catmg

Hello TheOddOne again

I think I have a better sense of the problem now. 

Consecutive odd number are like 1, 3, and 5 or 7, 9, 11. 

They are odd numbers that are right next to each other. 

Another way to write them is x, x+2, x+4, when x is an odd number. 

If x, y, and z are consecutive odd numbers then y = x + 2 and z = x + 4. 

Do you have anymore questions?

I'd love to answer them.

But next time, try to be a bit more careful when writing variables, it can get a bit confusing. 

=^._.^=

Hello TheOddOne (I love your profile picture)

The formula you used is x^2 - y^2 = (x+y)(x-y)

So  y^2 - x^2 = 344 is actually (y+x)(y-x) = 344. 

Since x = y + 2. 

Following your logic, y - x = 2 (consecutive odd number), so y + x = 172 (344/2). 

y = 85

x = 87

Which makes z 89.

I hope this helped. :)))

=^._.^=

Hi Guest!

Someone already answered, but I just wanted to show an alterior method. 

Btw, floor is just highest integer lower than x. So floor(3.6) = 3

floor(5/2) = 2

floor(10/2) = 5

(2+1)(5+1) = 18. 

So our answer is 18. 

=^._.^=

Hello Guest!

Let's start by setting the sides of our rectangle as x and y. 

2x + 2y = perimeter

x*y = area

Thus, our equation is x*y = 4(2x + 2y)

x*y = 4(2x + 2y)

x*y = 8x + 8y  # Distribute

x*y - 8x - 8y  # Subtract 8x + 8y to both sides

The next part is kinda complicated. 

(x-8)(y-8) = xy - 8x - 8y + 64

So (x-8)(y-8) = -64

The smallest possible perimeter will be when x and y are very close, but since it's not a square, x and y can't be equal, x-8 and y-8 both must be positive integers too. 

Out of our factors of -64, -8 and 8 are the closest to each other. However, this doesn't work because for y - 8 = -8, y is equal to 0.

The next closest factor is -4 and 16. 

x - 8 = 16

x = 24

y - 8 = -4

y = 4

Thus, our side lengths are 4 and 16 making the perimeter 40. :)))

I hope this helped.

=^._.^=

Hello Guest!

I tried a bit to answer the problem, but couldn't exactly figure it out. 

I found a previous post that is extremely similar. 

https://web2.0calc.com/questions/help-asap_64

I'm sorry I couldn't help. 

=^._.^=

Hello Guest!

Let's start by making the question a bit simpler. 

There are 12 people who shake hands once with each other. How many handshakes are there? 

Another way of looking at this problem is how many ways can we choose 2 people?

There are 12 ways to choose the first person and 11 ways to choose the second person. 

12*11 = 132

However, we must remember that choosing person a first and then person b is the same as choosing person b first, then person a. 

So, we divide by 2. 

132/2 = 66

Our final answer is 66 handshakes. 

I hope this helped. :)))

=^._.^=

I'm new to this forum too (just joined a couple days ago). 

I'd love to make some friends too, everyone seems so nice. 

During winter break, this forum helped me with math so much, so I decided to join and see if I could help others too. 

Thank you to everyone who is a part of this wonderful community. 

I hope everyone has a fantastic 2021. :)))))

=^._.^=

Hello Guest!

To start, let's turn the equation to the form ax^2 + bx + c = 0 so we can apply the quadratic equation. 

x(x - 3) = 2

x^2 - 3x = 2

x^2 - 3x - 2 = 0. 

Now we just plug everything in. :))))

Here's the formula if you need it: https://en.wikipedia.org/wiki/Quadratic_equation#/media/File:Quadratic_formula.svg

x = (3 + sqrt(17))/2 or x = (3 - sqrt(17))/2

Now, we just do addition. 3 + 17 + 2 = 22.

I hope this helped. :)))

=^._.^=

Hello Guest!

Since a square has 4 congruent side lengths. Thus, each side length is 150/4 = 37.5. 

As we see from the image, the longer side length of the rectangle is the same length of the square side length. (37.5) 

4 of the smaller sides of the rectangle is equal to the length of the square side length (37.5/4 = 9.375) 

In each perimeter rectangle, there are 2 long lengths and 2 short lengths. 

9.375*2 + 37.5*2 = 93.75. 

I hope this helped. :))))

=^._.^=

Hello Guest!

Because of absolute value, we have 2 options we need to test out (x^2 - 3x + 2 = 1 and x^2 - 3x + 2 = -1). 

Case 1: 

x^2 - 3x + 2 = 1

x^2 - 3x + 1 = 0 (Subract 1 from both sides)

With the quadratic formula, x = 3/2 + sqrt(5)/2 or x = 3/2 - sqrt(5)/2. 

Case 2: 

x^2 - 3x + 2 = -1

x^2 - 3x + 3 = 0

If you applied the quadratic formula, there wouldn't be any real answers. 

Answer:

x = 3/2 + sqrt(5)/2 or x = 3/2 - sqrt(5)/2. 

I hope this helped. :))))

=^._.^=