let's first off, convert the mixed fractions to improper fractions, and then, let's multiply both sides by the LCD, notice, the LCD will be hmmmm 4, so we'll multiply both sides by 4, to do away with the denominators.
![\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{7}{2}w+8=\cfrac{13}{4}w+10\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{4}}{4\left( \cfrac{7}{2}w+8 \right)=4\left( \cfrac{13}{4}w+10 \right)} \\\\\\ 14w+32=13w+40\implies w=40-32\implies \boxed{w=8}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B2%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%204%2B1%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B13%7D%7B4%7D%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Ccfrac%7B7%7D%7B2%7Dw%2B8%3D%5Ccfrac%7B13%7D%7B4%7Dw%2B10%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20by%20%7D%5Cstackrel%7BLCD%7D%7B4%7D%7D%7B4%5Cleft%28%20%5Ccfrac%7B7%7D%7B2%7Dw%2B8%20%5Cright%29%3D4%5Cleft%28%20%5Ccfrac%7B13%7D%7B4%7Dw%2B10%20%5Cright%29%7D%0A%5C%5C%5C%5C%5C%5C%0A14w%2B32%3D13w%2B40%5Cimplies%20w%3D40-32%5Cimplies%20%5Cboxed%7Bw%3D8%7D)
I got the answer of 21.5, but it doesn't have it in your option list :(
Answer:
No, the equation does not represent a direct variation.
Step-by-step explanation:
The answer is immediately evident: NO. The reason for this is that no direct variation equation includes a vertical intercept.
Here 2y = 5x + 1 becoems y = (5/2)x + 1/2; the y-intercept 1/2 is problematic.
If we were to drop the constant 1, then 2y = 5x, or y = (5/2)x; this represents direct variation with the constant of proportionality 5/2.
Answer:
40%
Step-by-step explanation:
A ratio is a comparison of two numbers that can be written in multiple ways such as:
Word: There are ___x for every ___ y
Fraction: y/x
Ordered pair: (x,y)
Ratio:x:y
Proportional is a type of relationship where, oh a graph, a line goes through the 0,0 point and when you divide y/x at any point, you will get the same answer.
Hope this helped!
