IM 7.2.8 Lesson: Comparing Relationships with Equations

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BZPjEGE3gp3LCZaLy2sc4kLIeYqKqpcYb4SrMz3IQNWgkd4ucbGZtq3b294DBTKjoU1e/ZcEVBSDZ0tw1LLUPWcD5oiPDWHqr/hhhto4K9foFc/XUUvTVtOL037Kp4iH/QADUnnxalfCjqvzlxFj70zhZ7+6BN6Zaa8xvRfnLpMg1fPNr48/Ut66qNPBL/Bf19JL01bSbiGwxwvKeMrn6ygOx77PfXr148QmDZon6j1/MKH4z6ut7a2Ul7+Tlcocm9d9VwnD37btuU5vHRoqXVBF+dqipDxiI4Mq0ctG1Yeru6xY8c8vGTYd12ekEuVjQOpqtdN8wA90Ac4VlfXOvyZD7eHz02kiIEoLKzp02YJpjU1dcQHorlyXj+tEdFhIdjP//XfqH/OzfSjO++hW2//iThuu+NOMnX8eOBddOuPJb1+A26mAbf82BjtZG380cC7Kefm26jfjTfSjwbeQ7cNHOjwhIzJ6mVz/Ud33Em33nEH3fqTu6j/jTfRz3/+c4P9k+h39LXa91h7WbHymx681DL640Pyr66po1Ur11CN0bHnlk1t64qVq6mqqqqHbGoZE3noas03ucJ6ZHq1tbVG+YIH98mG9VsE8PM589RJk9Havm0nbdy42SULl0XKeR3eXBdh6mOxchmqHqGiYf6HeVy4dJ7WfZtLG9dvEIureOqEeSxbtozWfP0NFRUVufgUFBS4zk20AXzAzwSt5DR2UWHhLtqyZRt9s2at6KsL58LtM0Qr3rmrUPK6cIEuXLgQ2hjBAn9+/k7x7RfGIXiFyW/HzgJhpYY55pk2JtuJE6fo/PmLdP782dB0CH6Y4IcPH3b6jNsQRrp//0Gqqd4dqjzc7mPHTiSP/Ky4jkazUCbMQ/6FuV4BZZ461cqsQk3B5+DBw6HyYOJYCIfZH8XPfjhqRsv2w1F9PTprWFEFUkWTMdHa2toiWViV36Mc1ddUBhTgX8OfD+unAjusnrKyirBYuehawHKpI/CJBazAqnMqXjPAwkJuWD91Yl9LwFLbYVpWWKgWsPS1GuV3WBaw9PurVwKWqpaoASuqL36thaX2cvC8BazguuOavfrPzxASLmGYFhYrEikAq7n5mHoptDz4+LmEYVha7e3t1sIy0JMWsPSV2CsBS520UQMW1pai+IW9hqXKYC0sVRvB8xawguuOa/ZKwGLhkEYFWADJqF1CPwtLld1EHnIBsPA9ShQ/u+huRst2DUtfj71+DQsA0hssLNVCRbdbC0t/8IOCtbD09WgtLH0dOhR6o4UF4SxgOV2slbGApaU+UdkClr4OHQoWsBxVBM5YlzCw6lwVrUvoUkegk17vElrACjQuXJUsYLnUEfjEAlZg1TkVLWA5qtDP2LeE+jrEWh3vh6VPLT0F6xKm11G6EtYlTKehLO5bCysLZSUpai2sJIrJ8rK1sLJUmE9xa2H5KCXoJWthBdVcop61sBK60MnJt+PR7ene0LBfp7kZ17WAlbGq0he0gJVeR+lKWMBKp6HM7lvAykxPGZWK6sNRNMa6hBl1ScpC1iVMqZ6Mb1qXMGNVJS1oLaykqsn+hrWwsteZt4a1sLwaCXZuLaxgevOtFYWFhYGPX2+xsFgeVmhv/3CU5Qw7tW8J9TXc698SInpIlLs1wPKJ4mctLH0tWwtLX4egYC0sM3oUVKqqahzAwgA1cYCwHx22sPzumbwG/gxYJukmo+W1sJKV07nOOuU1LB1amdYFT3yHxbxFJknfZkoT5Ziemse1ouJSsWc88wkztWtY+tq9JmtYsLDsFsl6necFLD1qqWszYKUuZebulSuI/FwcyfbZaLF1CfX7rde7hKqFBXXxU09fdQkKTJMtrMSd8HKwsMLacZTlQeuRjxKwELEElkhUP7awTPOD3lQ9gj4AC/JF8bMWlr6WI7Ow1IGCRXdYWFH8ogYsrB1E8YsSsKK0sDBOoo/8fCGKLiMLWPpqjgywuKkYkHAJT506RZcvX6ZLly6FeiCI4+HDjaHyYBkOHToigkbyucnUqysAPuLc4frFixdDla+7u5t2FRSFykOVYefOglB5qf0CuayFxbMzWHpNXMI5c+Z5Qmh3Gj+HVYBoL0uXLqPly5dTbm6uONatW+fk+VqQdN16SQ9116+T+dmzZ9Piz5YYoZ+uTYsXL6Y5c+ZQbu5awW/9+vVG5VP5r1ixiqZNmxGJXKtXr6RJk6d6eG1wyai2TSePsTBp0iSSfSl56NDz1uU+QQpeU6ZOp+bmZuNj3S8sO4L5Yt9/v3u617xh4eHF7N27Vywd6NL21vfyqq/fQ1jm8ZYL47yxsVkGUp0x/RPBlENLh5HW1e0mhKofOHAg/fd//hfqe9tP6Ae3DKTrbzV13C5o9b0lnt52B/3vvjfSP/e7ySAP/7b2ve0O+j/9bqT/88MBhDzLBBk5bzL9lxtvpf91XQ5df+vt1NeoDgeKflHbet3NP6L/fV0/Ra7bRb9Bzr633mlMvh/ccgf94JYf0/+87nohl2yD7Eu1PWbyt9P3b/oRfe9736MlS5YIyziMMa/S/ObrdVRcVEaYB3yo903mN27YStu35ws+puiizaDlbfu2rTsI/Pi+ys9bVr2XXb5W0MdyATyLPrCwYBrDNOcDIcI5byoFj359f0g/fXYo/XFZHv1h0QZ6Y/FG7UPQWbLRRe/Nz7bSc+Pm0YvTltHwJZscHiirHib4v7FkI/1+6lLBD3z/sMjNzwQP2eZNBPqDP/manv5oFv3x822OXDo8hP4WS/2J/BLZJ8gPmbuWfv3BVMFXtgF9tlnw/cNig/0n+G+ix96blqC/aIOr74LKyPJx/eGLt9KrM1fQf/zP/4XWrFljfJz7zZeysjIRhTyMeXXxolwaYL4AAyxR8HmYKaKdw8qCXHwwP1OyMp2TJ1uovLyS+iDys7owHsybTV/r8uWLNGDATfT4n8fTJw2XaFpNF02vPa1/gE5dp0NnWm0HTa8/Q39aE6O/bN7rXAcvlaea120H+Px5TQXNqDtDM+q6XTx1aav1p9R00diCRvrjsnyaXt/tkkctl00eelB1oZ5PKD1Bwz/fJuRimkK/ir75etB0RnwMTK7upGGLt9GUqk5Xe4LSVeuJNsf5zKzrpjE7DtN/+t4/EdzDKH7yZVNHFKwIuyfA1Y3ihzWsffsORMGK2to6xMsLAVhYjMSPgQsp5/Vbc0WQuHKFqH//fjRo5DgxASaUttCEslaaWNaifQhasVM0IXaKJsZaaUplO41cVUzvra+hyRVtLvooI8qVtTipThtA/731VTRyZYHgC/6CXqzVCH21bZPL2+ijvAM0/POtNLW6wwj98dBZXBde3YwrbKahi9YLHTr34nKJ81IDfRfvD/ThkPkbhEzcP6rsgfPcXoy32Ckhy4eb9grAys3doD+801DAPMJbQkw4/MzNqwRjlSbeVjc2NhrlBfrMQ0150Z2vJVpkPue8JZw3bx7ho73wfpK2sLD659CgUWNoZu0ZMUkmlbeS7pEY3CcFrYllJyVgrSxyAMuPByaA3/Vsr0nAqqGRK4skYCkAPKn8lDYPnqiiXWWt9NG2/fTGZ3k0pUoCY7bt9Svv4lHOD5GTJAFrk5BLrce641S9l20e/YUD/Th0gQQs0MC1bGklK8/ycXv/unkP/cM/RmdhJQBLzoWrVy/Hp5v5eSc/54lqP6wj1NAQzec8APzKyrhLyBZWeKBFdOXSZcrJuVEA1rS6bsITVR1IQfMJwIrTi7X0ACyVdo/yCsCo5TLN+wIWW1matNEGtb3g9bft0sKC65RpG4OUw+QfX3SUhizemLBSIRcsFkN9p7ZLAtZGKVOM+5LBU2+seHX44dY9cQsrN8wh79D2focV/8eQY7U4BQNm2MJByhYWXwtIskc1P3p4c8cuofe+97wHwSwvOBYW1rDwTU/YP1hYOTlxC6v+LE0wMJldA16hJ1xCxcJSy5nOg9f7G2ppxIoSmlJpZoIla+Oksjb6W/7BuIXVThN5YiuyJ6sb5Dq7hJCR68ONVwGAr+umErCkhaVLy1tfWmwS9AD6f91ybQErzLmm/vnZNGh4280uoXo9LJ7XALBgYUnAwuK0d1CZPI8SsHwtrJAABBNPWlhYnE6AiEndqbQkYG3s4eqqZUzlwwQstY3fJcBSgSSMvB9ghcEHNC1gGQIVC1h67hqDiQUsM1NdtbDMUExOxQKWIRCxFpYZELEWVvLJms0d7xpWNnWzLWsBK1uNJSmPdTLrEuoBiXUJ9fQHa866hEkmaIDL1sKyFlbKtT0LWBaw0uGKtbDSaSjD+9bC0p9sFrD0dWgtrAwnbAbFrIVlLSxrYcW/vOfFeNOpBawMkCjDIhawLGBZwLKAlSFc+BezLqG/XrK+al1CfXfGuoT6OrQWVtZTN2kFa2FZC8taWNbCSgoQmdywFlYmWsqgjLWw9K0Da2Hp69BaWBlM1gyLWAvLWljWwrIWVoZw4V/MWlj+esn6qrWw9K0Da2Hp69BaWFlP3aQVrIVlLSxrYVkLKylAZHLDWliZaCmDMtbC0rcOrIWlr0NrYWUwWTMsYi0sa2FZC8taWBnChX+x74yFFdbGW6xWaWHdIHYc/a7sh2VmoztsIdwidvqEhTVa7Dh6bfbDAn+0hVNn/3oDD5rwtpeJ6y/exmthYWFr3/b2Tp4Koaa9HrDmzVsQ4Y6jN9Ijb4+mGXXnaELsREprIru/ZCiDMr5F8qgVJc6e7tnRys7twARAsAux42hFyDuO8gZ+S7eHs4GfZwfTKLaXYVAPD7Dc/SkBq/6abpEcJmKpgGXSCPGjFaVL2NLSJvd0B2CpQSj8GmZCwbCw+g+4gR4dNZ6m13YTtvvFMbFc7xBPezz54wEtkE6u7KCRqwrpvY21NLm83eGl8lPzOm1gwAI/8BXtgGxOezTli9MCn0llp+jj/EM0XABWp7R0DOhPtDXeF9xupNjTfdjizXLHUciDMrBUyrnvoHc9+QQt9F/sJA1dtIkmxo47ukMbdOmjzSwT2i4Aa3ODEoTCHQgC49/0HCgvL6f29nYxjZg2pybmlkpjz549IsxXGPS9NOWe7vsc9rjvLePcDJhhem1tbTLM16xZn9Lhw40iNFBT01FqamoSB0IFcV4/PSp49P3BD+nng0fRR1v203trq+n93BqRIq915FbSe+uq6f11kt5fNtbTa3NzafjSbfTBhjrBB7wcfuuqRXnU0eK7tpo+2Fgn+Lw2dx2Br6C3rpLeQ5t05YKO1tVIuXIr6f0N9TRy5S56+e+rJC9DPIQe0GYc3OZ11fSnr8vppelf0V821Qt5RFvQZ0LfSlmuEyCVNKvovXW19Pspy2VfscwB6Dnt57rrKmW/iz6vpA827qa3lufTP/yXf6TFny0hTDr98S3nTDI6W7duJwAJ5pfZedXkogfaBQVFFIvFQpjDCVwAHxyxWDnt2lnsy8uUnEynrnYvlZfHqA8A69ChQwJQEDEW4IUDeSPHkcOCDqLE9u3bl37x6tv04ea99O7aKvrz2mp6d22N5sF0Euk7ubU0eO4aGrZki5gIKo931tWQOL6tFql6L0gek33o4s2C37vr6uiddWhHpZAP+SA0vXXeEW2tone+raQRKwrpxZkrhBtqij76gvWCvORfRaNWl9ALUyWIqLx6lg3eh0z3z9+W0fNTlgmQxDXIyve8+sj+HDLF5cqtpDc/20b/8b9+jxYuXEiHDx92xrw67tW87jzYtGmLCPUu6ci5Zoo+6Ehakm5+/k4R0h1zWrfdXD9ZW0tKYrRzZ4GLP9cxmYJ/dXWtAMg+s2fPFWGtYXrBNeSDzTtTKVzCG26Qi+7Tak7TpNIT0vwvPSHyOA96wI1AlOJJpccFjSkVrTTyy0LxZIUbhXt8MA9ZPjhPpoPYgwCtkV8Vy6g5JYm2TCiR7XHKasgoaCAu4fYGeuOzrQQZTcgAVwyHbKNsO+tqbEETDVuIIBSSF19HOtGRU0+HDs2SkzR0/nqaUCrbwtd1dSdczLjeJ8dOCLeWo+asW4+x52gAACAASURBVLeOEJLTb8zjmomxDzoIsY4gCuDFNE3RZ3qcYg0LVomfTFxGJ1XbDSDZu+eAr0xqOR1+XLfllBL5GWAS9k++JcyhR0Z+LCI/izdMJuL3xWmoYcOwboXApu/mVidi6hl4k+W3eO+sYSGQakWH+fBl/Jo/LufovIP0xufyLaEqs1/bdK85i+4V7UIuhx/agrUrgzoFUA1dsFEAlkm6/CZTrL/FWmlyRQshkGoiVL17DSuMeSADqbaFQboHzegX3d2BVAEwJn9M75pHzeG3Q0YHZ3wCXZsgFByqXn6CALkwCY3JF5NRsvFZA1yaUAKpet8SFiBUvQzzFWZ/QUfjBWB54hJ62qOjS26/WHTvhXEJeWKrgGUSOPxoRfmW8JoDls7gS1f32gBWz1D16dqZ7X287bJxCd2fKWSrw94KWAwoFrBYE5opu4SDRo2RLqFBd8I7aC1g6U1q1qfjEiqRn/me6TTa77C+G5GfNads2urWwjIEYhawLGAlA1RrYaXFoYwLWMCygJVyzcu6hPpAbAErYzxKW9AClgUsC1j8VtTQWPBaWhaw0uJQxgUsYBkapNYl1LdEMNHtGlbGczdlQRuqPqV6Mrpp3xIaAkc8sfHnZ3z3BaD0PtFNnluXUB+IrYWVET5kVMhaWIZAxFpY+hPbWlgZzdmMClkLKyM1pSxkLSxD4GgtLDPgaD9rSDlfM75pv8PKWFWpC9rvsPQntnUJ9XVoXcLU8zSbu9YlNGT1WJdQf2JblzCbqZu6rHUJU+snk7vWJTQEjtYlNAOO1iXMZNqmL2NdwvQ6yqiEdQn1J7Z1CfV1aF3CjKZrRoWsS2jI6rEuof7Eti5hRnM2o0LWJcxITSkLWZfQEDhal9AMOFqXMOV8zfimdQkzVlXqgtYl1J/Y1iXU16F1CVPP02zufgdcwhuduITO7pUGLB08neHCYEIjvRYuIfZax46j4O8cBjegY/nU/bBYXoefylszD9qImiM38EuEL2Ndm+Y5obSFhi5wb+AXBi/sRstbJOfm5mYzPwOXhUvY1tbhiijDG+4FJpqkYpgWlrfNUQIWwnxBj33mzp