Answer:
answer is (14x+6) hope it helps
Hello!
Ok so the summation of 1/4+1/2+3/4+5/8+3/10 = 97/40
we find this by finding the GCF of the set of numbers we have here. So we get 40 is the GCF. So we get:
10/40+20/40+30/40+25/40+12/40=97/40
Hope this helps! Any questions please just ask! Thank you so much!
Let the original fraction be
![\dfrac{n-1}{n}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn-1%7D%7Bn%7D)
Now let's increase both numerator and denominator by 2:
![\dfrac{n+1}{n+2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn%2B1%7D%7Bn%2B2%7D)
This produces a 1/12 increase:
![\dfrac{n+1}{n+2}-\dfrac{n-1}{n}=\dfrac{1}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn%2B1%7D%7Bn%2B2%7D-%5Cdfrac%7Bn-1%7D%7Bn%7D%3D%5Cdfrac%7B1%7D%7B12%7D)
The left hand side can be rearranged as
![\dfrac{2}{n^2+2n}=\dfrac{1}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7Bn%5E2%2B2n%7D%3D%5Cdfrac%7B1%7D%7B12%7D)
Invert both sides:
![\dfrac{n^2+2n}{2}=12 \iff n^2+2n=24](https://tex.z-dn.net/?f=%5Cdfrac%7Bn%5E2%2B2n%7D%7B2%7D%3D12%20%5Ciff%20n%5E2%2B2n%3D24)
Solve the quadratic equation:
![n^2+2n-24=0 \iff n=-6 \lor n=4](https://tex.z-dn.net/?f=n%5E2%2B2n-24%3D0%20%5Ciff%20n%3D-6%20%5Clor%20n%3D4)
So, in the first case, the original fraction is
![\dfrac{n-1}{n}=\dfrac{-6-1}{-6}=\dfrac{7}{6}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn-1%7D%7Bn%7D%3D%5Cdfrac%7B-6-1%7D%7B-6%7D%3D%5Cdfrac%7B7%7D%7B6%7D)
In the second case, we have
![\dfrac{n-1}{n}=\dfrac{4-1}{4}=\dfrac{3}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn-1%7D%7Bn%7D%3D%5Cdfrac%7B4-1%7D%7B4%7D%3D%5Cdfrac%7B3%7D%7B4%7D)
Step-by-step explanation:
Perimeter of rectangle = 2(l+b)
= 2(97+17)
= 2(114)
= 228cm