gb1falcon

For the first one, we can make use of the fact that f and g are inverses, so we can cancel to get f(f(27))=f(3)=1.

For the second one, set 

\(7^x\cdot7^7=8^x\)

\(7^7=\frac{8^x}{7^x}=\frac{8}{7}^x\)

\(log_\frac{8}{7}{7^7}=x\)

So b is \(\frac{8}{7}\).

For the third one, the expression is equal to

-1/6 + 0 + 1/6 + 1/3 + 1/2 + \(log_{64}{n}\)=2

\(log_{64}{n}=\frac{7}{6}\)

\(n=128\)

Part A: slope of a segment with endpoints (a,b) and (c,d) is given as \(\frac{c-a}{d-b}\), so in this case the answer is \(\frac{2-(-5)}{1-4}=-\frac{7}{3}\).

So for Part B, we can set up an equation: \(\frac{7}{3}=\frac{1-(-6)}{-5-y}=\frac{7}{-5-y}\)

So \(-5-y=-3\) and this equation is simple to solve.

I agree with you up until you solved the system of equations.

Using the second equation, I get A+B=1.

Substitute into the first:

2+1+C=0, so C=-3.

Then use the third equation:

A-3-2=0, so A=5.

Then B=-4. So (A,B,C)=(5,-4,-3)

I don't think so. Say the tank has x gallons. The tank capacity is 6x. Then x+2=3x, because 3(1/6)=1/2. Solve to get x=1, so the tank capacity is actually 6.

Thanks! Can you show me how you arrived at that solution so that I will be able to solve similar problems on my own?

This is another double question. Why are so many users reasking questions?

If I could find the original, I would.

However, simplify to get a=24-10b.

If the median of a list of distinct integers is 5.5, then the middle two are 5 and 6. The average can be as large as possible, but the smallest such list is 1,2,3,4,5,6,7,8,9,10, of which the average is 5.5

10+10 is 20.

If you mean the factorial button, not every calculator has one of those.