Melody

2x-y has to equal 18

just plug those values in and see which one works.   

Here is the best way for you to check by yourself.

Put your equation into here and you will see for yourself.

Thanks Chris :)

Do you have the answer? 

5 of the 9 letters of the word MINCEMEAT are selected.

MM EE INCAT       

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Find the number of possible selections which contain exactly 1 M and 1 E.

Does order count, you do not say?  I'll assume not.  I will also assume that both Ms and both Es are identical so that choosing one is exacly the same as choosing the other.  So I am counting the number of distinct outcomes.  This may not be what the writer of the question intended.

So i must chose 3 letters from INCAT       5C2 = 10  (edited after the interaction below) distinct combinations meet this description.

Of course if you were doing it for a probability question then some of these combinations are more likely to occur than others.

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Find the number of possible selections which contain at least 1 M and at least 1 E.  

M and E and 3 others not M or E                     5C3

M and E and M and 2 others not M or E          5C2

M and E and E and 2 others not M or E          5C2

M and E and E and another M and 1 others not M or E          5C1

Add those up to get the number of distict combinations.

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Guest i think you should explain your method. 

If you cannot explain it then that means you do not understand why it works.

I'm impressed too Gavin :)

Here is one of the answers Gavin found.     

The angles he is talking about have to be angles at a point as I will show in this diagram.

A cold water tap takes 3 minutes to fill the bath. A hot water tap takes 2 minutes to fill the bath. How long does it take to fill the bath when both taps are open at the same time?

It is easiest just to let the bath be a given size.

My little bath will be 12 litres

cold water  4L/min          hot water = 6L/min      

together 10L/1 min

10*(12/10) L per  1*(12/10) minutes

12L per 1.2min 

12L per 1min and 12sec

It will take 1 minute and 12 seconds to fill the bath.

In a certain pentagon, the interior angles are   a,b,c,d,e       where  are integers strictly less than 180

If the median of the interior angles is  61 degrees and there is only one mode, then what are the degree measures of all five angles?

Angle sum of a pentagon is  180*3 = 540 degrees. 

540-61= 479

479/4=119.75      since 2 are very little,  2 must be really big.

179+179=358

60+60=120

358+120=478  which is one too little

60,60,61,179,179 = 539    1 to little and there is 2 modes

60,61,61,179,179 = 540     right size but 2 modes

61,61,61,178,179 = 540     right size and only one mode.    

Same as Tertre so that is great :)

\(5^{12}-2 \cdot 10^6+2^{12}\\ =5^{12}-2\cdot 5^6 \cdot 2^6+2^{12}\\ =(5^{6})^2-2\cdot 5^6 \cdot 2^6+(2^{6})^2\\ =(5^6-2^6)^2\\ =[(5^3)^2-(2^3)^2]^2\\ =[(5^3-2^3)(5^3+2^3)]^2\\ =[(5-2)(5^2+5\cdot 2+2^2)(5+2)(5^2-5\cdot 2+2^2)]^2\\ =[3(25+10+4)\cdot 7(25-10+4)]^2\\ =[3\cdot 39\cdot 7\cdot 19]^2\\ =[3\cdot 3\cdot 13\cdot 7\cdot 19]^2\\ \)

So the highest prime divisor is 19.