Melody

m+m+2m

A mat + another mat + 2 more mats = 1+1+2=4 mats

When you are adding or subtracting with letters is is easier to think of  them as things.  :)

m+m+2m = 1m+1m+2m = 4m

a)  Choose 2 from 6 to be the first pair that is 6C2 =15

then choose 2 from 4 for the second pair   4C2 = 6

So I think that the answer for part a is      6C2*4C2 

$${\left({\frac{{\mathtt{6}}{!}}{{\mathtt{2}}{!}{\mathtt{\,\times\,}}({\mathtt{6}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{4}}{!}}{{\mathtt{2}}{!}{\mathtt{\,\times\,}}({\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)} = {\mathtt{90}}$$

There are 90 pair combinations.      

Now I don't understand the question for part b.  Do the 4 new ones partner each other of do they get thrown in before the original 6 get paired off?     I'm really confused now.    

I checked what you said and you are right google says it is a graph.  How silly is that.

The graph represents the equation

y=4(x+5) + 3(x+3) 

but that has nothing to do with your questions.   

Well Sasini, 

I only thought it might because your hair is already black.  

It may enhance the beauty that you and Rosala already possess.   

If my hair was black I would definitely use it.   

$$\\(1/64)^x = 1/512 \\
$turn both sides upside down and you get $
64^x=512\\\\
$method 1$\\
64^x=512\\
log64^x=log512\\
xlog64=log512\\
x=\frac{log512}{log64}\\
x=1.5\\\\
$method2$\\
64^x=512\\
64=2^6\quad and \quad 512=2^8\\
(2^6)^x=2^9\\
2^{6x}=2^9\\
6x=9\\
x=9/6=1.5$$

There is no (generalized) short cut.  Just do the division.   

$$\\\infty^{-0.001}=\frac{1}{\infty^{+0.001}}=\frac{1}{\sqrt[1000]{\infty}}
=\frac{1}{\infty}=0$$

$$\\1000^{1000}=(10^3)^{1000}=10^{3000}$$

so that is 1 followed by 3000 zeros   

you said add the exponents which is correct but you multiplied

$$\\(2.48*10^7)(3.5*10^{-12})\\
=2.48*10^7*3.5*10^{-12}\\
=2.48*3.5*\;\;10^{7-12}\\
=2.48*3.5*\;\;10^{-5}\\$$

I believe general form is

$$y=ax^2+bx+c$$

I do not know what canonique form is.  

tell me what it is and I will show you how to do the conversion.