document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153291>Question 1153291</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of sides of a polygon if the sum of the number of sides and the number of diagonals is 66.<BR>\n" );
document.write( "A. 11 <BR>\n" );
document.write( "B. 12<BR>\n" );
document.write( "C. 14 <BR>\n" );
document.write( "D. 16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775481 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=775481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "total number of diagonals: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n-3%29%2F2 ALIGN=MIDDLE  ALT=\"n%28n-3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n ALIGN=MIDDLE  ALT=\"+n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sides ALIGN=MIDDLE  ALT=\"sides\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if the sum of the number of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sides ALIGN=MIDDLE  ALT=\"sides\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the number of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=diagonals ALIGN=MIDDLE  ALT=\"diagonals\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66 ALIGN=MIDDLE  ALT=\"66\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Bn%28n-3%29%2F2=66 ALIGN=MIDDLE  ALT=\"n%2Bn%28n-3%29%2F2=66\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282n%2Bn%5E2-3n%29%2F2=66 ALIGN=MIDDLE  ALT=\"%282n%2Bn%5E2-3n%29%2F2=66\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2-n=132 ALIGN=MIDDLE  ALT=\"n%5E2-n=132\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2-n-132=0 ALIGN=MIDDLE  ALT=\"n%5E2-n-132=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor completely\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B11n-12n-132=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B11n-12n-132=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%5E2%2B11n%29-%2812n%2B132%29=0 ALIGN=MIDDLE  ALT=\"%28n%5E2%2B11n%29-%2812n%2B132%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B11%29-12%28n%2B11%29=0 ALIGN=MIDDLE  ALT=\"n%28n%2B11%29-12%28n%2B11%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n+-+12%29+%28n+%2B+11%29+=+0 ALIGN=MIDDLE  ALT=\"%28n+-+12%29+%28n+%2B+11%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=12 ALIGN=MIDDLE  ALT=\"n=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-11 ALIGN=MIDDLE  ALT=\"n=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> disregard negative solution\r<BR>\n" );
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document.write( " the number of sides is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "answer: B. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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