document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=305820>Question 305820</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the # of square units contained in the region bordered by the graphs of the functions y=3x, x=3y, 3x+y=30? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218959 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=218959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the # of square units contained in the region bordered by the graphs of the functions y=3x, x=3y, 3x+y=30?\r<BR>\n" );
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document.write( "put all 3 in y = mx + b form where m is the slope and b is the y-intercept (vertical intercept or point (0,b)):<BR>\n" );
document.write( "1. y = 3x or y = 3x + 0<BR>\n" );
document.write( "2. x = 3y --> x/3 = y or y = (1/3)x + 0<BR>\n" );
document.write( "3. 3x + y = 30 --> y = -3x + 30\r<BR>\n" );
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document.write( "1/3 = -1 * 1/(-3) = -1 * -1/3 = 1/3 so equation 2 and 3 are perpendicular (the slopes are negative reciprocals)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-5%2C+20%2C+-5%2C+20%2C+3%2Ax%2C+x%2F3%2C+-3%2Ax+%2B+30%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-5%2C+20%2C+-5%2C+20%2C+3%2Ax%2C+x%2F3%2C+-3%2Ax+%2B+30%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this is a right triangle<BR>\n" );
document.write( "equation 1 and 2 intersect at (0,0)<BR>\n" );
document.write( "equation 2 and 3 intersect at:<BR>\n" );
document.write( "(1/3)x = -3x + 30<BR>\n" );
document.write( "x = -9x + 90<BR>\n" );
document.write( "10x = 90<BR>\n" );
document.write( "x = 9, eq.1 y = 3, eq. 2 y = 3 (9,3)<BR>\n" );
document.write( "equation 1 and 3 intersect at:<BR>\n" );
document.write( "3x = -3x + 30<BR>\n" );
document.write( "6x = 30<BR>\n" );
document.write( "x = 5, eq.1 y = 15, eq. 2 y = 15 (5,15)<BR>\n" );
document.write( "from (0,0) to (9,3) is the base length is:<BR>\n" );
document.write( "base = sqrt((9-0)^2 + (3-0)^2) = sqrt(9^2 + 3^2)<BR>\n" );
document.write( "base = sqrt(81 + 9) = sqrt(90) = 3sqrt(10)<BR>\n" );
document.write( "from (9,3) to (5,15) is the height length is:<BR>\n" );
document.write( "height = sqrt((5-9)^2 + (15-3)^2) = sqrt((-4)^2 + 12^2)<BR>\n" );
document.write( "height = sqrt(16 + 144) = sqrt(160) = 4sqrt(10)<BR>\n" );
document.write( "area = 1/2 * base * height = 1/2 * 3sqrt(10) * 4sqrt(10)<BR>\n" );
document.write( "area = 2 * 3 * 10 = 6 * 10 = 60 square units\r<BR>\n" );
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document.write( " </SPAN>\n" );
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