document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214848>Question 214848</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0866099654/algebrahomeworkh>Geometry for Enjoyment and Challenge</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> i'm having trouble finding m<1 . . .\r<BR>\n" );
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document.write( "Given: <BR>\n" );
document.write( "<1 and <2 are supplementary<BR>\n" );
document.write( "<2 and <3 are supplementary<BR>\n" );
document.write( "<1= x^2+3y<BR>\n" );
document.write( "<2= 20y+3<BR>\n" );
document.write( "<3= 3y+4x\r<BR>\n" );
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document.write( "Find: m<1<BR>\n" );
document.write( "(does not require proof)\r<BR>\n" );
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document.write( "i've found x= -5.75+44.25, but i am confused on how to proceed ? how would you solve (-5.75+44.25)^2+3y+20y+3=180 ?<BR>\n" );
document.write( "please help, thank you !!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162314 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=162314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using the fact that the sum of supplementary angles is 180 degrees, we can write two equations in x and y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D%2BA%5B2%5D+=+180 ALIGN=MIDDLE  ALT=\"A%5B1%5D%2BA%5B2%5D+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+=+x%5E2%2B3y ALIGN=MIDDLE  ALT=\"A%5B1%5D+=+x%5E2%2B3y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B2%5D+=+20y%2B3 ALIGN=MIDDLE  ALT=\"A%5B2%5D+=+20y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get:<BR>\n" );
document.write( "1). <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B3y%29%2B%2820y%2B3%29+=+180 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B3y%29%2B%2820y%2B3%29+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Similarly for angles 2 and 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B2%5D+=+20y%2B3 ALIGN=MIDDLE  ALT=\"A%5B2%5D+=+20y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B3%5D+=+3y%2B4x ALIGN=MIDDLE  ALT=\"A%5B3%5D+=+3y%2B4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the angles.<BR>\n" );
document.write( "2). <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820y%2B3%29%2B%283y%2B4x%29+=+180 ALIGN=MIDDLE  ALT=\"%2820y%2B3%29%2B%283y%2B4x%29+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying 1). and 2). we have:<BR>\n" );
document.write( "1a). <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B23y%2B3+=+180 ALIGN=MIDDLE  ALT=\"x%5E2%2B23y%2B3+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2a). <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B23y%2B3+=+180 ALIGN=MIDDLE  ALT=\"4x%2B23y%2B3+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtracting 2a) from 1a) we get:<BR>\n" );
document.write( "3). <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-4x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor an x.<BR>\n" );
document.write( "3a). <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-4%29+=+0 ALIGN=MIDDLE  ALT=\"x%28x-4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute x = 0 into equation 1a) and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5E2%2B23y%2B3+=+180 ALIGN=MIDDLE  ALT=\"0%5E2%2B23y%2B3+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23y+=+177 ALIGN=MIDDLE  ALT=\"23y+=+177\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+7.6957 ALIGN=MIDDLE  ALT=\"y+=+7.6957\"   DISABLED_style= \"max-width:90%; height:auto;\" > or substitute x = 4 into equation 1a) and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%5E2%2B23y%2B3+=+180 ALIGN=MIDDLE  ALT=\"%284%29%5E2%2B23y%2B3+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2B23y+=+180 ALIGN=MIDDLE  ALT=\"19%2B23y+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 19 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23y+=+161 ALIGN=MIDDLE  ALT=\"23y+=+161\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 23.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+7 ALIGN=MIDDLE  ALT=\"y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So angle 1 can have one of two measures:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+=+x%5E2%2B3y ALIGN=MIDDLE  ALT=\"A%5B1%5D+=+x%5E2%2B3y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute x = 0 and y = 7.6957<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+=+0%2B3%287.6957%29 ALIGN=MIDDLE  ALT=\"A%5B1%5D+=+0%2B3%287.6957%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28A%5B1%5D+=+23.0871%29 ALIGN=MIDDLE  ALT=\"highlight_green%28A%5B1%5D+=+23.0871%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >degrees.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B2%5D+=+20y%2B3 ALIGN=MIDDLE  ALT=\"A%5B2%5D+=+20y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B2%5D+=+20%287.6957%29%2B3 ALIGN=MIDDLE  ALT=\"A%5B2%5D+=+20%287.6957%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28A%5B2%5D+=+156.914%29 ALIGN=MIDDLE  ALT=\"highlight_green%28A%5B2%5D+=+156.914%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >degrees.<BR>\n" );
document.write( "or...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+=+x%5E2%2B3y ALIGN=MIDDLE  ALT=\"A%5B1%5D+=+x%5E2%2B3y\"   DISABLED_style= \"max-width:90%; height:auto;\" > x=4 and y = 7.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+=+4%5E2%2B3%287%29 ALIGN=MIDDLE  ALT=\"A%5B1%5D+=+4%5E2%2B3%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+=+16%2B21 ALIGN=MIDDLE  ALT=\"A%5B1%5D+=+16%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A%5B1%5D+=+37%29 ALIGN=MIDDLE  ALT=\"highlight%28A%5B1%5D+=+37%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >degrees.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B2%5D+=+20y%2B3 ALIGN=MIDDLE  ALT=\"A%5B2%5D+=+20y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B2%5D+=+20%287%29%2B3 ALIGN=MIDDLE  ALT=\"A%5B2%5D+=+20%287%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A%5B2%5D+=+143%29 ALIGN=MIDDLE  ALT=\"highlight%28A%5B2%5D+=+143%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees.<BR>\n" );
document.write( "As you can see, in both cases, the sums of angle 1 and angle 2 are 180 degrees. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );