document.write( "Question 126330: HI!
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\n" ); document.write( "\n" ); document.write( "graph the following information and see the q uestions below and answer them\r
\n" ); document.write( "\n" ); document.write( "mass of loonies (g) , #of loonies\r
\n" ); document.write( "\n" ); document.write( "21 , 3
\n" ); document.write( "63 , 9
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\n" ); document.write( "\n" ); document.write( "a) what is the mass of 33 loonies?
\n" ); document.write( "b) What is teh value of 133g of loonies?
\n" ); document.write( "c) A bag contains 152 g of coins. Is it possible that it contains only loonies? EXplain\r
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\n" ); document.write( "\n" ); document.write( "Ps: the graph should be according with the questions I mean the values for teh x and y axis
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Algebra.Com's Answer #92552 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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Finding the equation and graphing
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\n" ); document.write( "\n" ); document.write( "Let x=mass of loonies (g) and y= # of loonies\r
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\n" ); document.write( "\n" ); document.write( "When \"x=21\", \"y=3\". So we have the first point (21,3)\r
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\n" ); document.write( "\n" ); document.write( "When \"x=63\", \"y=9\". So we have the second point (63,9)\r
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\n" ); document.write( "\n" ); document.write( "So let's find the equation of the line through the points (21,3) and (63,9)\r
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\n" ); document.write( "\n" ); document.write( "First lets find the slope through the points (\"21\",\"3\") and (\"63\",\"9\")\r
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\n" ); document.write( "\n" ); document.write( "\"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\" Start with the slope formula (note: is the first point (\"21\",\"3\") and is the second point (\"63\",\"9\"))\r
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\n" ); document.write( "\n" ); document.write( "\"m=%289-3%29%2F%2863-21%29\" Plug in \"y%5B2%5D=9\",\"y%5B1%5D=3\",\"x%5B2%5D=63\",\"x%5B1%5D=21\" (these are the coordinates of given points)\r
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\n" ); document.write( "\n" ); document.write( "\"m=+6%2F42\" Subtract the terms in the numerator \"9-3\" to get \"6\". Subtract the terms in the denominator \"63-21\" to get \"42\"\r
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\n" ); document.write( "\n" ); document.write( "\"m=1%2F7\" Reduce\r
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\n" ); document.write( "\n" ); document.write( "So the slope is\r
\n" ); document.write( "\n" ); document.write( "\"m=1%2F7\"\r
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\n" ); document.write( "\n" ); document.write( "Now let's use the point-slope formula to find the equation of the line:\r
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\n" ); document.write( "\n" ); document.write( "------Point-Slope Formula------
\n" ); document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\" where \"m\" is the slope, and is one of the given points\r
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\n" ); document.write( "\n" ); document.write( "So lets use the Point-Slope Formula to find the equation of the line\r
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\n" ); document.write( "\n" ); document.write( "\"y-3=%281%2F7%29%28x-21%29\" Plug in \"m=1%2F7\", \"x%5B1%5D=21\", and \"y%5B1%5D=3\" (these values are given)\r
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\n" ); document.write( "\n" ); document.write( "\"y-3=%281%2F7%29x%2B%281%2F7%29%28-21%29\" Distribute \"1%2F7\"\r
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\n" ); document.write( "\n" ); document.write( "\"y-3=%281%2F7%29x-3\" Multiply \"1%2F7\" and \"-21\" to get \"-21%2F7\". Now reduce \"-21%2F7\" to get \"-3\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=%281%2F7%29x-3%2B3\" Add \"3\" to both sides to isolate y\r
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\n" ); document.write( "\n" ); document.write( "\"y=%281%2F7%29x%2B0\" Combine like terms \"-3\" and \"3\" to get \"0\" \r
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\n" ); document.write( "\n" ); document.write( "\"y=%281%2F7%29x\" Remove the zero term\r
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\n" ); document.write( "\n" ); document.write( "So the equation of the line which goes through the points (\"21\",\"3\") and (\"63\",\"9\") is: \"y=%281%2F7%29x\"\r
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\n" ); document.write( "\n" ); document.write( "The equation is now in \"y=mx%2Bb\" form (which is slope-intercept form) where the slope is \"m=1%2F7\" and the y-intercept is \"b=0\"\r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph the equation \"y=%281%2F7%29x\" and plot the points (\"21\",\"3\") and (\"63\",\"9\"), we get this: (note: if you need help with graphing, check out this
solver)\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"y=%281%2F7%29x\" through the points (\"21\",\"3\") and (\"63\",\"9\")\r
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\n" ); document.write( "\n" ); document.write( "Notice how the two points lie on the line. This graphically verifies our answer.\r
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Jump to Top\r
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\n" ); document.write( "\n" ); document.write( "\"what is the mass of 33 loonies?\"\r
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\n" ); document.write( "\n" ); document.write( "To find the total mass (which is x) simply plug in \"y=33\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=%281%2F7%29x\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"33=%281%2F7%29x\" Plug in \"y=33\"\r
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\n" ); document.write( "\n" ); document.write( "\"33%2A7=x\" Multiply both sides by 7 to isolate x\r
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\n" ); document.write( "\n" ); document.write( "\"231=x\" Multiply \r
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\n" ); document.write( "\n" ); document.write( "\"x=231\"\r
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\n" ); document.write( "\n" ); document.write( "So 33 loonies weigh 231 g\r
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Jump to Top\r
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\n" ); document.write( "\n" ); document.write( "b)\r
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\n" ); document.write( "\n" ); document.write( "\"What is teh value of 133g of loonies?\"\r
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\n" ); document.write( "\n" ); document.write( "First let's find the number of loonies (which is y)\r
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\n" ); document.write( "\n" ); document.write( "\"y=%281%2F7%29x\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"y=%281%2F7%29133\" Plug in \"x=133\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=133%2F7\" Multiply\r
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\n" ); document.write( "\n" ); document.write( "\"y=19\" Divide\r
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\n" ); document.write( "\n" ); document.write( "So there are 19 loonies that weigh 133 g. So multiply the value of one loonie by 19 to find the total value. \r
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Jump to Top\r
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\n" ); document.write( "\n" ); document.write( "c)\r
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\n" ); document.write( "\n" ); document.write( "\"y=%281%2F7%29x\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"y=%281%2F7%29152\" Plug \"x=152\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=152%2F7\" Multiply\r
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\n" ); document.write( "\n" ); document.write( "\"y=21.714\" Divide\r
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\n" ); document.write( "\n" ); document.write( "Since you cannot have 21.714 loonies, there must be other types of coins.
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