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kmullis6

  • one year ago

Please help, I'll give fan & medal

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  1. kmullis6
    • one year ago
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    Directions: Complete the conjecture based on the pattern you observe in the specific cases. Conjecture: The product of a number (n - 1) and the number (n +1) is always equal to _____. \[3\times5=4^{2}-1\] \[4\times6=5^{2}-1\] \[5\times7=5^{2}-1\] \[6\times8=7^{2}-1\] \[7\times9=8^{2}-1\] \[8\times10=9^{2}-1\]

  2. misty1212
    • one year ago
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    HI!!

  3. misty1212
    • one year ago
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    it is not clear? what do you think \[9\times 11\]would equal in that pattern?

  4. kmullis6
    • one year ago
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    99 so odd number. that's the types of questions i'm answering right now.

  5. misty1212
    • one year ago
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    lets look more carefully

  6. misty1212
    • one year ago
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    the right hand side of each equal sign is some number squared minus 1 right?

  7. kmullis6
    • one year ago
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    Yes

  8. misty1212
    • one year ago
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    and that number, the number being squared, is half way between the other two numbers right?

  9. misty1212
    • one year ago
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    the number in the middle of \(n-1\) and \(n+1\) is just \(n\)

  10. misty1212
    • one year ago
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    so what they are showing you, by example instead of by algebra, is that \[(n-1)(n+1)=n^2-1\]

  11. kmullis6
    • one year ago
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    so the answer is n?

  12. misty1212
    • one year ago
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    lol no, the answer is \(n^2-1\)

  13. kmullis6
    • one year ago
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    oohhhh ok. sorry haha :P thank you (:

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spraguer (Moderator)
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