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A and B are complementary      they sum to 90^o

^{3x+2       +      8x   = 90     solve for  'x'       then angle B =   8x}

Angle B  and  C are supplementary ....they add to 180^o

    ^{then angle   C     =   180 - angle B       (you found angle B above)}

Angle B and C add to form a straight line (180^o)      .....and note that angle C = angle A

3x-2      +      12x+2       =    180^o

Now you can solve for 'x'    then angle C = 12x+2    ....and this equals  angle A

haha ok :)

Fine, do it then.  

This is a combination problem. Every day you invite 5 people out of the n people, so it would be c(n,5). c(n,5) has to be more than 365. c(10,5) is 252, so that is too little. c(11,5) is 462, so the correct answer is 11.

Well, that is good logic, but we can make use of parintasees to make even more values.

Thx so much!

Use elimination method

First add the 2 equations

\(x+x+xy^2+-xy^2=250y+-240y\\ 2x=10y\\ x=5y\\ \)

Now sub that into either original equation and solve for y there might be more than one answer.

See if you can go from there.

Don't forget to check your answers.

In the diagram, the four points have coordinates A(0,1), B(1,3), C(5,2), and D(4,0). What is the area of quadrilateral ABCD?

Your answer was answered yesterday bu EP  (possibly after you made this post but still about 24 hours ago)

AND you have not responded in any way.

Is it that you know how to complain but you do not know how to say thank you?

Yes thank you, I can see that your are correct, I have overcounted  

So I needed to looked at the 3 scenarios separately and then add the probablities together.

2 girls+5 boys

3 girls+ 4 boys

4 girls + 3 boy

Yes the triangle is impossible.

BM cannot be 117

Here is an illustration why.

when you choose 2 girls then 5 other members you overcount (you can choose all 4 girls by choosing the first two, then choosing the other 2 girls and other 3 boys when you choose the other five, OR by choosing the last two girls first, then choosing the first two girls +other 3 boys)

Let f(x) be a polynomial such that f(0) = 4, f(1) = 5, and f(2) = 10. Find the remainder when f(x) is divided by x(x - 1)(x - 2).

Ok, please justify your response (why do you think so?) 

1 * 3/4 * 2/4  *  1/4  = 6/64 = 3/32

melody that is incorrect

One question per post.

100^100    mod 7

=  (100mod7)^100   mod 7

=  2^100                   mod 7

=  2^(3*33)  *2          mod 7

=  (2^3)^33   *2         mod 7

=  1^33   *2               mod 7

=  2

I am assuming base 10

My pleasure!

When you put a regular pentagon and a square next to each other, their sides create an angle of 162º. 

The internal angle of a pentagon is 108º  and of a square 90º.        360º - ( 108º + 90º ) = 162º

I'll let you find that n-gon.  

Radii are:    7cm,  14cm,  and  21cm  

Since you don't specify base b, that means the answer will be the same in any base from 2 to 10:

11011_2 * (2 - 1) + 1001 = 100100 = 36_10

11011_3 * (3 - 1) + 1001 = 100100 = 252_10

11011_4 * (4 - 1) + 1001 = 100100 = 1040_10

11011_5 * (5 - 1) + 1001 = 100100 = 3150_10

11011_6 * (6 - 1) + 1001 = 100100 = 7812_10

11011_7 * (7 - 1) + 1001 = 100100 = 16856_10

11011_8 * (8 - 1) + 1001 = 100100 = 32832_10

11011_9 * (9 - 1) + 1001 = 100100 = 59130_10

11011_10*(10-1) + 1001 = 100100 = 100100_10 

check your numbers; something's not right