document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134085>Question 134085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi ,<BR>\n" );
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document.write( "I was hoping you could help me with two more question. I have tried to find a formula but I can't and I'm wasting too much time. My class is tomorrow evening.<BR>\n" );
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document.write( "1. Determine two numbers whose sum is 15 and the sum of its square roots is 137. I know the answer is 11 and 4 but what formula do I use. <BR>\n" );
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document.write( "7. The perimeter of a rectangle is 20 inches and its area is 24 inches squared. Determine the lengths of its sides. I know that the sides are 6\" and 4\" but I need to show my work. I just used logic to find the numbers. <BR>\n" );
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document.write( "8. The perimeter of a rectangle es 24cm and its area is 32 cm squared. Find the lengths of its sides. Again I know that the answer is 8cm and 4cm but what is the formula?<BR>\n" );
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document.write( "I really appreciate the help<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Anne <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 #98049 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=98049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the first place, you have a problem with the way you stated question number 1.  If two numbers have a sum of 15, they can't have a sum of their square ROOTS be a larger number, and certainly not 137.  Since you gave the answers as 11 and 4, then the question must have read:  '...the sum of their squares is 137.'\r<BR>\n" );
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document.write( "Presuming that to be true, here's how to solve it.\r<BR>\n" );
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document.write( "First number: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Second number: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square of the first number: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square of the second number: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sum of the numbers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By ALIGN=MIDDLE  ALT=\"x%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sum of the squares: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We are given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=15 ALIGN=MIDDLE  ALT=\"x%2By=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=137 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=137\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve the first equation for either of the variables:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15-x ALIGN=MIDDLE  ALT=\"y=15-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute this value into the second equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%2815-x%29%5E2=137 ALIGN=MIDDLE  ALT=\"x%5E2%2B%2815-x%29%5E2=137\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand and simplify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B225-30x%2Bx%5E2=137 ALIGN=MIDDLE  ALT=\"x%5E2%2B225-30x%2Bx%5E2=137\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-30x%2B88=0 ALIGN=MIDDLE  ALT=\"2x%5E2-30x%2B88=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The lead coefficient is an integer factor of all the coefficients, so divide:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-15x%2B44=0 ALIGN=MIDDLE  ALT=\"x%5E2-15x%2B44=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor the trinomial:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%2A+-11+=+44 ALIGN=MIDDLE  ALT=\"-4+%2A+-11+=+44\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-11=-15 ALIGN=MIDDLE  ALT=\"-4-11=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%28x-11%29=0 ALIGN=MIDDLE  ALT=\"%28x-4%29%28x-11%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11 ALIGN=MIDDLE  ALT=\"x=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check the answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B11=15 ALIGN=MIDDLE  ALT=\"4%2B11=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+%2B+121+=+137 ALIGN=MIDDLE  ALT=\"16+%2B+121+=+137\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=================================<BR>\n" );
document.write( "Perimeter = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L+%2B+2W=20 ALIGN=MIDDLE  ALT=\"2L+%2B+2W=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Area = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LW=24 ALIGN=MIDDLE  ALT=\"LW=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve the perimeter equation for either variable:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L=20-2W ALIGN=MIDDLE  ALT=\"2L=20-2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=10-W ALIGN=MIDDLE  ALT=\"L=10-W\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute in the Area equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810-W%29W=24 ALIGN=MIDDLE  ALT=\"%2810-W%29W=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10W-W%5E2-24=0 ALIGN=MIDDLE  ALT=\"10W-W%5E2-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-W%5E2%2B10W-24=0 ALIGN=MIDDLE  ALT=\"-W%5E2%2B10W-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2-10W%2B24=0 ALIGN=MIDDLE  ALT=\"W%5E2-10W%2B24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28W-6%29%28W-4%29=0 ALIGN=MIDDLE  ALT=\"%28W-6%29%28W-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=6 ALIGN=MIDDLE  ALT=\"W=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=4 ALIGN=MIDDLE  ALT=\"W=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Traditionally, the width is shorter than the length, so the width is 4, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2B8=20 ALIGN=MIDDLE  ALT=\"2L%2B8=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L=12 ALIGN=MIDDLE  ALT=\"2L=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=6 ALIGN=MIDDLE  ALT=\"L=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "===============================\r<BR>\n" );
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document.write( "Do problem #8 the same way I just showed you for problem #7 </SPAN>\n" );
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