CPhill

0

To see why....note that    5!  ends with a 0......so.....multiplying this  by any other non-zero units digit(s)  will  always produce a "0"

Mid-point rule

(4 + x) / 2   =  8                 (3 + y) / 2   =  19                   

4 + x  =  8 * 2                      3 + y  =  19 * 2

4 + x  =16                            3+ y = 38

x = 16 - 4                              y =  38 - 3

x = 12                                   y = 35

Sum  =  35 + 12  = 

47

We have 5 choices  for  each  digit....so....

(5) (5)  = 

25

sqrt (1,000,000) -(1,000,000) ^(1/3)  =

1000 -   100  =

900

Each side will be  10 / sqrt (2)  cm long

The area  =  (side)^2  =    (10 / sqrt (2))^2  =      100 / 2 =      50 cm^2

Using the square of the distance formula

(2a - 4)^2  + ( a - 4 - -7)^2  =  (2 sqrt 2)^2

( 2a - 4)^2 + ( a +3)^2  = 8

4a^2 - 16a + 16 + a^2 +6a + 9 = 8

5a^2 -  10a + 17 = 0

This will not produce  real number values for "a"

But....the product of all possible values for "a" =   17 / 5

320 (7/16)  =   140  were orange

320 - 140  =  180  were lemon

Let x be the number of lemon ones he gave  away

So

[ 140 - 30 ]  / [ 180 - x ] =  11/15

110  =  (11/15) ( 180 - x )

(15/11) (110)  = 180 - x

150  = 180  - x

x = 180  - 150  =   30

(37 + 20sqrt 3)^2  =

37^2  +  2 * 37 * 20 sqrt (3)   +  (20 sqrt 3)^2  =

1369 +  1480 sqrt 3  + 400*3   =

1369 + 1480 sqrt 3  + 1200 =

2569 + 1480 sqrt 3

No....just for fun.....I used to be a tutor at a junior college....I found that I liked it a lot

After he sent 3/5 he had 2/5 left

So

3800 ( 2/5)  -  210  =

1520  - 210  =

$1310  = what he had left