CPhill

Very nice, BuilderBoi   !!!!

Let's suppose that there are 100 students at the  school

Then

21 play football

13 play basketball

25 play  either

N ( play  either)  = N(play football)  + N (play basketball)   - N (who play both )

     25            =             21                +          13      -     N (who play both)

     25   -  21     -13     =    - N (who play both)

             -9  =  -  N (who play both )

              9   = N ( who play both )

M =  3C

F = C + 56

So.......

(C) + ( 3C) +( C + 56)  =   676

5C +  56  = 676

5C  =  676  -  56

5C  =  620

C =   620  / 5    =   $124

M =  3 (124) = $ 372

Don't see anything !!!

1.

Either 

5x^2  =   -7        impossible

or

21 + x  = -7    ⇒  x  =  -7 -21  =  -28   but this is not in the  domain of the  second function

or

2 - sqrt (x)    =  -7

So

sqrt (x) =  2 +7

sqrt (x)   =9        square both sides

x   =81              this is in the domain of the  third function

So   g^-1(-7)  =   81

In a sale Tommy bought a kettle and a toaster. He paid a total of $105. The amount paid for the kettle is 2/5 the cost of the toaster. The total price before the discount should have been $133. The toaster was reduced by 20%. How much was the kettle reduced by?

Call the original prices K , T

K + T =   105

(2/5)T + T  =105

(7/5)T  = 105

T = 105 * 5   / 7  =    $75

So

K  = 133 -  75  =  $58

But with the discount the toaster now costs  75 (.80)  = $60

So  ......the kettle's new cost must be  105 -  60 =   $45

So.....the discount on the  toaster  =   1  - 45  / 58   ≈ .224 ≈  22.4%

2.5 L =   2500 cm^3

So

2500  =   pi * r^2  * height

2500 = 17 pi  * r^2

r^2   =   [ 2500 / (17/pi ] 

r = sqrt [ 2500 / (17 pi ) ]  ≈  6.84 cm

A discount of 25%  means  the price is 75%  of what it originally cost....and this  is  taxed at  12%

So....

cost =     (186)(.75) ( 1.12)   =  $156.24

In triangle PMR  Draw atltitude MS   to  PR

Now  triangles  MPS and  QPN are similar

So    MP  /  QP   =  PS  / PN       

          1/2 =  PS /PN   ⇒   PS   = 4   ⇒  MS = (1/2) QN  =  5

And triangles   RSM  and  RNO   are similar

So    SR   = 12      MS  = 5     RN  =  8

MS / SR   =  ON  / RN

5 / 12  =  ON / 8

40 /12  =  ON   =   10/3

And since   triangle RNO  is right, then

OR   = sqrt   [ RN^2  + ON^2  ]   =   sqrt  [  8^2  + (10/3)^2 ]  =

sqrt [  64 +  100 / 9  ]  =  sqrt  [ (576 + 100) / 9  ]   =   sqrt  [ 676 ] / 3  =   26  / 3

Call the roots a, b

By Vieta

The sum ot the roots  =   a + b  = (3/2)......square both sides ⇒  a^2 + 2ab + b^2  = 9/4   (1)

The product of the  roots =  ab  = 29/2   ⇒       so    2ab  = 29    (2)

Sub (2)  into (1)

a^2  + 29   + b^2  =  9/4

a^2 + b^2  =  9/4   - 29

a^2  + b^2  =   -107 / 4