the third side
here 5+6 is greater than 10
5+10 is greater than 6
6+10 is greater than 5
hence triangle can be formed with sides 5, 6,10
From the question, we know that the solutions of the system
![(s,c)](https://tex.z-dn.net/?f=%28s%2Cc%29)
is (14,6), which means the speed of the the boat in calm water,
![s](https://tex.z-dn.net/?f=s)
, is 14
![\frac{km}{h}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bkm%7D%7Bh%7D%20)
, and the speed of the current,
![c](https://tex.z-dn.net/?f=c)
, is 6
![\frac{km}{h}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bkm%7D%7Bh%7D%20)
. To summarize:
![s=14 \frac{km}{h}](https://tex.z-dn.net/?f=s%3D14%20%5Cfrac%7Bkm%7D%7Bh%7D%20)
and
![c=6 \frac{km}{h}](https://tex.z-dn.net/?f=c%3D6%20%5Cfrac%7Bkm%7D%7Bh%7D%20)
We also know that w<span>hen the boat travels downstream, the current increases the speed of the boat; therefore to find the speed of the boat traveling downstream, we just need to add the speed of the boat and the speed of the current:
</span>
![Speed_{downstream} =s+c](https://tex.z-dn.net/?f=Speed_%7Bdownstream%7D%20%3Ds%2Bc)
![Speed _{downstream} =14 \frac{km}{h} +6 \frac{km}{h}](https://tex.z-dn.net/?f=Speed%20_%7Bdownstream%7D%20%3D14%20%5Cfrac%7Bkm%7D%7Bh%7D%20%2B6%20%5Cfrac%7Bkm%7D%7Bh%7D%20)
![Speed_{downstream} =20 \frac{km}{h}](https://tex.z-dn.net/?f=Speed_%7Bdownstream%7D%20%3D20%20%5Cfrac%7Bkm%7D%7Bh%7D%20)
<span>
Similarly, to find the the speed of the boat traveling upstream, we just need to subtract the speed of the current from the speed of the boat:
</span>
![Speed_{upstream} =s-c](https://tex.z-dn.net/?f=Speed_%7Bupstream%7D%20%3Ds-c)
![Speed_{upstream} =14 \frac{km}{h} -6 \frac{km}{h}](https://tex.z-dn.net/?f=Speed_%7Bupstream%7D%20%3D14%20%5Cfrac%7Bkm%7D%7Bh%7D%20-6%20%5Cfrac%7Bkm%7D%7Bh%7D%20)
![Speed_{upstream} =8 \frac{km}{h}](https://tex.z-dn.net/?f=Speed_%7Bupstream%7D%20%3D8%20%5Cfrac%7Bkm%7D%7Bh%7D%20)
<span>
We can conclude that the correct answer is </span><span>
C. The team traveled at 8 km per hour upstream and 20 km per hour downstream.</span>
The answer is
y = ((x-z)-a)/m