Answer:
B
Step-by-step explanation:

If the ratio of the dimensions is 4:7 and the shorter dimension is 10ft, we know that the 10ft corresponds to the 4 in this scenario. We can set up the equation as follows:

You have to multiply by 2.5 to get from 4 to 10. And since we want to make sure we are maintaining the ratio, we have to multiply the denominator, 7, by 2.5 as well.

This means your shorter side has a length of 10ft and your longer side has a length of 17.5ft.
AREA
The formula for the area of a rectangle is: 
So we can plug our dimensions into the formula: 
So 175 is our area. But we can't forget about units! Since this is area and we multiplied our units together, our units would be squared. That means our answer is <u>175 square feet</u>.
PERIMETER
The formula for the perimeter of a rectangle is: 
We can plug our dimensions into the formula: 
So 55 is our perimeter. Of course, we can't forget about our units. Because this is perimeter, we only added our units together, so they don't change. That means our answer is <u>55 feet</u>.
Answer:
13
Step-by-step explanation:
count A up to C
Answer:
Step-by-step explanation:
a.
An implicit expression is a relation of the form y = f(x) where f is a a function with x as a variable.

On integrating both sides, we get

We know that
.
Therefore,
![\int \frac{dy}{y(4-y)}=\int \frac{1}{2}\,dt\\\frac{1}{4}\int \frac{1}{y}+\frac{1}{4-y}\,dy=\int \frac{1}{2}\,dt\\\frac{1}{4}\left [ \ln y-\ln (4-y) \right ] =\frac{t}{2}+C](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7Bdy%7D%7By%284-y%29%7D%3D%5Cint%20%5Cfrac%7B1%7D%7B2%7D%5C%2Cdt%5C%5C%5Cfrac%7B1%7D%7B4%7D%5Cint%20%5Cfrac%7B1%7D%7By%7D%2B%5Cfrac%7B1%7D%7B4-y%7D%5C%2Cdy%3D%5Cint%20%5Cfrac%7B1%7D%7B2%7D%5C%2Cdt%5C%5C%5Cfrac%7B1%7D%7B4%7D%5Cleft%20%5B%20%5Cln%20y-%5Cln%20%284-y%29%20%5Cright%20%5D%20%3D%5Cfrac%7Bt%7D%7B2%7D%2BC)
As
,

So, ![\frac{1}{4}\left [ \ln y-\ln (4-y) \right ] =\frac{t}{2}-\frac{\ln 3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5Cleft%20%5B%20%5Cln%20y-%5Cln%20%284-y%29%20%5Cright%20%5D%20%3D%5Cfrac%7Bt%7D%7B2%7D-%5Cfrac%7B%5Cln%203%7D%7B4%7D)
b.
![\frac{1}{4}\left [ \ln y-\ln (4-y) \right ] =\frac{t}{2}-\frac{\ln 3}{4}\\\ln y-\ln (4-y)=2t-\ln 3\\\ln \left ( \frac{y}{4-y} \right )=2t-\ln 3\\\frac{y}{4-y}=e^{2t-\ln 3}\\y=(4-y)e^{2t-\ln 3}\\y\left ( 1+e^{2t-\ln 3}\\ \right )=4e^{2t-\ln 3}\\y=\frac{4e^{2t-\ln 3}}{1+e^{2t-\ln 3}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5Cleft%20%5B%20%5Cln%20y-%5Cln%20%284-y%29%20%5Cright%20%5D%20%3D%5Cfrac%7Bt%7D%7B2%7D-%5Cfrac%7B%5Cln%203%7D%7B4%7D%5C%5C%5Cln%20y-%5Cln%20%284-y%29%3D2t-%5Cln%203%5C%5C%5Cln%20%5Cleft%20%28%20%5Cfrac%7By%7D%7B4-y%7D%20%5Cright%20%29%3D2t-%5Cln%203%5C%5C%5Cfrac%7By%7D%7B4-y%7D%3De%5E%7B2t-%5Cln%203%7D%5C%5Cy%3D%284-y%29e%5E%7B2t-%5Cln%203%7D%5C%5Cy%5Cleft%20%28%201%2Be%5E%7B2t-%5Cln%203%7D%5C%5C%20%5Cright%20%29%3D4e%5E%7B2t-%5Cln%203%7D%5C%5Cy%3D%5Cfrac%7B4e%5E%7B2t-%5Cln%203%7D%7D%7B1%2Be%5E%7B2t-%5Cln%203%7D%7D)
Answer:y=3/20+12m+6
Step-by-step explanation: The equation for these types of problems are y=mx+b
the y is the second number, so in the first one the y would be -6, so you replace the y with the -6 and the x with -12
so now the equation is -6=-12m+b
you add the -12m to the other side to make 12m+6=b
now onto the second one, the 9 is the y and the 8 is the x, now the equation is 9=8m+b
this time you replace the b with the equation you got earlier (12m+6=b)
So the equation is 9=8m+12m+6
minus the 6 on both sides
3=8m+12m
add the m's
3=20m
3/20=m
Now you replace the m and the b
y=3/20x+12m+6
(Hopefully im sorry if this isnint correct :) )