CPhill

Excellent, IWTH  !!!!

A "Best Answer "   .

Sorry, IWTH.....you sometimes gotta' be  fast on the  draw around here    ...LOL!

However.......you can also post your solution  and  I'll give it a point.....

78/6  =  $13  for each pizza

18/6  =    $3   for each ice cream

Each just   paid   $13 + $3 =   $16

Looking at this another way.....the total  bill = 78 + 18 =  96

Splitting this 6 ways =   96/6 =  $16

If we join the  centers of each circle, we  will  form a 3-4-5  right triangle

The area of this triangle  is     (3*4)/2  =  6

The  angle formed by  the lines joining the  two  lager circles to  the  center of the  smallest  circle  =  90°

So   the area of  the sector  of 1/4  of the smallest circle with a central measure of 90° is pi (1)^2 *(90/360)  =  pi/4

The  angle  (theta) formed  by   joining  the center  of the larger circle with the  two smaller circles can be  forund as

arcsin (3/5)  ≈ 36.87°

So  the  area of  a sector  in the larger circle  with a central measure of 36.87° is given by

pi ( 3)^2  (36.87/360)  ≈  .9271 pi

And in the  circle with a radius of 2 we are  looking  for the area of a sector with a central angle measure  of (90-36.87) =  53.13°  =     pi  (2^2)  ( 53.13 / 360)  ≈  .5903 pi

So.....the area of the  gap  ≈  6  - pi ( 1/4 + .9271  + .5903)  ≈ .448 units^2

Total people in the  office =  50 + 24 + 5 + 17 =  96

24 / 96   =    1/4   =  25%  have blond hair

The point of tangency  is  the center of the  rectangle   =  ( 50,25)

The center of the  circle on the top left  =   (r, 50)    where  r is the  radius

So  the  distance  from  ( r, 50)  to  (0 ,50)  =   the distance from (r , 50)  to  (50,25)

Using  the  square of the distance  formula we have that

r^2   =   (r  -50)^2  +  ( 50 -25)^2

r^2  = r^2  - 100a  + 2500  +  625

100r  =  3125

r =   31. 25  = the radius

I know  a few

a)  Here are both graphs :   https://www.desmos.com/calculator/lzspxc52ys

b)   and c).....the line of symmetry is  x  = -1    ( I believe this is also the mirror line )

d) (x + 4) /(x -2)   has no interval of  increase  ...it decreases on (-inf, -2)  and (-2, inf)

Conversely  ( -2) /(x + 4)  has no interval of  decrease  ....it increases  on ( -inf, -4)  and (-4 , inf)

e)  Sorry.....I do not know the answer to this one......

Note that we can  factor the top expression as

(sqrt (x) + sqrt (y) ) ^2  = 64              take the  positive root

(sqrt (x)  +  sqrt (y) = 8

And the  secomd equation cam be factored as

xy ( sqrt (x) + sqrt (y) )   =  32

xy ( 8)  =  32

xy =   32/8   =   4

So   using the  first equarion 

x + y   +  2sqrt (xy)  =   64

x + y +  2sqrt (4)  =  64

x +   y  + 2*2  =  64

x +  y  +  4  = 64

x + y =   64   - 4   =  60

We  have the form

(x - h)^2           (y - k)^2

______   +     ________   =  1

  a^2                  b^2

a  =(1/2) length  of major axis  =   (1/2)(20)  = 10........a^2  = 100

b = (1/2) length of  mi,or axis =     (1/2) ( 16)  = 8  .....b^2   =64

(5,3)  =( h, k)

So we have

(x   -5)^2            (y - 3)^2

_______    +     ________   =  1

   100                     64

The  area  of    ABC  = (1/2)(AC)(BC) sin  ACB  =  (AC))BC) sin ABC  / 2

And the area of triangle FCE = (1/2)  (AC/3) ( 2BC/3) sin ACB  =   (AC) (BC) sin ACB / 9

So  [ FCE ] / [ ABC ] =    2/9     ⇒    [FCE] = (2/9) [ ABC]

And each of the  white  areas    =   2/9   area of ABC

So  their total area  =     3(2/9)area of ABC  =  2/3 area of ABC

So    area of DEF / area of ABC   =     [  area of ABC  -  2/3 area of ABC ] / area of ABC   =    1/3