document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120778>Question 1120778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Eliana wants to make a diorama or an art contest. SHE starts with a rectangular sheet of a cardboard box is 12 inches long and 8 inches wide. SHE PLANS to make the diorama box baby cute cutting identical squares from the corners and folding the sides to create a box with an open front. \r<BR>\n" );
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document.write( "Write the function v(x)=(12-2x)(8-2x)x in factored form. <BR>\n" );
document.write( "Select all the following that are true. Explain your reasoning. <BR>\n" );
document.write( "A. V(x)=(12-2x)(8-2x)x <BR>\n" );
document.write( "B. V(x)=4x(6-x)(4-x)<BR>\n" );
document.write( "C. V(x)=-4x(x-6)(x-4)<BR>\n" );
document.write( "D. The zeros of y=v(x) correspond to the values of x that result in a diorama box with volume in 36 in^3.<BR>\n" );
document.write( "E. The graph of y=v(x) crosses the x-axis at (0,0), (4,0), and (6,0) <BR>\n" );
document.write( "F. The graph of y=v(x) shows that there is only one value of x for which the volume of the diorama box will be in 36in^3.<BR>\n" );
document.write( "G. The graph of y=v(x) has a turning point between x=0 and x=4. <BR>\n" );
document.write( "H. The only portion of the graph that represents the possible volumes of Eliana's diorama box is the portion for which 0 < x <4. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736462 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=736462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "C is false because <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (6\ -\ x)\ =\ -(x\ -\ 6)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (4\ -\ x)\ =\ -(x\ -\ 4)\">, so factoring out -1 from each of the binomial factors would result in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (-1)(-1)(4x)(x\ -\ 6)(x\ -\ 4)\ \not=\ -4x(x\ -\ 6)(x\ -\ 4)\">\r<BR>\n" );
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document.write( "D is false because the function is a volume function.  That is the value of the function IS the volume.  So a zero of the VOLUME function is a place where the VOLUME is ZERO.\r<BR>\n" );
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document.write( "F is false.  Draw a line at y = 36 across your graph.\r<BR>\n" );
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document.write( "The rest is true.<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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