document.write( "Question 411529: A polygon of n side has \"n%28n-3%29%2F2\" diagonals. How many sides has a polygon with 77 diagonals?\r
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Algebra.Com's Answer #289255 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
a ploygon of n side has(n-3) diagonals. how many sides has a polygon with 77 diagonals.\r
\n" ); document.write( "\n" ); document.write( "the sum of first integers n is s=(n+1). find how many integers are required to add up to 66\r
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document.write( "Both those formulas are wrong. A polygon with n sides has \"n%28n-3%29%2F2\" diagonals,\r\n" );
document.write( "not n-3. The sum of the first n integers n is \"S=%28n%28n%2B1%29%29%2F2\", not n+1. \r\n" );
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document.write( "I will answer using the correct formulas, not the ones given.\r\n" );
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document.write( "How many sides has a polygon with 77 diagonals?\r\n" );
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document.write( "\"n%28n-3%29%2F2=77\"\r\n" );
document.write( "\"n%28n-3%29=154\"\r\n" );
document.write( "\"n%5E2-3n=154\"\r\n" );
document.write( "\"n%5E2-3n-154=0\"\r\n" );
document.write( "\"%28n%2B11%29%28n-14%29=0\"\r\n" );
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document.write( "n+11=0          n-14=0\r\n" );
document.write( "   n= -11          n=14\r\n" );
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document.write( "We discard the negative answer.  The correct solution is a 14-sided\r\n" );
document.write( "polygon.\r\n" );
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document.write( "How many integers are required to add up to 66?\r\n" );
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document.write( "\"%28n%28n%2B1%29%29%2F2=66\"\r\n" );
document.write( "\"n%28n%2B1%29=132\" \r\n" );
document.write( "\"n%5E2%2Bn=132\"\r\n" );
document.write( "\"n%5E2%2Bn-132=0\"\r\n" );
document.write( "\"%28n-11%29%28n%2B12%29=0\"\r\n" );
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document.write( "n-11=0       n+12=0\r\n" );
document.write( "   n=11        n=-12\r\n" );
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document.write( "We discard the negative answer.  The correct solution is the first\r\n" );
document.write( "11 integers:\r\n" );
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document.write( "1+2+3+4+5+6+7+8+9+10+11=66\r\n" );
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document.write( "Edwin
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