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This is \(n^2(n+5)\).

Because of that n^2 we know it's a square. We just need \(n+5\) to be a perfect square.

We get that the smallest n is 4, and we can go all the way up to n = 95. The number of perfect squares from 4 + 5 = 9 to 95 + 5 = 100 is 8.

You are very welcome!

:P

xy  =  1/9

x(y + 1)  =  7/9   --->   xy + x  =  7/9   --->   1/9 + x  =  7/9   --->   x  =  6/9   --->   x  =  2/3

y(x + 1)  =  5/18   --->   y( 2/3 + 1 )  =  5/18   --->   y(5/3)  =  5/18    --->   y  =  1/6

Now you know the values of both x and y, so (x + 1)(y + 1) = ...

**This explanation is really confusing to read without an image. Draw a picture and mark out the equal sides. Label the angles as you read the solution. 

Call angle XYW = a. Because XW = WY, YXZ = a.

Then, from the exterior angle theorem, ZWY = 2a. Because WY = YZ, angle WZY = 2a

Since the sum of all the angles of a triangle is \(180^\circ\), WYZ = 180-4a

Then, since XY = XZ, 180-4a+a = 2a.

Solve for this to find a = 36

This is AoPS homework.  Stop trying to cheat on your homework.

There are 6 choices for each question; one of which is correct.

To get 3 incorrect:  5/6

To get 7 correct:     1/6

To get e incorrect  and  7 corect:  (5/6)  x  (1/6)  =  5/36.

I'm not trying to cheat, I am just asking for help as for what to do next...

Numbers 3 and 4 have been answered here:

These questions have already been answered in another thread.

Can you explain why it's 108?

Are there answer choices? This question feels a bit incomplete because we need the statements to see what we're comparing. 

You get the maximum total benefit for 10 units.

Do not cheat on your AoPS homework.

1. The total surface area is 66.

2. The total surface area is 108.

3. By the sine law, AC = 4*sqrt(3).

Ok for number 2 what you do is if you rotate (-3,2) 90 degrees you flip the x and the y and the sign for the -3 switches to + so point B is (2,3) then to reflect it you flip the numbers so it's (3,2) Sorry I didn't explain it that well but there are lots of khan academy's also Good luck on you pr AoPs TeSt

If  (4a + 3b) / (a - 2b)  =  5

then              4a + 3b  =  5(a - 2b)

                     4a + 3b  =  5a - 10b

                            13b  =  a

Therefore, substituting 13b for a:

       (a + 11b) / (a - b)  =  (13b + 11b) / (13b - b)  =  24b / 12b  =  2

im sorry im new just please answer 

Please correct me, but please post this as off-topic post as this is science

Anyways thanks for the link

Did you mean google translate?

sin(x)  =  cos(2x) - 9/8

Using the identity:  cos(2x)  =  1 - 2sin²(x) ...'

                                                   sin(x)  =  [ 1 - 2sin²(x) ] - 9/8

                          2sin²(x) + sin(x) + 1/8  =  0

                         16sin²(x) + 8sin(x) + 1  =  0

                                      [ 4sin(x) + 1 ]²  =  0

                                            4sin(x) + 1  =  0

                                                   4sin(x)  =  -1

                                                     sin(x)  =  -¼

marshlands prevent flooding in a nearby town by soaking up the water from the flood and the water flows underground so that the water doesn't reach the nearby town 

Maybe if you got less than 0 points like -10~-1 but not necissary banned they would flag it for moderation or becuase you said the bad word(The second word or the word after "I")?

^{_{EDITED:reason = wrong spelling :(}}

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