0felxCbJp6+fJFysnJoUdHJvbDEhMOk1rjmFSGEFFMQ+YBWCNWltD7G2rlFsnx+yjLh5hwTj2un32quoQypNgppT3Z00vI0rMu9IUtkod/vlXEJXTL3rN8Klp8T9AAuMVahG7E9TjY4b+EwxZvEg8A7isuj3Nj/OP94AUsI32EBxnCkwn52mhyZQt9uPVa7ofFWzJzmgR5Al7evXuv2NM9YPWsqkUJWFjDElFzogAsaEF1CWfWnpF7hBsIpoqnMKy1CWUIzHpS5BE0Af/tw3/8ACgY+Py0Hh87RTj4XNdSYMASFlZlu6CNdkwsR1v0g8VyW9FegASCUCAu4dTqNiGrbvu5PuirvHCdLaypVdirXsoiygh9J3TKNIKkou/i/QFrDlslO+0woD/IxX2N4L14mH20pV7EJczN3ZDVBA1auLKyOtLIz83NzUGbmlU9P8DyWmFZEUxRuLWlM0IL6+pVCVj9+8lAqvVnROh1DhAQZKD3qCOe0vKpn8olhFXgWAmwzjRdJwDW+xuqCZGmJ1e20xS0QzzV45afJv2EFYM93U/Ft0jeSlNquqQlZ4I+aHgtrFgLjSuQLuFkBE6Nu9vcHhGg1ID+HEutTLqETn+gPXGezrUAsgrrypGvjSALXML//N/+iaJyCWEZdHR0pZiO5m7BJUTUnCh+foAVFl8EUkX0IZdLyOjIqUnmCPszYMBNNOjt8SJUvRio5adEpGRESw56iEGtTCg8sSdXd9KoFQX03vo6x52R5VqlVeJEZQ7Ol9sLcASfkSsLaGq1jJojZKuQFhGXC5qKtT60t+KUmGzCJVyaT9OqEfnZjP7QXmmlSpAQuiprIYT5+sPiDYIXtwNygK+QUaPfVH0I/qUn6fWF8ag58f4xKZ9ob8UpMR4+3NKgRM0xOcr9aVVUVIk1LNxNzK1wXMIw17C80gGw9u5NRH52y6fK6q2Z/TnCfFVWlkvAApjwL6FQvmImvXTpEuX070ePjBoXD1Wvrj0FW38R6y0+61DSwioQYb7E5FPKOBaWalEo95PRTHYd9MX2Ml8ViskwuRRrWK0kU3NysaWAqDkyLmGH8TUkYR0qegFgDVm4QawBJSyrRL9x+WS6yeQ69wfctiHz19O40lPGdcftQHsBgh9u3i0Aa+3atWYGdxoqMlR9pwJWaSpo3A4DsJJhgohL6AEsbnqyOnw/21SGqq+iPrP+PkdEiEXI7rAOIDEi7F533XWU838foMffmSTiEz48YrRIEatQ53h45Fjx9vFhpjNqHN33uzfp54PfFtd1aKeri6Aa//bqKLrv92/SoJHjCG1JVyeb+y4djRpH9w99h+59bpiwVF33WHbNVKX5q+F/obueGUyPjBrjyAQdi8NU38XpPPzWGLr7N4PpVyPGmO+zEbJPZNvH0i+HvEP/4R/+gRYv/iy0Ma/OJRH5uWaPwwvzAYdaxkQeNHfs2CVC1YNeGDzUdpYUy1D16rWw+NZU75YuYRSAxUK88PxzdP9Dv6Inf/s7euLZ5+nXz7wgUuT1j98maDz3Av38/ofo/kcepSeeM8nDv53//vAg+sX9D8X5K+0wIFdCR5Lurx5/gu77+b+HwsvbB489+Rv62b/90tHrr5/zl99bL8j548/+VvB6/BnIKcdHEDo96jznpvXUsy/QY795ju66817aunW7cdDwTl6cewGL54NfWd1rCFUfi8VClwtgCMDauaModF7QSV3dbiori+izBjb/0HHbt2+n0tJSoVSkYRzosJUrV9KGDZtCoe9t8/r16wU/8FXvec/Ve9nmS0pKBO28vDz67LOloeqP21ZYWEiLFn8WCS/wXLhwsUt/3A4TqbcvPl+6jE6fPs1DM9TU/jVHX72R/zUHTa6urqWuLvm2xLSP61XJ/v376fjxk97LoZyDz4EDBxzaJmXz0jpz5ozQo8MsxAzWHWNlFSFycJOOxcqdC165nRsGMqBdGiunCxcuGKCWnoQFrPQ6SlfimgCWfFvSlq5tRu7v2bOHmpqOGqGVjgj4gF8Uv46ODuHLhzmhWY5z585RUXEpn4aaQp7CwuJQeajEIZcFLFUj2efhFjY07M++YoAakQMWBmRVVQ21tLQEaG72VfDFb7SA1ZB9IwPUaG9vJ9USCUAi4ypnz551ARaDJKcZE8qgIGgWFBRF8iYNzSkoLLaAlUG/pCrSqwELguOLX7yejOIHwGpuPhYFKwGMeJ0cxY8trLB4ATgYkM6fP+8CLObJ9/ncRAqabGGFRZ/pCl5FJXTx4kUTTU9Lw7qEaVWUtsA1sbAAWFFZWPX1UbuEbsDiyZG2J7IoAJoArLAtLG57lC4h1ADAYt5ZqCVQ0cKiEmthBdJcotJ3wsJqbW1NSBxiLlKXsPE4RWlh4fVuFBM7SsCCPFEDlrWw9CagBSw9/blqR+oSArB2R7P4CAvrWgKWCpRq3qX8ACdhApZfO62FFaCTPFUsYHkUonMaqYUl3hK6XUKdtqeqy4CVqoype73dwrJvCfVGigUsPf25alvAcqkj0IkFrEBq61HJLrr3UEnWFyJfdEcLsejeK9ewrIWV9QD0VgjTJfTywrl1Cf20kt01a2Flp6+Upa2FlVI9Gd20FlZGakpbyFpYaVWUtoC1sNKqKPMC8kt3u4aVucZ6lrQWVk+dBLkSxvYyydphLaxkmglw3VpYAZTmqWItLI9CAp5aCyug4pRq1sJSlKGbtRaWrgbl7pRRf4dl3xLq9Zu1sPT056ptLSyXOgKdWAsrkNp6VLIWVg+VZH3BWlhZqyx5hd5qYXn//JxcA/p3sIYV5Z+f7VtC/T6zFpa+Dh0KUVtY4BfFr7d/OKrGFwhTnxaw9LVrAUtfhw6FqAEr6v8SOoKGmLEuoRnl9kaXEBbxdwKwotxepjfuh9XbLSxMhCh+UVtYUcYlbGpqCkWF3r7B/Oq1G/hBg/ZLd/1xZAFLX4egEDVgtbd3mml4Gir2O6w0CsrmdhiA5UV9bk/ULqFdw2LNB0vRj735s4a2to5gismylhz34VhY3qZ8J1zC3vhfQuxs2hvXsJLtOOoduCbOAVhFRSWR7POF9kZpYVVWVkYaqj4sl9Dbzwi/1atdQkTNwZ7kUfwQQvvYsRNRsBJ8ouo4RB1CMA/8klmXOkKrNPFhZZRBKEpKYi6Z1LboyORXt7gkRpcvX/a7ZfxadXU1dXV1G6frR3DfvgN09Gi4wVe4X44ePR49YM2ZM0/sbY3XyWEfu3YVUkNDAx07dsz4cfz4cYcm8jt37iQ82cLg5aUJPviGCHy5HUePhyMjgHHz5s1CLublbY+p8yNHDlHu+o2R6BCTLDd3g5hsptrvpaP2ybrcDdTc3By6bMePHhMBW8Ma914ZMcd43JsYH6lolJdXUm1trXjIADsAZGFhSEtLG+Fta59Zsz6lQ4cO0eHDjaEff/zjCHr++edp8GtD6NXBr4sDebPHMEH3iSeeoGee/a1h2v5tBZ8nn3xS4TVMyfvXCSLza68Ppd/9/iV6/PEnQqHvbdOLL79Ejzz6ML36+hB67bX48fpQwRtt8ZbXOh/8Oj0y6DF65dXXzNL1jC/IgXYOGvQwvfzqK6HyYn089uvHRb8Nfv01Mq039A3zeW3wMHry6afomeeeda7xPb00MZ5fHZzo96effoZGjx4jPm9g/Dh06EgoOIJQ9Yhl0Aeh6sGssRFHczzlc7PpDTfcQP98811073PD6J7fvGL2eFrS++lvXqV7n32NbnngCbr9kWfpnmdeNcvH0+6fPjuYfvzwb+jm+58g8JZyvSzTeJtMynrHYy/Qzb94jH4KuQzQv/vpeFuFXGr+FfrJr39PA/71EYKMgpcoizLucvryvUxoB3jd/fRLif5ytc3AeIG+cDzzKt30b48KnvptT90ujMUbf/E4od/AK6FvKbMZ/rI/0E+3PvAU/fjhZ8QcMEM7rrOn421H+tTL9LPfDqX/cX0O/fKXv3RhBtbPJJaYxQ4Zqr6M+sydO5+uXg3fl8d6wYABA+iBYe/RuKKj9FHeARqdd5D+tv2A1jE67xDh+Nt2pnWQRu84TH9YtIlGflVIY/JxT49Hqvpjdhymt74qFvzAV5Y9aES2HrTyD9K7a6to8Oxv6OOdR4zKhb6Qekzo6i+b6umVWatp9A5VhwedvvOWT6WnZPfAF2MB91+ZuZL+lrdP5E2MDcEzP0Ef56D7cf4hemnmSvpw6x6jOvSTEWPi9flr6d1vqwRvKReP1YSu/epmdk3SEvMA437JFhrx5U6Flwke0JscAx/H5+yE4mP0o0eeowceeMBvKc34NbxlhavbZ968BXTp0hXjDJggL9DBt83JyaFH/zSOZtSfp8kVbTS5oiWeIq9xlEs6k8pbaVJFO02t7qBRq2P0wcbdNKWq3U27XIOPTxsnVbXTBxvrBL9pNV0OL7RFSyYfXlMq2+nj/CP0x2X5pPIyxWdS+SlXmyeUnKRhn20WvFieSWXm5UL7QX/Y4s0inVzOfWZofMTpT6nokPSrO+gPn2+hCSXHXfKa0qNKZ1rNaXrzizzCRJ9a1UGTyuLjr7yNTOhSjPn4WMOYePvrMvpgfb3kZXgMTorPWfCcufeisFYffPBBnuoixXznw3VD88RZw4KFBeuHgYUoDPC6IngAsB4Z+THNqOmmiWUtRg8ocWLZSUETA2bUigJ6N7eaJpe3GeXjbTd4vbO+WvDDhBD3AZzxw1te5xw0P9q2n4Z/vo2m1HQal0vqMNEv4wqbaeiijQSg5HZPKGshHHxuKp0QO0VDF+YSUqZpig/oQDamhz4btmi9sPSZV1gpdDd86XbhAUyMyXEBXl5dB+UPAGSdTa5spz+tKqH31lW7+iwoba7namsM86yFptd2011PvUhewNLEpaTV5W4NcZcw7Ne7+LMFeACwBo0aQzPrzwglTyg1MPChwLgSRcfFWkRnjVxZRO+trxFPUFZ8GCkAEXxGrCjpMUgmlMnONcI3PthHbz9Ab362TViOJujyYOd0YizRJ+MLj0nAqmiXOo7r2QRfLw3wH7pgA41nwAqDV0yCFgALQDy+qNkBR297TJ1PdQDrgLConLFqYuzj4VF6UswlANeUinYauapYAhb3maGHizM+4vSm15+hu556KWLAqpBrWGEDFmDz8uWL1H+ABKwZdWfMDhRlkmGg4akWGWBVSMACP7ZE5BPppAOkOoNffbohD8ASFlZVwurRoZ+qbg8Ly6PnVHWD3Bsyf71jLWCCeCdJEJpMg1PQSADWUbPj0AccEhbWAWlVhQHEcb5wOR3AUqziIHpLVQfjEHMYgPXQQw8ltYpM3oh8PyzVwjIOWJ6Bcq0BK1Vn69zDQMFC7DUDLI+edWTx1gWgwMJSgcVbxtT5NQWsEHUoxj1bWCECFvrhO2BhJVxCC1gJtyubSWgBK5jevDq2gKWvRwtYBp881sLSH5CY5D1cQoN95AURa2Hp95m1sAw6odYl1B+Q1sLS1yGA0lpY+nq0FpbBp7e1sPQHpLWwzOgQY1F+1hBfdDc4zr1WqrWwrIWV9i0Sntb4rEF9S+gdSKbOrYVlBkSshaWvR2thGXzyWAtLf0BaC8uMDq2FZcbqsZ81GAJIa2GZmdh20V1fj9YlNAOOgopddNcfkNYl1NchLEfrEurr0bqEhiweDEjrEuoPSOsSmtGhdQnNWD3WJTQEkNYlNDOxrUuor0frEpoBR+sSGgJH6xLqT2rrEprRoXUJDU1q6xKaGZDWJTSjR+sSmrF6rEtoCCCtS2hmYluXUF+P1iU0A47WJTQEjtYl1J/U1iU0o0PrEhqa1NYlNDMgrUtoRo/WJTRj9VxzlxDWgrq7JSaIqUOYxvEdRwUfg7S9bYRL+P6GWvnXHN4iOQR+kOP/HwtLbkXt1YXOueoSsqym+o63Rub2Rf4d1ufbxD5mQp6wNvCLtYh93MPawM/bF9Pqz9CdEe446gSh4D3dGQcTe7vzFTMpfzj66KjxYrdCHjxhpCpgYXCGwYNpyjWsOue/hDzZ+L6pFNtJI2jHX7GB39LtxrZITtU+ub3MJvFdG+TyTvxUdbO9pwJWtnUzKa9OOPTZkIUbI9vT/Y0v8hXAMvdgFnLHARDyYdyPWhWLb5EsA25koptMy3D/o6+uqUuIiDZh/xiwBo34WGxgL5Vk4kmdoIEoJFAmNuMfsbIkyZ7uKK8eegMIgx/BLsAPfCEX2pDpIEhbDtsSi62JTyYsrKX5IQEW6wU6OSn2w0IkG0wEtMGoXKoVGqeNfdYlj0SfptWPSscvH8NW1Qkdgj7kGbZ4E40vCn+LZIyJxG4N8XGBNqGtnPq1O9NrQjbIeFIC1ooiEQpO9Fk8KIuODieVoc3xcaGMAd4iOcowXyLyMyys8+fPi3D1CPd18eLFeP4SXbp0yTnn69mmoIHjwoULIgjFIyPGEkIfjS8+ZuxAnENBr+QoTSw5LgboiK920DvfVtKE0hPG+Pi1GUEAwAex4CaXtsZ5meWJcFTgjfSjrfvoD0s2ir+XjCuJy21Ql6qMH+88TEPmbxD6xPVxJYk+c3RuiDfoDZ6zTlg93AaVH1/TSbnNAC3INWZXY6hjA21F0AmEFPto835Hf9wOHVn86gKYR60oEuNxUslJo7KhL8YVHafxpXIsIqTYT379kohLyJjgxQvvOZfLNgUunTzRRuXlldRnxvRPqLq6lmpr652jpqaO+FCvB8nX1Ui6lVU1dN1119HPXhhOb39TSm8t3yEmOVKdA0DB9Ud8WSDpriikl2esoNdmrzHCg+n7peAJPuA3YsUuems5DimT2ja+ln26S8QhRD3QQ5zA5yd9Fuelp7t0bRm+ZAs9P2ERjVhR6MiUro7O/efGLzTeX359gD6DXLB8dNqbUd2vCuj5iUtpyMJcGvmVHBto05vL843xZhnRTy/OWEGDZ38rggi/9aU5Hl5ZMYdv+uUguueeewlRmYENwAw1DYIX3jo1NTWCZlFhjEpLy6jPnDnzqLOzUxxdXd1Onq+ZTPv9sB89NPyvwuzH03v0rsOE1MQBWmN2HRG0xhY00fCl2+jtr4uda+DB903wS9A4QqNWlwh+eGKDx+idR2RqSD7Z7iM0ZucRej+3hoYuyBXujEn9JeRJ9Mdft+6j1+asobEFjUKvaAfrELL61cn2GmTA8bf8Q/Tqp1+LlGkYka/giBxnBXJsfIx0V6OQCzEemVdYKfQEsPpgfa1oR0J/R0i0RXf8x