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The area of a regular octagon is given by the formula \(A = 2s^2(1 + \sqrt{2})\), where \(s\) is the side length of the octagon.

We know that \(s = 5.5\text{ in}\), so we just plug in that value into the equation to get:

\(A = 2(5.5^2)(1 + \sqrt{2})\)

\(A = 60.5(1 + \sqrt{2})\)

\(A = 60.5 + 60.5(1.414)\)

\(A = 60.5 + 85.547 = \fbox{$146.047 \text{ in}^2$}\) :D

We can't say what the individual  costs might be.....but....let's just say that each is at the midpoint of its interval

So....the estimated mean  with this assumption  is

[ 4(25)  + 8(75)  + 7(125) + 10(175) + 11(225) ]  / [ 4 + 8 + 7 + 10 + 11 ]  =

5800  /  40   =  

145

185 / 6 = \(30 \frac{5}{6}\)

Your stament is very confusing... "Also, the question asker..." do you mean just the asker??...

We can use  the Law of Cosines to solve this

Call the side length of the tetrahedron, S

The slant  height  =  height of the equilateral triangle  = AM  =  BM  =   (√3/2)S

AB = the side length

So  we have that

AM^2  =  BM^2  + AB^2  -  2 ( BM * AB) *  cos (ABM)

(3/4)S^2  =  (3/4)S^2  + S^2 - 2 ( 3/4)S^2  * cos (ABM)  

0  =  S^2 - (3/2)S^2 * cos (ABM)       divide through by S^2

0 = 1 - (3/2)cos (ABM) 

-1 = -(3/2)cos(ABM) 

(2/3)  = cos (ABM)

This is a homework problem in an online course so I don't want to add anything too useful. However, I'm a big fan of CPhill. You have an extensive understanding of math, so I trust you know Diophantine Equations. There may be infinite answers in R, but not in Z+. Happy solving! 

Since dividing by 10 gives R3, the number must end in a 3. Since remainder of /9 is 1, the multiple must be (3-1).

8*9 = 72.

72+1 = 73, which satisfies bullets 1 & 2.

73/11 = 6R7.

Answer's 7.

If you don't understand anything feel free to ask.

Hello, this is an active homework problem in an online course. The post is the exact question. Please don't give an answer for this. Thanks for understanding!

To the OP - Look back over your class transcripts. Did you see any problems in class that looked like the left side of these equations? The first term is the product of two variables, and the next two terms are variable*constant. Is there a Factoring Trick that might apply here?

Remember to ask on the message boards for the class if you get stuck, and don't go asking for solutions online. Keep working hard!

A 1 step stair case requirest 4, 2 step 10, so we need 6 more. 2-3 step needs 8 more,so following the pattern we get 10 toothpicsk from 3-4, 12 from 4-5.

10+12 = 22.

If you don't understand anything feel free to ask.

Here's what I get  :

( 1, 1 , 2)

5(1)  =  5 novels

5(1)  =  5 autos

4(1)+ 1(1)  =  4 novels + 1 auto

4(1) + 1(1)  = 4 autos + 1 novel

3(1) + 1(2) =  3 novels + 1 linear

3(1) + 1(2)  =  3 autos + 1 linear

2(2) + 1(1)  =  2 linear + 1 novel

2(2) + 1(1)  =  2 linear + 1 auto

1(2) + 3(1) =  1 linear + 3 novels

1(2) + 3(1)  =  1 linear + 3 autos

2(1) + 1(1) + 1(2)  =  2 novels + 1 auto + 1 linear

2(1) + 1(1)  + 1(2)  = 2 auto + 1 novel + 1 linear

Did I miss any  ????

oh ok but once i read what it meant i didnt really think it was rudde (that much anyways) but thank you

Must say, TacoBell, your creativity definitely is... quite extensive.

I have a feeling you tried your best not to say it rudely... I mean not like i care, but your choise of word caught me a little off, my creativeness has never been called quite extensive. (I need to search what extensive means) 

It means 'covering or affecting a large area.'

awww, imagin if my story of pi was right, imagine that!

OK  !!!

Thank you!

The idea is to get x  by itself

y  =  (1/2)x + 1      subtract 1 from both sides

y - 1   =   (1/2)x       multiply both sides by 2

2(y - 1)  =    x

Correct   !!!