document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=874981>Question 874981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.find two numbers whose sum is 13 and whose product is 40\r<BR>\n" );
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document.write( "2.the area of a rectangle is 94sq. units and its perimeter is 38units.<BR>\n" );
document.write( "find the length and width of the rectangle.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #527857 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=527857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.find two numbers whose sum is 13 and whose product is 40<BR>\n" );
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document.write( "Try pairs of factors of 40.<BR>\n" );
document.write( "1*40  NG<BR>\n" );
document.write( "2*20 NG<BR>\n" );
document.write( "etc<BR>\n" );
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document.write( "2.the area of a rectangle is 94sq. units and its perimeter is 38units.<BR>\n" );
document.write( "find the length and width of the rectangle.<BR>\n" );
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document.write( "P = 2L + 2W = 38<BR>\n" );
document.write( "L + W = 19<BR>\n" );
document.write( "L*W = 94<BR>\n" );
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document.write( "L = 19 - W<BR>\n" );
document.write( "Sub for L<BR>\n" );
document.write( "(19-W)*W = 94<BR>\n" );
document.write( "W^2 - 19W + 94 = 0<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-19x%2B94+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-19x%2B94+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-19%29%5E2-4%2A1%2A94=-15 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-19%29%5E2-4%2A1%2A94=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -15 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -15 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+15%29+=+3.87298334620742 ALIGN=MIDDLE  ALT=\"sqrt%28+15%29+=+3.87298334620742\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28--19%2B-i%2Asqrt%28+-15+%29%29%2F2%5C1+=++%28--19%2B-i%2A3.87298334620742%29%2F2%5C1+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "  Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-19%2Ax%2B94+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-19%2Ax%2B94+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "No real number solution.<BR>\n" );
document.write( "The max area of a rectangle of given perimeter is a square.<BR>\n" );
document.write( "For P = 38, side length = 9.5<BR>\n" );
document.write( "Area = 9.5^2 = 90.25 sq units<BR>\n" );
document.write( "94 is not possible. </SPAN>\n" );
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