document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204158>Question 204158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use Euler's formula to answer the question.\r<BR>\n" );
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document.write( "A polyhedron has 15 vertices and 31 edges. How many faces does it have?\r<BR>\n" );
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document.write( "(I know that the formula is v+f=E+2, would I just subtract 33 from 15 to get the correct number of faces?)\r<BR>\n" );
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document.write( "Thank you so much for your help on this problem... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154117 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154117\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> euler's formula states that:<BR>\n" );
document.write( "V - E + F = 2<BR>\n" );
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document.write( "if the polyhedron has 15 vertices and 31 edges, simply plug into the formula to get your answer.<BR>\n" );
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document.write( "V - E + F = 2 becomes:<BR>\n" );
document.write( "15 - 31 + F = 2 which becomes:<BR>\n" );
document.write( "-16 + F = 2 which becomes:<BR>\n" );
document.write( "F = 18<BR>\n" );
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document.write( "plug back into Euler's formula to check:<BR>\n" );
document.write( "15 - 31 + 18 = 2<BR>\n" );
document.write( "-16 + 18 = 2<BR>\n" );
document.write( "2 = 2 <BR>\n" );
document.write( "this is good<BR>\n" );
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document.write( "you stated the equation as V + F = E + 2 which looks ok.<BR>\n" );
document.write( "V = 15<BR>\n" );
document.write( "E = 31<BR>\n" );
document.write( "plug into your equation to get:<BR>\n" );
document.write( "15 + F = 31 + 2<BR>\n" );
document.write( "this gets you:<BR>\n" );
document.write( "F = 31 - 15 + 2<BR>\n" );
document.write( "which means you would subtract 15 from 31 as you stated and add it to 2 in order to get your answer.<BR>\n" );
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document.write( "you just need to substitute into the euler equation and you'll get your answer easily.<BR>\n" );
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document.write( "you have to move things around but that's normal arithmetic.<BR>\n" );
document.write( "15 + F = 31 + 2<BR>\n" );
document.write( "subtract 15 from both sides of the equation to get:<BR>\n" );
document.write( "F = 31 - 15 + 2<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "F = 16 + 2 = 18<BR>\n" );
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