Melody

I do not have time to do it all right now but it is easy enough anyway.

use the rule below:

Let BC= x

set up a quadric equation.

Find x using the quadratic formula

Find CD using the ythagorean theorum.

All done   

The rule was copied from this site:

You have made a small mistake Max :)

\((r+2)^2=(r+1)^2\\ r+2=\pm (r+1)\\ \text{clearly r+2 can not equal r+1}\\ r+2=-(r+1)\\ r+2=-r-1\\ 2r=-3\\ r=-1.5\)

It would have been easier just to solve it as it was.

\(r^2 + 4r + 4 \equiv r^2 + 2r + 1 \pmod{55}\\ 2r \equiv-3 \pmod{55}\\ r \equiv -1.5 \pmod{55}\)

Kristen has three skirts,

two pairs of pants,

four sweaters,

and two pairs of shoes.

how many different skirt/pant, sweater, and shoe combination can she choose from for school tomorrow? 

3*2*4*2 = 48

The work can be 1,2 or 3 letters long.

If it is 1 letter then there are 5 choices

If it is 2 letters then there are 5 choices for the first letter and then 5 choices for the second letter. 

   That is 5*5 = 25 posibilities

If it is 3 letters then there are 5 choices for the first letter and then 5 choices for the second letter and 5 for the third

   That is 5*5*5 = 125 posibilities

So that makes

5+25+125 = 155  possible words    

Good luck Midway :)

|x+1|>-3/2

The absolute value of any expression must always be greater or equal to zero.

Since it must be greater or equal to zero it MUST also be greater than any negative number.

Hence  x can be any real number.

I have tried to post an answer but the site froze up and I lost it all.

Here is the short version

solve tan 2x = - cot (x + pi/3)

I solved by graphing.

Herer is the full graph

I'm confused

You have written on the pic  BC=5

but in the writing it says  |BC|=3,4       do you mean 3.4?

Anyway, what is BC?

CPhill is being modest, he is definitely good enough to be a maths teacher.

In fact I know that he did used to get paid for teaching maths.  ;)

Your secret is out Chris