document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248262>Question 248262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help with these word problems I am terrible at word problems. I listed the problems below along with what I could figure out. Thanks in advance.\r<BR>\n" );
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document.write( "Solving Quadratic Equations by Factoring\r<BR>\n" );
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document.write( "1. Address book. The perimeter of the cover of an address book<BR>\n" );
document.write( "is 14 inches, and the diagonal measures 5 inches. What are<BR>\n" );
document.write( "the length and width of the cover?\r<BR>\n" );
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document.write( "  x^2+14=5^2<BR>\n" );
document.write( "x^2+x^2+14=25<BR>\n" );
document.write( "2x^2+14=25<BR>\n" );
document.write( "    -14=-14<BR>\n" );
document.write( "   2x^2=11 don't know if this is right thus far and where to go from here.\r<BR>\n" );
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document.write( "2. Throwing a wrench. An angry construction worker throws<BR>\n" );
document.write( "his wrench downward from a height of 128 feet with an<BR>\n" );
document.write( "initial velocity of 32 feet per second. The height of the<BR>\n" );
document.write( "wrench above the ground after t seconds is given<BR>\n" );
document.write( "by S(t)-16t^2-32t+128.\r<BR>\n" );
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document.write( "   -16(t+4)(t-2)is what I have so far!!\r<BR>\n" );
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document.write( "a) What is the height of the wrench after 1 second?<BR>\n" );
document.write( "b) How long does it take for the wrench to reach the<BR>\n" );
document.write( "ground?<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 #180934 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=180934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x^2=11<BR>\n" );
document.write( " don't know if this is right thus far and where to go from here. <BR>\n" );
document.write( "if this were right you would divide by 2<BR>\n" );
document.write( "x^2=11/2<BR>\n" );
document.write( "then get sqrt <BR>\n" );
document.write( "x=sqrt(11/2)\r<BR>\n" );
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document.write( "Address book. The perimeter of the cover of an address book<BR>\n" );
document.write( "is 14 inches, and the diagonal measures 5 inches. What are<BR>\n" );
document.write( "the length and width of the cover? <BR>\n" );
document.write( "It appears you are too anxious to do the problems that you aren't reading them.<BR>\n" );
document.write( "what is 14?<BR>\n" );
document.write( "14 is the perimeter.<BR>\n" );
document.write( "What is the perimeter.<BR>\n" );
document.write( "Someone who walks the perimeter of the ranch walks around the edge of the ranch.<BR>\n" );
document.write( "so the perimeter is the walk around the rectangle or circle. since it is an address book It is a rectangle maybe a square.<BR>\n" );
document.write( "In either case P=2L+2W <BR>\n" );
document.write( "in the case of a square L=W<BR>\n" );
document.write( "so we have now 2L+2W=14<BR>\n" );
document.write( "2(L=W)=14<BR>\n" );
document.write( "l+w=7\r<BR>\n" );
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document.write( "the diagonal measures 5 inches<BR>\n" );
document.write( "What is the diagonal of rectangle?<BR>\n" );
document.write( "It is the hypotenuse of the right triangle formed by the sides L and W\r<BR>\n" );
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document.write( "so we know that W=7-L<BR>\n" );
document.write( "using the Pythagorean theorem a^2+b^2=c^2<BR>\n" );
document.write( "but we have W^2+L^2=5^5<BR>\n" );
document.write( "and W=7-L<BR>\n" );
document.write( "substitute 7-L for W<BR>\n" );
document.write( "and we get and that (7-L)^2+L^2=5^2<BR>\n" );
document.write( "multiply it out using FOIL<BR>\n" );
document.write( "(7-L)(7-L)<BR>\n" );
document.write( "first<BR>\n" );
document.write( "7*7=7^2=49<BR>\n" );
document.write( "outside<BR>\n" );
document.write( "7*-L<BR>\n" );
document.write( "inside<BR>\n" );
document.write( "7*-L<BR>\n" );
document.write( "last<BR>\n" );
document.write( "-L*-L=L^2<BR>\n" );
document.write( "putting it altogether and rearranging to normal format<BR>\n" );
document.write( "L^2+L^2-14L+49=25<BR>\n" );
document.write( "2L^2-14L+24=0<BR>\n" );
document.write( "divide by 2<BR>\n" );
document.write( "L^2-7L+12=0\r<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=quadratic.solver>SOLVE quadratic equation with variable</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-7x%2B12+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-7x%2B12+=+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=%28-7%29%5E2-4%2A1%2A12=1 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-7%29%5E2-4%2A1%2A12=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--7%2B-sqrt%28+1+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--7%2B-sqrt%28+1+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+4 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-7%29-sqrt%28+1+%29%29%2F2%5C1+=+3 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-7%29-sqrt%28+1+%29%29%2F2%5C1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-7x%2B12 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-7x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-7x%2B12+=+1%28x-4%29%2A%28x-3%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-7x%2B12+=+1%28x-4%29%2A%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4, 3.\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-7%2Ax%2B12+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B12+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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