CPhill

-x^2  -6x + 1 + 3x^2 + 4x  - 3  simplifies to

2x^2  - 2x - 2

The coefficient on the x^2  term will  come  from the multiplication of these terms

-5x^2  *  - 2  =    10x^2

-7x *  -2x    =     14x^2

1 * 2x^2     =        2x^2

                          _____

                          26 x^2

Seat  a Democrat  in any seat

Then we  have 4!  ways to seat  the other Democrats  and 5!  ways to seat the Republicans

So

4!  * 5!  = 

24 * 120  = 

2880  ways    { as RainbowSquirrel found !!! }

A =  (1/2) (9) (4)  =  18 units^2

x = -y^2  - 3y    -5

This is a parabola that opens to the left

The only way a line can intersect the parbola at one point is if it interesects it at the vertex

The y coodinate of the vertex is     - (-3) / (2 * -1)  =  3/2

So  the x coordinate of the vertex = k    is

-(3/2)^2 - 3 (3/2)  - 5

-9/4 + 9/2   - 20/4   =

9/4  - 20/4  = 

-11/4   =  -2.75  =   k

41 take only Spanish

By cases

                             Spanish Total       Chinese Total          Total Students

If  2 take both            43                         48                          91

If  3 take both            44                         49                          93

If 5  take both            46                         51                          97

Let A be the number originally in  Box A

After he moved 10% of the pencils in B to A it  contained

A + .10 (480)  = 1.30 A

A + 48 =  1.30 A

48 = 1.30 A - A

48  = .30A

A = 48/.30   =   160

So......there were 160 + 48 =  208  pencils in the box after this

He sol 75%  of these...so

208 (.25) =  52 remained after this

And he gave   75%  of these away....so

52 (.25)  =  13 remained at the end

CORRECTED  ANSWER

(a)   The new paint  has   8 equal parts

(5/8)  is paint P       and   (3/8)  is paint Q

So.....the   profit made is     180  -  (5/8)140  - (3/8)(160)  =    180  -  87.5 -  60  = $32.50

% profit   =  profit / cost to produce  =   32.50 /  (87.5 + 60)  ≈   .22  ≈  22%  

b)  P : Q =  5 : 3           Q : R   =  2 : 5

     P  : Q  = 10 : 6       Q :  R =    6 : 15

So   P :  Q  :  R =   10 : 6 : 15 

c)   Cost to produce one litre of the new mixture     

We have  10 + 6 + 15 =   31 equal  parts

P= 10/31    Q =  6/31    R  =  15/31

(10/31)(140)  + (6/31)( 160)  + ( 15/31)( 256)  =   $200

For a 40% profit it needs to sell at    

Profit   / Cost to Produce =   .40

Profit  / 200 = .40

Profit  =  200 * .40  =  80

200 + 80    =  $280

V _cube =  side length^3

V_cube  =  (2x)^3    =   8x^3

Total number of points required =   11 tests *14 points each  =  154

Total  points so  far =  94

Points needed on  last 3 tests =   154 - 94   =  60 = sum needed

100 / 12  =     (N)  /  3.5

3.5 * 100 / 12  =  (N)

29.16  =  N

You need 30  sticks