CPhill

Melody's  method  is known as " dimensional analysis".......!!!!

2. Find the domain of {x^2 + 10x + 21}/{x^2 + 4x - 21}. (Express your answer using interval notation.)

The domain will only be restricted by all the values of x that make the  denominator  = 0 

So we have

x^2 + 4x  - 21    =  0       factor

(x + 7)  ( x - 3)   =   0

Set  both  factors to 0  and solve for x   and we havethat   x  = -7   and  x = 3

So....the domain is   (-infinity, -7) U ( -7, 3) U (3, infinity)

\(f(x) = \left\{ \begin{array}{cl} 2x + 1 & \text{if } x \le 3, \\ 8 - 4x & \text{if } x > 3. \end{array} \right.\ \)

Find the sum of all values of x such that f(x) = 0

0  =  2x +  1    subtract  1  from each side

-1  = 2x           divide both sides by 2

-1/2  = x

And

0  = 8 - 4x     add 4x to both sides

4x  = 8          divede both sides   by  4

x  =  2       [  not  in the domain  of the second function ]

So  the  sum  of all  values  such that f(x)  = 0   is  just   -1/2

Hey...it's like I always say..."Any port in a storm."

LOL!!!!!.....

According the the  mid-point rule

[ sum of x coordinates of  both endpoints / 2  , sum of the y  coordinates of both endpoints / 2 ]  = midpoint

So

[ ( 6 + x / 2 ]  = 2    multiply both sides by 2

6 + x   = 4   subtract  6 from  both sides

x  = -2     

[ ( 5 + y ) / 2 ] =  -11    multiply both sides by 2

5 + y  = -22    subtract  5 from both sides

y  = - 27

So.... N  = (x , y )  =  ( -2,  -27)

Assumig the "y"  angles are vertical ...we have that

7y - 92  = y  - 3       add 92 to both sides....subtract y from  both sides

6y   = 89

y  =  89/6  =   ( 14 + 5/6  )°

So....each  of these vertcal angles measures  (14 + 5/6  - 3)°   =  (11 + 5/6)°  = (71/6)°

So....the measure of each of the  other two vertical  angles  =    [ 360  - 2* (71/6) ] / 2 = 

[ 360  -  (71/3) ] / 2  =     [ 1080 - 71 ] / 6  =  (168 + 1/6)°  =  (1009 / 6 )°

So...

3x - 1  = 1009/6

3x  =  1009/6 + 1

3x = 1009/6 + 6/6

3x  = 1015 / 6

x = (1015 / 18)°  = (56 + 7/18)°

Here's another way to see this .....

We want to permute  any 2 of the 11 team members....this will give us all the possible pairings of passes between any two team members

So  P (11,2)   =  110 

But since the ball is passed three times between  each of these....then  3 * 110   = 330 possible passes

  |a - b| + |b - c| + |c - a| = 20

Let us suppose that  a > c > b      with  a, b and  c  >  0

So...we actually have

( a - b) + (c - b) + (a - c)  = 20    simplify

2a - 2b   = 20

a - b   = 10   and  since  a > b

Then

l a - b  l  = 10