Melody

Anonymous is correct!

I did it the right way but I forgot that the answers to these types of questions always have to be checked.

and x=-4 simply does not work!

Taking my own little equation

|2x-8| = 9X+20

LHS = |2*-4-8|=16

RHS = 9*-4+20 = -16  not equal LHS

So as Anonmous has so adamantly stated, the ONLY answer is x=-12/11

THANK YOU ANONYMOUS!

Note: I should have checked x=-12/11 too, but it will be correct.

Does this answer satisfy you Anonymous.  If not please say so - we are all here to learn.

$$csc^{-1}(2)\\\\
=sin^{-1}\left(\frac{1}{2}\right)\\\\
= 30^0 \quad or \quad \frac{\pi}{6}\;radians\\\\\\

cot^{-1}(-\sqrt3)\\\\
=tan^{-1}\left(\frac{-1}{\sqrt3}\right)\\\\
=tan^{-1}\left(\frac{-1}{\sqrt3}\right)\\\\
= -30^0 \quad or \quad \frac{-\pi}{6}\;radians\\\\\\$$

You do not need to take points off yourself Chris, I thought your answer was worth a tick!      

It was a good point to reiterate - and yours was perhaps a little clearer.  

Logs are expontents (or powers or indices- these are all the same thing)

$$10^2=100\\
log_{10}100=2$$

See the power is 2, the log is 2  THE LOG IS THE POWER

-----------------------------------------------------------------------------------

You use logs when you need to find an exponent (index).

eg      $$17=10^x$$

We need to get rid of the 10. We do that by taking the log (base 10) of the RHS but we have to keep the equation balanced so we do it to the left side as well

$$log_{10}17 = log_{10}10^x\\

log_{10}17 = x\\

x= 1.2304489 \qquad\mbox{(correct to 7dp)}$$

Thanks Chris,

Aziz had already done that but perhaps your working is a bit clearer.

Thank you Anonymous for pointing that out  

I think that you each have half the solution.

The difference between 5 and 3 =2

The difference between 3 and 5 is also 2

So the difference between 2 numbers n1 and n2 is  |n1-n2|

So the problems becomes

|2x-8| = 9X+20

This has 2 solutions

$$\begin{array}{rllrrll}
2x-8&=&9x+20 &or& \qquad 2x-8&=&-(9x+20)\\\\
-7x&=&28 &or& 2x-8&=&-9x-20\\\\
x&=&-4 &or& 11x&=&-12\\\\
x&=&-4 &or& x&=&\frac{-12}{11}\\\\


\end{array}$$

Also,

A function that is even has the y axis (x=0) as an axis of symmetry       f(x)=f(-x)

A function that is odd has point symmetry about the origin. This means that if it is rotated 180 degrees it will be the same.     f(-x)=-f(x)

This is what 2^x looks like.  You can see that it is not symmetrical about the y axis.

And it does not have point symmetry about (0,0) 

so it is not an even function or an odd function.    

You can also use the distance formula (which comes directly from pythagoras' theorem)

$$x_1=3\qquad x_2=6 \qquad y_1=-2 \qquad y_2=4$$

DragonSlayer, I sincerely hope that you are learning something by copying/repeating everybody elses answers!

Some (unknown) people have shown you how annoyed that they get when you do this.  

If you want to comment on this statement then you can do so by private message.

It is just

$$\frac{450}{6000}\times 100 \;\;percent$$

$${\frac{{\mathtt{450}}}{{\mathtt{6\,000}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\frac{{\mathtt{15}}}{{\mathtt{2}}}} = {\mathtt{7.5}}$$

7.5%