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Correct! (It's the piano. Sorry if you think I said the keyboard was the correct answer. )

I think that was the original answer, but 'key'board occurred to me first 

Let the number of blue marbles is B and the number of red marbles initially is R.

There were 2/5 as many red marbles as blue marbles in a box.

This gives us the equation

R=(2/5)​B  ------(1)

After 44 blue marbles were removed from the box, there were 3/2 times as many red marbles as blue marbles. After removing 44 blue marbles, the new number of blue marbles in the box is B−44.

At this point, the number of red marbles is R(since it remains unchanged).

The second statement gives us the equation 

R=​(3/2)(B−44)​B ------(1)

Now from the equation (1) and (2) we have,

2/5B = 3/2(B - 44)

=> 4B = 15(B - 44)

=> 11B = 15 * 44

=> B = 60.

So, there were initially 60 blue marbles in the box.

To find the number of red marbles, we can use the first equation:

R = (2/5)B = 2/5 * 60 = 24.

The number of red marbles is 24.

The first function is defined  for  all x since  no real number makes the  denominator = 0

So....it's only the  second  function that we need to  consider

The quantity under the  root cannot be less than 0....so.......x cannot  be  less than 4

So  the domain is  [ 4, infinty )

Factor the numerator on the  left side

[ (x + 5) ( x - 5) ] / (x + 5)  < x + 5     simplify

x  - 5  <  x + 5

This is true  for  all real  numbers   except for  x  = -5  (because looking back  at the  original problem, it  makes the  denominator on the  left = 0 )

So  x< -5   and  x >  -5

Well that's inconvenient, be careful which user you ban! 

I don't think so.....

A piano ???

QR = PQ   = 1

Extend QR to TS   let the  intersection point   be  M

This sets up  right triangle  MRS with angle SMR = 90 degrees.....and  hypotenuse RS

MS =  4 - PQ = 4 -1 =  3

MR  = 5 - QR = 5 - 1 = 4

And using the P Theorem..... RS  =  sqrt ( MS^2 + MR^2)  = sqrt ( 3^2 + 4^2)  = sqrt (25) =  5

Perimeter  = 

PQ + QR +RS + TS +  TP

 1   +   1  +  5 +  4 + 5  = 

16

Check out my other riddles! Just go into my account and find my riddles! 

A keyboard! Well, if you launched it out of a cannon I suppose it open quite a few doors...

I won't mind if my posts get flagged, because I was part of that big conversation that was over 100 comments long, and the other ones... (Please no ban)

Since I've been using this website for a month, cipherstream may be one of several things going on there. I've heard of him. You thought he was a nice guy because he was able to solve a math problem. He continued using chatgpt to respond to questions, which turned out to be wrong so that he could make people get wrong answers. Honestly, I don't know what is up with these users that want to start the fun.

We can solve this problem using the discriminant of the quadratic equation. For a quadratic equation of the form ax^2 + bx + c = 0, the discriminant is b^2 - 4ac. If the discriminant is positive, the quadratic equation has two distinct real roots. If the discriminant is zero, the quadratic equation has one real root. If the discriminant is negative, the quadratic equation has no real roots.

In this problem, we are given the quadratic equation x^2 - (a + 1)x + a = 0, and we want to find the product of all values of a for which the equation has exactly one real solution.

Using the quadratic formula, we can solve for x:

x = [(a + 1) ± sqrt((a + 1)^2 - 4a)] / 2

The equation has exactly one real solution when the discriminant is zero:

(a + 1)^2 - 4a = 0

Simplifying this equation, we get:

a^2 - 2a + 1 = 0

Also, can you unban people?

How do I help the variables A and x? we can use the quadratic formula, but what are we suppose to solve for?  (4+-sqrt(8))/2, or 2+-sqrt(2). 

Yes, IP bans could be helpful, but it would also impact users who happen to have the same IP or are in the same building and such

Also, Melody might remove this question because she does not know what is going on and this question might take over the entire forum. 

Nice thought, but the ants at my house get all wiped out, because of the ant bait traps we have :)