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Here's what I tried (maybe I will figure it out with Melody's advice. Who knows?):

So, first let's order the numbers from least to greatest:

1/10 = 0.1

3 1/2=3.5

2 4/5=2.8

So, our order is 1/10, 2 4/5, 3 1/2.

First, I will try to make the biggest number that I can.

Since, as Melody said:

So, to find the biggest number, I will have something like this: (big thing + big thing)/(small thing) 

So we will have (2.8+3.5)/0.1 = 6.3/0.1 = 63 for our biggest number.

Now I will try to make the smallest number that I can.

We can have the reciprocal of the biggest number we can get, which we just found to be 33. So, the smallest number is 1/63.

So, our answer is 63 - 1/63 = 62 62/63.

Wow, I just solved my own question. Thanks a lot for your help Melody. I wouldn't have solved it without your suggestions and hints (or your help).

Thanks a lot .

Now let's do the next problem. 

By the double-angle formula for sine:

\(\sin(2x)=2\sin(x)\cos(x)\\~\\ \sin(2x)=2\sin(x+\frac{\pi}{4}-\frac{\pi}{4})\cos(x+\frac{\pi}{4}-\frac{\pi}{4})\\~\\ \sin(2x)=2 \Big[\sin\Big((x+\frac{\pi}{4})-\frac{\pi}{4}\Big)\Big]\Big[\cos\Big((x+\frac{\pi}{4})-\frac{\pi}{4}\Big)\Big] \)

By the difference formulas for sine and cosine:

\( \sin(2x)=2 \Big[\sin( x+\frac{\pi}{4} )\cos(\frac{\pi}{4})-\cos(x+\frac{\pi}{4})\sin(\frac{\pi}{4})\Big]\Big[\cos(x+\frac{\pi}{4})\cos(\frac{\pi}{4})+\sin(x+\frac{\pi}{4})\sin(\frac{\pi}{4})\Big] \\~\\ \sin(2x)=2 \Big[\sin( x+\frac{\pi}{4} )(\frac{\sqrt2}{2})-\cos(x+\frac{\pi}{4})(\frac{\sqrt2}{2})\Big]\Big[\cos(x+\frac{\pi}{4})(\frac{\sqrt2}{2})+\sin(x+\frac{\pi}{4})(\frac{\sqrt2}{2})\Big] \\~\\ \sin(2x)=2 (\frac{\sqrt2}{2})\Big[\sin( x+\frac{\pi}{4} )-\cos(x+\frac{\pi}{4})\Big](\frac{\sqrt2}{2})\Big[\cos(x+\frac{\pi}{4})+\sin(x+\frac{\pi}{4})\Big] \\~\\ \sin(2x)=2 (\frac{\sqrt2}{2}) (\frac{\sqrt2}{2})\Big[\sin( x+\frac{\pi}{4} )-\cos(x+\frac{\pi}{4})\Big]\Big[\sin(x+\frac{\pi}{4})+\cos(x+\frac{\pi}{4})\Big] \\~\\ \sin(2x)=\Big[\sin( x+\frac{\pi}{4} )-\cos(x+\frac{\pi}{4})\Big]\Big[\sin(x+\frac{\pi}{4})+\cos(x+\frac{\pi}{4})\Big] \\~\\ \sin(2x)=\sin^2( x+\frac{\pi}{4} )-\cos^2(x+\frac{\pi}{4}) \)

By the Pythagorean identity:

\(\sin(2x)=(\,1-\cos^2(x+\frac{\pi}{4})\,)-\cos^2(x+\frac{\pi}{4})\\~\\ \sin(2x)=(\,1-m^2\,)-m^2\\~\\ \sin(2x)=1-2m^2\)

Becca do not post a lot of questions at once.

Post one or 2 at the most and learn from the answers that you get.

You should not be using this site to get you homework done for you.

Have you tried to examine my answer to find the floor in my logic or is it more your style just to get everyone else to do you thinking for you ?

I would not answer most people in this way. I am more than happy to own my errors.

But you are just using this place as a cheat site.

thanks you helped me alot ill add the formulas you used to my notes

Why don't you answer my question.

What is the closest combinations you have come up with?

You have posted a lot of questions.  11 questions in the last 50 minutes. Do you just want people to do all your homework for you?

I suppose it is obvious that you do.

TY so much I was stuck on that for so long

Actually, the answer was 90.8. Do you know how?

L + L + 5 + 2L =36...........................(1)
L + L + 5 + 2[L + 5]=36....................(2)

From (1) above:
L =31/4 =7.75 - inches - the shortest piece
7.75 + 5 =12.75 - inches-the 2nd longest piece.
7.75 x 2 =15.5 - inches -the longest piece.
From (2) above:
L =21/4 =5.25 - inches - the shortest piece
5.25 + 5=10.25 - inches - the 2nd longest piece
10.25 x 2=20.50 - inches- the longest piece
15.50 + 20.50 =36 - inches - the sum of the longest pieces.

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For a circle,

A=pi x r^2

169pi=pi x r^2

169 = r^2

r = sqrt(169)=13

So, diameter is double the radius and the answer is 2 x 13 = 26.

When you solve (x^2-25)/(x+5), you get that the top factors to (x+5)(x-5), which cancels out with the bottom to get x-5, so you know that the line must be y=x-5. Since (x+5) canceled out, the x-value for the hole is x=-5. Plugging that in to the line y=x-5 yields (-5,-10) which results in the answer being the bottom right graph, which you selected.

Yes, yes I know. I have tried all of these problems before I post them. I just kept getting a different answer than the correct one, so I was trying to see if anyone else got it right so that I could learn from it. But thanks anyway!!! Does anyone know how to solve this problem?

Ah, I see. That's a nice solution. Thank you!!!

Oh, I see. I thought we had to add the digits when solving in base 8, so I got really confused. Thanks a lot for your help!!! I like the proof!

Thank you for your help!!! 11 is the correct answer.

You answer is not right becasue  3/5.3 = 0.5660377...

10^8 / 10^2 = 10^6

0.5660377 * 10^6 = 566037.7

This is the answer 

(x) = a(x - 2)2(x + 5), a ≠ 0

Use the given point (0,-10) to find a.

-10 = a(0 - 2)2(0 + 5) = a(4)(5) = 20a

a = -10/20 = -1/2

P(x) = (-1/2)(x - 2)2(x + 5)

Your welcome

i got 566.038

\(\frac{3*10^8m/s}{5.3*10^2 Hz}\\ =\frac{3*10^6m/s}{5.3 \;oscillations/sec}\\ \approx \frac{566038m}{oscillations}\\~\\ wavelength = 566038m\;\;\text{to the nearest metre}\)

Imagine you have 3 baskets of apples and 2 bowls of apples.

Each basket contains 5 apples. And each bowl contains 3 apples.

How many apples do you have altogether?

It would be   (5 + 5 + 5 + 3 + 3) apples  =  21 apples

Now for the real question:

There are 3 squares and 2 triangles.

We know each square contains 4 square units. And we know each triangle contains 1.5 square units.

The question is.... How many square units are there altogether?

I figured it out, thank you so much! 

1/2 is the maximum, negative 1/2 is the minimum

Sorry guest I have just hidden your great answer temporarily.

I want the asker to tell me the closest she/he has gotton so far.