# All Questions

##### Uchiha Sasuke

13 hour ago (08:25)##### Uchiha Sasuke

13 hour ago (08:22)##### Lê Quốc Trần Anh Coodinator

18 hour ago (03:22)-
Nguyễn Mạnh Hùng 13 hour ago (08:44)
We have:

\(a+b=29\Rightarrow\left(a+b\right)^2=841\)

\(\Leftrightarrow a^2+2ab+b^2=841\)(1)

Other way:

\(ab=204\Rightarrow2ab=408\) (2)

Put (1)-(2) we have:

\(a^2+b^2=841-408=431\)

##### Lê Quốc Trần Anh Coodinator

18 hour ago (03:21)-
Nguyễn Mạnh Hùng 13 hour ago (08:50)
\(\left\{{}\begin{matrix}2a+b=19\left(1\right)\\2c+d=37\left(2\right)\end{matrix}\right.\)

Put (1) + (2) we have:

\(2a+b+2c+d=56\)

\(\Rightarrow2a+2c=32\) (because b + d = 24 )

\(\Rightarrow a+c=16\)

So a + b + c + d = 24 + 16 = 40

##### Lê Quốc Trần Anh Coodinator

18 hour ago (03:20)-
Nguyễn Mạnh Hùng 13 hour ago (08:54)
We have the recipe:

\(x_n=\left(n-1\right).d+x_1\)

with d = distance.

According to the recipe, we have:

\(x_{2011}=\left(2011-1\right).3+\left(-4\right)=2010.3-4=6026\)

##### Lê Quốc Trần Anh Coodinator

18 hour ago (03:20)##### Lê Quốc Trần Anh Coodinator

18 hour ago (03:20)##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:23)##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:23)##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:22)-
Nguyễn Mạnh Hùng 12 hour ago (09:22)
Call three two-digit prime number is a, b and c.

Suppose: a < b < c

We have: \(\left\{{}\begin{matrix}c=43\\b-a=10\end{matrix}\right.\)

But a + b + c = 79 => a + b = 36.

=> b = ( 36 + 10 ) : 2 = 23

=> a = 23 - 10 = 13

=> a x b x c = 23 x 13 x 43 = 12857

##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:22)##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:22)-
Nguyễn Mạnh Hùng 12 hour ago (09:31)
When Simba left, the distance from Simba and Mary is 55 miles.

Simba travel faster than Mary the number of mph is:

65-55 = 10 (mph)

So the time Simba catches up to Mary is:

55 : 10 = 5,5 ( hours)

Or 14 : 30 from the beginning

##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:20)-
Nguyễn Mạnh Hùng 12 hour ago (09:37)
Each day, all three plant produce the number of cars is:

100 + 80 + 70 = 250 (cars)

So, need the number of full days to produce 1600 cars is :

1600 : 250 = 6,2 days

So need 7 full days to produce 1600 cars

##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:19)##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:18)##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:17)##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:17)##### Lê Quốc Trần Anh Coodinator

19 hour ago (02:17)##### Uchiha Sasuke

Yesterday at 12:22##### Uchiha Sasuke

Yesterday at 03:54-
Nguyễn Mạnh Hùng Yesterday at 08:23
For a = 15 and b = 6.

=> a # \(b=15.6+15^2+6^2=90+225+36=375\)

(a#b)@a = \(\dfrac{375}{3}\)- a = 125 - 15 = 110

Uchiha Sasuke selected this answer. -
Uchiha Sasuke Yesterday at 12:23
Thank you very much