document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199950>Question 1199950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the maximum number of non-overlapping regions into which 10 additional straight lines can subdivide this figure. \r<BR>\n" );
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document.write( "Figure: https://ibb.co/99bk08m\r<BR>\n" );
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document.write( "Thanks so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848149 by </B><A HREF=/tutors/aboutme.mpl?userid=textot><B>textot(100)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=textot><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=848149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Initial Regions:**\r<BR>\n" );
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document.write( "* The rectangle is already divided into 4 smaller rectangles.\r<BR>\n" );
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document.write( "**2. Effect of Each Line:**\r<BR>\n" );
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document.write( "* **First Line:** At most, it can intersect existing lines twice, creating 2 new regions. <BR>\n" );
document.write( "* **Second Line:** At most, it can intersect the first line and existing lines twice, creating 3 new regions.<BR>\n" );
document.write( "* **Third Line:** At most, it can intersect the first two lines and existing lines twice, creating 4 new regions.<BR>\n" );
document.write( "* **And so on...**\r<BR>\n" );
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document.write( "**3. General Pattern:**\r<BR>\n" );
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document.write( "* Each subsequent line can potentially intersect all the previous lines at most once, creating one additional region for each intersection.\r<BR>\n" );
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document.write( "**4. Maximum Regions:**\r<BR>\n" );
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document.write( "* **Initial Regions:** 4<BR>\n" );
document.write( "* **First Line:** 4 + 2 = 6 regions<BR>\n" );
document.write( "* **Second Line:** 6 + 3 = 9 regions<BR>\n" );
document.write( "* **Third Line:** 9 + 4 = 13 regions <BR>\n" );
document.write( "* **Fourth Line:** 13 + 5 = 18 regions<BR>\n" );
document.write( "* **Fifth Line:** 18 + 6 = 24 regions<BR>\n" );
document.write( "* **Sixth Line:** 24 + 7 = 31 regions<BR>\n" );
document.write( "* **Seventh Line:** 31 + 8 = 39 regions<BR>\n" );
document.write( "* **Eighth Line:** 39 + 9 = 48 regions<BR>\n" );
document.write( "* **Ninth Line:** 48 + 10 = 58 regions<BR>\n" );
document.write( "* **Tenth Line:** 58 + 11 = 69 regions\r<BR>\n" );
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document.write( "**Therefore, the maximum number of non-overlapping regions into which 10 additional straight lines can subdivide the figure is 69.**\r<BR>\n" );
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document.write( "**Note:** This assumes that the lines are strategically placed to maximize the number of intersections and, consequently, the number of regions.<BR>\n" );
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