Question

Indicate whether the statement below is true or false, in regards to the pattern above.

The number of squares in each figure, y, is equal to the xth odd number squared plus 4.
A. true
B. false

Answer 1

This question builds off of the question from your earlier thread: http://openstudy.com/study?source=email#/updates/503bb40ce4b007f90031040f

And the difficult part is converting a word problem into an equation and vice-versa.

I will start by showing you a simple similar equation and sentence. Does the equation y = 2x -1 give the xth odd number?

The ordered pairs for this sequence would look like (1,1), (2,3), (3,5).. and so forth.

Answer 2

Sorry to be dumb but what does xth mean

Answer 3

To fill in blank 4 i had 53 and for blank 5 i had 85 @datanewb

Answer 4

No, that's not dumb. You stated exactly which part of the word problem you didn't understand, and sometimes that is not easy. What is meant, is if you take the ordered odd numbers (1,3,5,7,9,11...) Then the first odd number is 1. The second odd number is 3. The third odd number is 5. If x = 4, then the xth odd number would be ___? It would be 7. So, does the equation
\[ y = 2x-1\]gives the xth odd number. Try it, for x = 1, it gives the odd number 1. For x = 2, it gives the odd number 3. Do you understand?

Answer 5

Yes, that is correct, @chicagochica5. Filling in blank 4 (that is for x = 4) you should have
\[ y = (2x-1)^2 +4\\ y=(2*4 - 1)^2 +4 \\ y = (8 -1)^2 +4 \\ y = (7)^2 + 4 \\ y = 53 \] Similarly, for x = 5, you get the value y = 85.

Answer 6

Sorry I am really not understanding even tho you are explaining it.I guess it is the equations. The reason I got 53 is because I took 29 + 24 and i got 53 and then i took 53 + 32 to get 85. We have the same answers but different ways of answering

Answer 7

That you found another method of predicting the next stage is not a bad thing! It is impressive actually. Sometime later, reread this thread and maybe it will make more sense.

In the meantime, there is a way to get the answer without using any equations! Look back at the picture you attached. Notice for the first set of squares above the number one. In the center, there is a single square, and it is surrounded by 4 other squares.

Then, for the second set of squares above the number 2, can you see that it is a 3 by 3 block of squares surrounded by 4 other squares.

Finally, for the set of squares above the number three, can you see that it is merely a 5 by 5 block of squares surrounded by 4 additional squares?

Answer 8

Yes @datanewb, I understand that. Thanks for going through all that explaining... How do I get the answer for the question tho?

Answer 9

That's good, @chicagochica5! Well, once you see that much, you pretty much have the answer!

At first the center 'block' of squares is 1 by 1, then it is 3 by 3, then it is 5 by 5... for the next stage it would be a 7 by 7. This corresponds to the "xth odd number squared." So, yes, that much of the statement from the question is true.

Then for all stages there are those 4 squares surround the "block' of squares. That much is constant and corresponds to the part of the question that say " plus 4." So, yes that is true as well.

Now putting it all together: The number of squares in each figure, y, is equal to the xth odd number squared plus 4.

Answer is A) True

Answer 10

Well thank you so very much!! You took alot of your time to explain this to me! You are very smart and should be a teacher if you are not already. It is still confusing but I think I am kind of understanding it. Thanks again I really appreciate it :)

Answer 11

Thank you and your welcome. I really appreciate that. I am not a teacher, but maybe some day. For now I still have a lot to learn myself. Glad I was able to help a little bit. :)