CPhill

Remember......a^m * aⁿ  = a ^m+n     ......so.....

3²⁵ * 3²⁶   = 3 ^{25 + 26}  = 3⁵¹

This plausibly looks to represent the  combined volume of two cones, both with a radius of r ...... one with height "a"  and the other with height "b"

None  of them......however, if the equation is supposed to  be

y = 2x + 3  .......then   (1, 5)  and (0.5, 4)    are OK

2 adult tickets and 3 student tickets cost $12.

1 Adult ticket and 2 student tickets costs $7.

How much does each kind of ticket cost?

Let x be the price of a student ticket and y be the price of an adult ticket.....and we have

3x + 2y = 12

2x +  y  =   7    which implies that   y = 7 - 2x...........subbing this into the first equation, we have

3x + 2 [ 7 - 2x]  = 12  simplify

3x + 14 - 4x  =  12

-x  + 14 = 12        add x to both sides and subtract 12 from both sides

x = 2       the price of the student ticet is $2

And using  y = 7 - 2x, the price of the adult ticket  is : 7 - 2(2)   =  7 - 4 = $3

1/20  + 1/10   =

1/20 + 2/20  =

3/20

Here's a "mathematical" solution......let the digits of the number be a and b, in that order.....and we have

[10a + b] mod 5  = 2   (1)         and          a + b = 6   (2)

Manipulating (2), we have

 b = 6 - a

Subbing this into (1), we have

[10a + 6 - a] mod 5  = 2

[9a + 6] mod 5 = 2     (3)

(9a mod 5 + 6 mod 5 )  = 2

9a mod 5  + 1   = 2    subtract 1 from both sides

9a mod 5   = 1       and, since our number is < 50....the only multiple of 9 that results in a remainder of 1  when divded by 5  on [ 0, 50)   is when a = 4, i.e., 9a = 36

And using (3),   

[ 9(4) + 6] mod 5  = 2

42 mod 5  = 2 

And our number is 42....

The "formula"  [ identity] for tan 2x =

2tanx / [ 1 - tan^2x]

[ 2-y ]/ [4+y]   +  3(y+2)/y     

[2-2] / [ 4 + 2]  + 3[ 2 + 2] / 2  =

0    +  12 / 2    =

0 + 6  =

6

What expression?????

These three :

100 – (0.8(3x))

100 – (1 – 0.2)(3x)

100 – (0.8x + 0.8x + 0.8x)