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(3)

Opposite angles in a  cyclic quadrilateral are supplementary

Therefore......

angle ABC  +  angle ADC    =   180

       66       +   angle ADC   =  180             subtract  66 from both sides

                       angle ADC   =  114°

Thanks very much. Great explanation! I love this site and the things you guys do! I miss reading MAD Magazine Lol.

Let the  row length  =  L

This implies that, since the number of total chairs is the same in each case, we have 

5L + 3  =  3L +  21         subtract 3L,  3 from  both sides

2L  =  18     divide both sides by 2

L  =  9     [ 9 chairs in a row  ]

So......the total number of chairs =  5(9) + 3  =  48

Here's my answer to this  :

https://web2.0calc.com/questions/3d-geometry-please-help

x^2 + y^2   = 4

(x-3)^2 + (y -5)^2  = 25

Expand the second equation

x^2 - 6x + 9 + y^2 - 10y + 25   = 25       sub the first equation into this for x^2, y^2

4  - 6x + 9 - 10y  + 25  = 25       simplify

13 - 6x - 10y  =  0

10y  = 13 - 6x

y =   [ 13 - 6x ]  / 10   sub this  into the first equation fo y

x^2  + ( [ 13  - 6x ] / 10)^2    = 4        multiply through  by 10^2  and simplify

100x^2 + 169 - 156x + 36x^2 = 400

136x^2  - 156x  - 231  = 0

Solving this for  x  produces

x = ( 39 + 25√15)  / 68          and     x  =  ( 39  - 25√15)  /68

And  using a little  technology   [ because of the messy math  ]  when  x  holds the  first  value, y = [ 13 - 6x ] /10  =

(65  - 15√15) / 68

And  when  x holds the second value, y =   [65 + 15√15) /68

So  letting A =  [  ( 39  - 25√15)  /68  ,   ( 65 +15√15)  /68  ]   and  B = [  ( 39  + 25√15)  /68 ,  ( 65  - 15√15)  /68

We can ignore the denominators when calculating the  slope.....so we have

[ 65 - 15√15]  -  [ 65 +  15√15  ]               -30√15               -3

_________________________  =         ________  =     ____

[39 + 25√15 ]  - [ 39 -  25√15 ]                 50√15                 5

Cool.....never heard of Tebibyte before ....thought it was a typo in the question .....

 I found that Tib and TB   they are close enough in value they are often used as synonyms, though they are not EXACTLY the same value...as your answer shows

    same methodology to solution though.....  THANX !

cot = 3/5 = cos/sin       This can occur in Q I  or Q III

Remember   cos^2 + sin^2 = 1  ?

(3/x)^2  + (5/x)^2  = 1       x = sqrt 34      sin = 5/sqrt34    cos = 3/sqrt34   OR   sin = - 5/sqrt34    and cos = - 3/sqrt34

    (not sure why  did all of that ....but there it is)

arctan 5/3 =  1.03 R       AND   4.17 R

Not sure how text got that answer!

#1 Answer: 55 degrees

#1 Explanation:

The angles added up are 665 degrees.

The angles of a hexagon add to 720 degrees.

The missing angle is therefore 55 degrees.

#2 Answer: 9 (square units)

#2 Explanation:

The diagonal of a square forms a right triangle, with the diagonal as hypotenuse and two sides as legs.

The two sides are equal.

If we let one side have length x, then

x^2+x^2=(3sqrt2)^2

by Pythagorean Theorem.

2x^2=18

x^2=9

The area of the square is x^2, and we found it to be 9.

A useful formula is that the area of the square when you have the diagonal is (diagonal^2)/2

You are very welcome!

:P

N mod 5 =3,  N mod 3 =2, solve for N

LCM of [3, 5] = 15

N = 8 Number of chairs

15n + 8 = Full solution, where n =0, 1, 2, 3.......etc.

Note: I assumed that arranging the 3 chairs leaves 2 chairs and NOT 21. If the leftover chairs=1, then n = 13 chairs.

https://web2.0calc.com/questions/please-help-asap_117

If you cannot have a leading zero, there are 4 choices (1, 8, 6, 9) for the first digit.

The second digit can be any of the 5 digits (0, 1, 8, 6, 9).

The third digit can also be any of the 5 digits.

The fourth digit can be any of these 3: (0, 1, 8).

The fifth digit is determined by the choiice for the third digit; so are digits six and seven.

ou get 4 x 5 x 5 x 3 choices.

This is what Wolfram/Alpha gives as the sum which appears to be an irrational number !!!

https://www.wolframalpha.com/input/?i=%E2%88%91%5B+%283n%5E2+%2B+9n+%2B+7%29+%2F+%28n%5E2+%2B+3n+%2B2%29%5E2%2C+n%2C+0%2C+123456789+%5D

∑[ (3n^2 + 9n + 7) / (n^2 + 3n +2)^2, n, 0, 123456789 ] =3.289868109.............etc.

12 r + 30 s = 557.59

21 r + 10 s = 582.75    Multiply this equation by -3 to get

-63 r - 30 s = -1748.25   now add it to the top equation

-51 r          = - -1190.66    divide by - 51 to find r =  $23.35         Now I think YOU can calculate the salmo price ! 

If the 6-9 thing counts   AND you cannot have leading zeroes, you have 5 choices for each position in your 7 digit positions (except there can be no leading zero)

4 x 5 x 5 x 5 x 5 x 5 x 5  =   5^6 x 4 =......

Can we never talk about this.

You can also get your answer by multiplying 1/3 with the possible answers, 3 and 1/3 to see if the product will be equal to 1.

What is the value of  if \( x\cdot(3x+1)  is what appears on my screen. Please reformat it for readability!

I feel dumb now.

I was just saying that as a joke, your answer is correct.

Why must I imagine this scenario? Aren't we only looking at what's given in the problem, not anything outside of it? Imagine if I asked you to solve for the volume of a pyramid, and then saying "wait, in real life, a pyramid like that would never be constructed!" That's not the point here. Even if you're rounding to the nearest hundredth, that's not very hard to do; what's important is the process to get to the answer, not so much the answer itself.

Imagine a waiter saying the bill is $23.34627450980392, and the next thing you know, you're trying to cut a penny.

I'm not trying to be rude, but did you take the time to read through CU's solution? It was an example problem, not the actual problem itself. What CU intends to do here is teach you the steps of the problem, not just how to read the answer and enter it in some website. Please take the time to actually try to learn what he's teaching you here. Using his method, you would get the answer of 83, which you already said yourself is wrong.

not if the question doesn't say to do so... for all we know the question wants the exact value in dollars

If the answer is in dollars, shouldn't you round the nearest hundredth?