Melody

| x - 3 | < 7

The thing to notice here is that x-3 must be less than 7 units from 0 on the number line .. so...

-7 < x-3 < 7

-4 < x < 10

I like it too :)

Thanks Alan, your solution is really neat :)

The only answer is 5.  I did this by examining a table of values.

There is bound to be a more elegant way of doing it but I do not know what it is.   

\(\left\lfloor n^2/4 \right\rfloor - \lfloor n/2 \rfloor^2 = 2\)

So I can see that for all even numbers, positive and negative the answer will be zero.

For the odd numbers a pattern emerges.

It is clear to me that the only integer value of n to make this true is 5

These links don't work and you should be asking ust about speific problems, not asking us to do your homework for you!

She has not posted anything since 26th May 2017  :(

what is the inverse of f(x)=1/3x-7 ?

\(y=\frac{1}{3}x-7\\ y+7=\frac{1}{3}x\\ 3(y+7)=x\\ x=3(y+7) \)

So the inverse of

\(f(x)=\frac{1}{3}x-7\qquad is\\ f(x)=3(x+7)\)

See how the inverse is the refletion of the original function about the line y=x  ?

All inverse functions are the reflection of the original function about the line y=x !!    

If the parabola is in the from

\((x-h)^2=4a(y-k)\)

then

The vertex is (h,k)

The focal point is  (h,k+a)      That is a units up from the vertex

and 

The directrix is   y=k-a

Guests answer is correct but your formula is wrong

This is what it should be.

S=n(n+1) / 2