CPhill

Well...let's  check your answer

11 (.25)  + 12(.10)  + 4 ( .05)  =

2.75  + 1.20  + .20  =

3.95 + .20  =

4.15   ⇒       looks good  !!!!

9x^2 + 24x + a  + 6x + x^2  =

10x^2 + 30x   +  a

We need     

( [sqrt 10] x   + sqrt a ) ( [sqrt 10 ] x  + sqrt a )

So that

2 sqrt (10 a)   =  30

sqrt (10a) = 15      square both sides

10a  = 225

a  = 225 /10  =  22.5

Check

( [sqrt (10)x + sqrt (22.5) ] ^2 =

10x^2 + 2 ( sqrt 10 * sqrt 22.5 )x  + 22.5  =

10x^2 + 2 sqrt (225) x  + 22.5  =

10x^2 +  2 * 15x   + 22.5   =

10x^2 + 30x + 22.5

Since the series is arithmetic  (difference between terms is  constant ), we can  solve this :

12 - ( y + 6)  =   3y  -12        simplify

6 - y  =  3y -12

6 + 12  =  4y

18  = 4y

y = 18/4   =  9/2

Thx, geno !!!

Note that we can write this as :

x^4 + 4x^3 - (3x^2 + 14x + 8)

x^3 ( x + 4) -  (3x + 2) (x + 4)     simplify as

(x + 4) ( x^3 - 3x  - 2 )

Looking at the second factor, 2 is a root....so (x - 2) is also a factor

So....using  sythetic division to reduce the second polynomial to a quadratic, we have

2 [   1   0    -3      - 2   ]

            2     4        2

   _________________

       1   2     1        0

The remaining polynomial  is   x^2 + 2x + 1    which factors as  (x + 1)^2

So.....the factorization is

(x + 4) ( x - 2) ( x + 1)^2

The probability =  1 minus  the probability that none of the top three geography students are selected  =

1 -   (any group of 4 that does not include the top three students)  / ( the total possible groups of four)

1 -  C(25 , 4)  / C (28 , 4)   =

1 -  12650  / 20475  =

1 - 506 / 819  =

313 / 819

Since we have a triangle

When  x = 0 , y = 8 ⇒   this is the height of the triangle

When y = 0, x =  4  ⇒  this is the base of the triangle

Area =  (1/2) base * height =   

(1/2) (4) (8)   =

16 units^2

Since WXYZ is a parallelogram.....then angle X  is supplementary to angle W  =  135°

The area of the parallelogram  =     WX * XY * sin (135°)  =  10 * 144 * (1/sqrt 2)  = 1440 / sqrt 2  = 

(1440) (sqrt 2 )  / 2   = 

 [720 * sqrt 2 ] units^2

Very nice, EP  !!!!

Answered under the link above

Call the number of pineapples originally in Stall B =  P

Call the number of watermelons originally in Stall A = W

And we  know that   (3/4)P =  W  

When Stall A  sells  52 watermelons and gets 52 pineapples from Stall B, it  still contains

W fruits =  (3/4)P

And, at the end, Stall B contains P -52   pineapples

And the  ratio  of the  number of pineapples in Stall B to number of fruits in Stall A =  7/15

So

P - 52               7

_____  =       ____           cross-multiply

(3/4)P              15

15 (P -52) = 7(3/4)P

15P - 780 =  (21/4)P

15P - (21/4)P  = 780

(60 - 21) / 4  * P = 780

39 / 4  * P  = 780

P  =  780 * (4/39)    =   20 * 4  =   80  pineapples in Stall B at first

(3/4) P  = (3/4) * 80  =   60  watermelons in Stall A at first  

Total cost of all the fruits at first  = 60 ( $4)  + 80 ($2.50)  =  $240 + $200  =  $440