CPhill

6 * 87   =   522 points

5 * 88   =  440 points

The grade dropped  is    522  - 440  =    82

Call the total number of  marbles in the  bag before we added any  N

The blue  ones=  (4/7)N

The yellow =  (3/7)N

So

[ (4/7)N + 5 ]          13

__________  =   ____    cros-multiply

[ (3/7)N - 3 ]            3

3 [ (4/7)N + 5 ]  =  13 [ (3/7)N - 3 ]    

(12/7)N + 15  =  (39/7)N - 39

(39/7)N - (12/7)N  = 15 + 39

( 27/7)N =  54

N =  54 ( 7/27)  =  14

The number of blue originally =  (4/7)(14)  =   8

Surface area of prism  =

2 [ 23* 84 + 84*28 + 28*23  ] =    9856 in^2

No. of inches of cloth necessary =  ceiling [ 9856/60  ]  ≈  165 in

No. of feet  of cloth  =   165  /12   ≈  13.75 ft

500 grams =  1/2 kilograms

4 (1/2 kg)  =    

2  kg

j =  4(5)^2 - 2(2)^2 + 5  =  97

2k  = 2 [  3(1)^2  - 2(4)^2  + 1 ] =   2 [ -28 ]  =   -56

j + 2k  = 

97  -  56   = 

41

Assuming  that A and B could be the same digits  we have

[ 96  - 00  ]  /  4   +   1   =

96 / 4   +   1   =

24  +  1  =  

25 such numbers

Yep.....you are correct, BB  !!!!

333332

[ ( 10!) / (5 * 10) ] mod 17    =     3   

2x^2  = -2y^2 + 12x - 4y  + 28     rearrange  as

2x^2 - 12x + 2y^2 + 4y   =  28          divide through by 2

x^2  - 6x  + y^2  + 2y  =  14             complete the square on x, y

x^2 -6x + 9   + y^2  + 2y + 1  = 14 + 9 + 1

( x - 3)^2  +  ( y + 1)^2  =   24

The radius of the square =   sqrt (24)

The diameter= the side of the  square   =  2sqrt (24)

So.....the area of the square  =   ( 2sqrt (24))^2  =   4 * 24  =   96 units^2