document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256439>Question 256439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ron was doodling in his notebook and noticed the following: 3 segments can be drawn between 3 points, 6 segments can be drawn between 4 points, and 10 segments can be drawn between 5 points.<BR>\n" );
document.write( "a. find an equation giving the number of segments \"y\" as a function of the number of points \"x\".<BR>\n" );
document.write( "b. according o this formula howmany segments can be drawn between 70 points.<BR>\n" );
document.write( "c. how many points are needed to draw 45 segments between them. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188648 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=188648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here the pattern is 1,3,6,10, . . . <BR>\n" );
document.write( "The formula is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+%28x%2A%28x%2B1%29%29%2F2 ALIGN=MIDDLE  ALT=\"Y+=+%28x%2A%28x%2B1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where x is the number of points<BR>\n" );
document.write( "--<BR>\n" );
document.write( "If x = 70, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+%2870%2A%2870%2B1%29%29%2F2 ALIGN=MIDDLE  ALT=\"Y+=+%2870%2A%2870%2B1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2485 segments<BR>\n" );
document.write( "--<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45+=+%28x%2A%28x%2B1%29%29%2F2 ALIGN=MIDDLE  ALT=\"45+=+%28x%2A%28x%2B1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90+=+x%2A%28x%2B1%29 ALIGN=MIDDLE  ALT=\"90+=+x%2A%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 9, x+1 = 10.<BR>\n" );
document.write( "We need 9 points for 45 segments </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );