Math Is Fun Forum

blank_brunette

Member

Registered: 2008-03-27

Posts: 46

Help Me Pretty Plz!!! Numbers!

OK, IM LEARNING ABOUT OOPPS... ok anywayz im learning aabout squared, rectangular and triabgular numbers, and on one of my worksheets it says that i have to detren=mine if the certain number is triangular, rectangular, or squared. I have the equations for them, i think:
Squared=x^2
Rectangular=x(x-1)
triangular=x(x-1)/2

now, i have to determine weather 110 is a squared, rectangular, or triangular number....Will someone please tell me how i do this?????????

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In this world of cheerios, be a fruitloop! ♥

SvenBee

Member

Registered: 2008-03-08

Posts: 106

Re: Help Me Pretty Plz!!! Numbers!

Using your example where the number you are looking at is 110, to determine if it is squared, rectangular, or triangular set it equal to each of the terms then solve for x. So:
110=x^2
110=x(x-1)
110=x(x-1)/2
Whichever gives you a whole number for an answer is the solution... I think. I'm not 100% sure on this but I think that's how this goes. Some confirmation from someone would be nice. x_X

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e...the red-headed stepchild of math.

blank_brunette

Member

Registered: 2008-03-27

Posts: 46

Re: Help Me Pretty Plz!!! Numbers!

yeah but iF I DO THAT, THEN....WAIT...I HAVE TO REPLACE X W/ 110? WELL THAT DOESNT MAKE SENSE.......im confused!!!

Last edited by blank_brunette (2008-05-13 13:03:30)

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In this world of cheerios, be a fruitloop! ♥

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Help Me Pretty Plz!!! Numbers!

Yeah, that's right, and also
the square root of 110.25 is
halfway between the answers.

And the square root of 220.25 is
not something.50, so it is not
the triangle one.

It is the rectangle one.

The add a quarter trick is
something I know about for 2
numbers that are off by 1 and
the middle average number is
squared.

Like 5.5 times 5.5 should be
30.25 or
5 x 6 = 30
and 5.5 is halfway between
5 and 6.

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igloo myrtilles fourmis

SvenBee

Member

Registered: 2008-03-08

Posts: 106

Re: Help Me Pretty Plz!!! Numbers!

No you don't replace it with x, you set it equal to x.

So:
Squared: 110=x^2
Triangular:110=x(x-1)/2
Rectangular:110=x(x-1)

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e...the red-headed stepchild of math.

blank_brunette

Member

Registered: 2008-03-27

Posts: 46

Re: Help Me Pretty Plz!!! Numbers!

ok...either i am really retarded, or neither of you have answered the question...i just wanted to know how u found out how 110 was an rectangular number...?

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In this world of cheerios, be a fruitloop! ♥

SvenBee

Member

Registered: 2008-03-08

Posts: 106

Re: Help Me Pretty Plz!!! Numbers!

Lets take it slowly this time... The formula to determine whether it's rectangular is x(x-1) and the number you want to check is 110. I hope you're following me O.o. So... you set them equal to each other like this: 110 = x(x-1) then you solve.

Step 1.
110 = x(x-1)
Step 2... distribute the x.
110 = x^2-x
Step 3... subtract 110 from both sides.
x^2-x-110
Step 4... apply the quadratic equation.
...
Step 5... determine solutions.
The answers turn out to be 11 and -10
Since you're answers are integers (and therefore rational numbers) then you know that the number is rectangular.

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e...the red-headed stepchild of math.

blank_brunette

Member

Registered: 2008-03-27

Posts: 46

Re: Help Me Pretty Plz!!! Numbers!

ok umm.........i have another equation thats easy but im stumped on putting it into factored form...i think im doing it wrong..
3x^2+14x+8....................how do i convert this isnto factoer form
?

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In this world of cheerios, be a fruitloop! ♥

SvenBee

Member

Registered: 2008-03-08

Posts: 106

Re: Help Me Pretty Plz!!! Numbers!

Factor form? I'm assuming that this is the same thing as factoring it.
There are several different methods.
Here's a hint: quadratic formula or completing the square.
Post again if you want more help.

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e...the red-headed stepchild of math.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Help Me Pretty Plz!!! Numbers!

That one can also be factored directly though.

3x² + 14x + 8
3x² + 12x + 2x + 8
3x(x+4) + 2(x+4)
(3x+2)(x+4)

The 14 was split into 12 and 2 because two numbers were needed that multiplied to give 3x8=24.

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Why did the vector cross the road?
It wanted to be normal.