document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132077>Question 1132077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car's value depreciates as it accumulates miles. Use the tables below to determine the rate of depreciation for Car 1 and Car 2. After how many miles do the cars have the same value?<BR>\n" );
document.write( "A table of 'Car 1' showing data of Miles and Value as (25000,$22960), (50000,$19680), (75000,$16400)?and (100000,$13120) respectively.<BR>\n" );
document.write( "A table of 'Car 2' showing data of Miles and Value as (25000,$20376), (50000,$17806), (75000,$15236)? and (100000,$12666) respectively.\r<BR>\n" );
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document.write( "A. The cars will have the same value at 1,160,000 miles.<BR>\n" );
document.write( "	B.	The cars will have the same value at 116,000 miles.<BR>\n" );
document.write( "	C.	The cars will have the same value at 11,600 miles.\r<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 #748949 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748949\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> examination of the point pairs for each car yields the following:\r<BR>\n" );
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document.write( "the value for car 1 is depreciating by 3280 dollars every 25000 miles.<BR>\n" );
document.write( "the value for car 2 is depreciating by 2570 dollars every 25000 miles.\r<BR>\n" );
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document.write( "the change in the value of y divided by the change in the value of x for car 1 is therefore equal to -3280 / 25000 = -.1312.\r<BR>\n" );
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document.write( "the change in the value of y divided by the change in the value of x for car 2 is therefore equal to -2570 / 25000 = -.1028.\r<BR>\n" );
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document.write( "y is the value of the car.<BR>\n" );
document.write( "x is the number of miles the car has been driven\r<BR>\n" );
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document.write( "the equation for the value of each car is y = mx + b<BR>\n" );
document.write( "m is the slope which is the change in the value of y divided by the change in the value of x.<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "the equation for car 1 becomes y = -.1312 * x + 26240\r<BR>\n" );
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document.write( "the equation for car 2 becomes y = -.1028 * x + 22946\r<BR>\n" );
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document.write( "i'm assuming you know how to derive the value of the y-intercept so i won't get into it here.\r<BR>\n" );
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document.write( "the cars will have the same value when the equation for car 1 is equal to the equation for car 2.\r<BR>\n" );
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document.write( "this occurs when -.1312 * x + 26240 = -.2018 * x + 22946\r<BR>\n" );
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document.write( "solve for x in this equation to get x = 3294 /.0284 = 115985.9155.\r<BR>\n" );
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document.write( "round this to nearest 1000 to get x = 116000.\r<BR>\n" );
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document.write( "that's selection B.\r<BR>\n" );
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document.write( "a graph of both equations and their intersection is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/122301.jpg\" alt=\"$$$\" >\r<BR>\n" );
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