+UDH4z7N7/YQSNXF9PYXU1OXxmRjfUYn0ewUm9/9HkRqp4xoqury8GPjo4OJ8/3ddIjR5qovLxchvmKZA3r6hUZ5uvtsWLRHTH7eIFaJ2X/nGnALJ5S1SkWwfH2DmtMfC+MFMFTEfkZcQmnVnY6vNAu4/zK2pQwX500UQnYapxXeasAxSGLNon1Mj/6xmSMx28ctlCuYTm8DI0RQU+hhfWdoYvkGpbDKyRdIvRWYg1LxqkET5O6Y3oY96O+LhFrqpDRuGxKnE2x6P6kdAl5/TusF3agH+lnDRDkyiUbNYfBNWiKAegK8yUW4/VeGqRqSxRBKHiyjS896YT54mup2hboXlxfeIjJQKrhL7oDOFTAwouhQG3PYBF+SmUrjVxVSO/lVsoXJRnUyaQt8kWIO+L39PprEfk50kCqFrAyGRypyvQALEMDMhnPKACLeWNS2LiEeg8fgGNY32FxP3F6TT9rwCcHYf+czxpGjemF32HZPd15IAdNLWDpgRX0bgHLIIpZwNIfkNbC0tchJva1dAmDAnom9SxgWcBKu96AwW+j5ugDibWw9HVoAcsClgWsRRuNLuAmsxQsYFnASgU3kb4lREOsS6g/IK1LqK9D6xKa0aFddDf4xkuYxvHdGuCyJXuqm7huXUIzE8BaWPp6tC5hKhsty3vWwtIfkNbC0tehtbDM6NBaWNbCSmsJWsAyM9nsW0J9PVrAsoBlAWvBhvC2sFHGlwUsC1hpHUTrEuoPEmth6evQuoRmdGgtLOUJqLsYbhfdzQxK+9ccfT1iLKr/JdQd26nq20X3tHZT5gWshaU/+K2Fpa9Da2GZ0aG1sKyFZdew7BpW2jFgLay588VHnZnbSsFKWgtL/8lmLSx9HVoLy4wOrYVlLay0T1cLWGYmm31LqK/HXg9Yl65Evx8W7ziayozWved86b6qOLT/3PGmbwCs0XkH6Y3PtoYUNcc9kCNbdI/JaEdR7oeF3U2jiJrDi+7oN/Sf7njz1ldp8qI7ojgh7y2rc45/Ioj68U0QZ+w+S3dFFJcQG4Cm/S+hqe1Or1yVLuTly1epf//+hLiEM2vPGFWm0xExuS2x2HnxGv01RwygkHYCnVzeTh/lHaDhn8cBKyQ+rE8HsCrkdru4zuDpzXOdoKnz15zSk863WCqvoHSdEF/QVVxfbGEhCkxguhl6BBKwZFzCyeVtNKmsTUTS4bZo81fGwJSKdrGf+3vrqgl5bdqQUegtsaUzaEIGDvP14IMPBlsjyrIWAKuyslLu6Q7rx+9nCrRAGyF/cnJy6JGRHxvdwE8Gd0zE00NYL8SCQ4QSbPyPwWmk45IMUGlhVYk95LF/d4JXok2Ja24LJtPr4ukWB2NskfzGZ3k0uVrlFYxugn88Tp6QMZF3AMv1tE7cV5/uCVrB2jLeteNogocuXVlf0uOxgj4bsnADTUAYriT9aur65Eq5pzssLOzB78T48+g6KD8ObgpgAa+3VxaLPd05RmZQut56Dp+4vq5F5GcRlxBRc7Dfetg/LLrDwnr87XEikKrJwQ7lIqgFp1MqWlMEUg02obwdyOewet7bWCtCYXnNcG4Tlw2aisECwEIQiryDCQsr5MkGwELAUVgGaDv6DOBpuu9A27Gw2PUwJVs8MjIiZ7P+AViQa2xhs3ON75lOJ5e3JL7DEtYVrBbzriHaDV5iT/d11TTV9ZBJyG5CPuhyWl033fXkK+RnYZk0dBiXWlraEhbWxcuX+DqpzNS8UyBgBlbcgP7SwppZf9aZALoK5MkjrBA8wRABV0TNKUgS+dls52Hwv79eWlhTqhKuk5TLgKWgmPx4QiM0FSysKTVdoU82x8KqMuRepAChcfEgFOOFCyL1xn2rO0bU+qCJQ0SZLgrfwkJUpTe/yBPBQzBWpIUlwV9tl24eMkkLq1SEqjdpYXn7AefTd5+lO598yRewAkJEymrt7Z3kRH5mC4sBypumpJThzStXpEv46NtjCW8YJlXgSW3u4MEwqaKNJle0SF9+fQ1hPcskHy8tDAzXjqNOuKhT8TBcejImQnmdEu7tx/mHaPjn26RLKHjp0U/Io+pJ5hGhGBM7YWFJXsK1wcPBAH+mAZdmyPz1Ys1Ejg1eN9GUzxlnLB8mdouQa0xRc6hjA7rFuOQv3TEuMdnlAbm4TXoygi70yIvuWMMCX9NzDGDL40VGzekJWIwdGcJCxsXa2jokYMElPHPmjAhXj3DyCFsfxnH27Fnq378f/erNj4Qy8fQ2cSB4pJcOwscjAvOf11SIdQrvfZPnCBkOPm8tLySEqgJtuBo4TPAZXyTpCHpFR+kvm+pliKo4LxM8ktH4OO8gvTbvW5pQctyILMn44PrYoiYaPHudSPk8VXmde+iz1+fl0ugdh0KXC5b/sMWbRb+NLT5K4wp5vHJqapwcFePvrWW76E/fxESYeh0dJavL8w3gOPDx39H999/fAy9M4gho4Th27IQMVT992iwRqp5D06vhphHCXr0eJM80qjhU/e+G05++Kac/frmL3vxql0iRD3q8uXxnj7ojVxaJ0PGD56wVa0tBaWdSD+HpX5u7ToQIH7WiiNT2ADQzoZFZmR0i/PjQJZvohcmfi0X+zOoFbwM+n3h+woKkvN76qsCYfNDVs+MX0YjlkibOTegPtLwYLAAAEZZJREFUbXxzeaFoJ9NDnz03YZFw1cLWIcbEC5M+pz8s2kQIKR8WP8gGXi/O/EpEtfaOxaB8WWdcH3MW1zCHb/zFYyJUPYenD4IPmdYpKS6nsrIK6jN79tx4mPou4lDTSE0eCFENeghV/6s3PxR+PMKfc+hz3VSlJZ4ARUdFyO5Rq2MizLoffYTv9rue7bWxu5rp7a/LxOCHFcR01TZlSzNZecj2wYY6Eb9vXHFzUtmS1c/2+t+2NdDg2d+I75VYrmxpZFoe9F/9dJXQXxi6QzuYLvT42pw1NHr7PiNjIJWMcKtfX7Ce8E3gmAIZPj5V+SD3pFyNgj7WyxCbEDIGoZWqDusPZeAeDnz0BRGq3osVp0+fNoofoN/UdDSx6B56qPqrRLzoPghrWLVnCW++Ev48+/UG0rJWmladCFUP0zUUPvG1CHzKwGtYyIOXWD9w1ir0ZMJiLLcfaxXyLeG2pOHjuayJFB9WDlm4kVguEzT9aPCCMz7mVOVV8371Mr0m1zcTC914OQK54BpmSiNoualVbfTmsu00On8/TRbraXrjIVU70E8jVxfT+7k1xvos2VjGh6N3JnlLmPHCVBYFU344GsbCWdj/JURH8it3Xnz0fumudjZPEt0UHSoAK/6lu8oDeV36an3Qc4WqT/HWTa0XNI91DLz+hz5BQ7yJjQNoUJrJ6oE2f+nOeuM0WZ1sroOWHB9yITzKUPXiLWHePvEgQ5tZLk6zkcNblmkgxVgctbpEvCXkPvOWD3LOPNS6XsAKAzNUPHN91gAwCfunAtbM+jPO4Mcg0jmgRK7PeXTWiBWF8gM6z4ejXNZUCl5sYfEgAW3uXFN8sKCPgYPPGvCWEFaCKdrJ6MCtwMSGXFyGdcznplLIB8BCapKHSovzeOuJD0cByKban4wOdPfG59uEZQz+3AZOk9XL9LpKU3zpvrKI3l1b5eqzTGklK8dt5RTlAFh3P/1yZJ81pLSwwgAvBix81jCj7pzrKYOJaOKAQkEHgwQL7wCSZCYtl9Xl61hYK4scSwQ0TdFX2wdeXgtLvR8kz+3kVKWBCS0+a4iDvnrPVJ75YhIAsHDOhykeKh3Qhh5hOcLlVe+FkcdYhIWFBw34srycmuQJXqqFZYK22k7OIxUfjj71Ej3wwANhwEUPmq7PGvC3mbB+bCoCsMR/CQVgSQsrGaJncx3Kw2cMah0vYKEMH2o5E3kMQvzZFAAJvliMRHvM8TtBE2InnIGuWliCl6aFqupA6FKh57WwwI/LcKrW182zS2hOd9LSRbsSbT8hASv+52fdNqerjw9H+TssAAi+NxPtiX8QnK5+uvsJuU6JdSvxoMZ/CYVVjLGj58GItnrmD/qHd2t46KGHwoIOQZfxI3ILC6A4YMAAGjRqDM2o63YmNA9OE6kYEGUt0sJaVexYWCptLqNe08kDsLwuoUPP4F8w0G7wEhbW0u3OorvDSxlU2tfi7R5beJSGLJYuoao35NVzXX6gxf8lFF+6Q5aYIR6ePgAv6BEWVhT/JQRwuABL7SdP23T0yHKN+tr8Ghb/xQw8xN/EytuEhXVnRLs1ALkcwJo3b8E128APCtDpJG9dfhqksrC8dXTPUwKWOjgN5KEvr0uo2/5U9dkllJZjwkpNVSfoPfQdvnTnPgxKJ3m9hNUrACvi7WXQb6bHO2RVaYo1LDyo4xZWcl0E7cuEDtnC8vsvYRgmlwNYc+2Oo1qgaQEr6OB31wNQeV1C8xNO8kSfRfmWMKmFZeAhpupIPKhDBaxEn1nAMth51sJKDCx1QGebj9rCsoCl128WsAzadvyWUK5hhbSBXxz0LGDpDXwGNgtY+nrEWLQWlj6QWJfQkEVnXUL9SQ2AtC6hvh6thaUPjA4Fa2HpD8jevuhuXUK9MWIBy4Eb/YwFLL3BCCvEApa+DqFHu+iur0e76G7IRcOAtGtY+gMSerRrWPp6tGtY+sYOKNg1LEMAadew9Cc1wNGuYenr0bqEZsBRULEuof6AtC6hvg6tS2hGh9YlNGTxWJfQzIC0LqEZPVqX0IzVY11CQwBpXUIzE9u6hPp6tC6hGXC0LqEhcLQuof6kti6hGR1al9DQpLYuoZkBaV1CM3q0LqEZq8e6hIYA0rqEZia2dQn19WhdQjPgaF1CQ+BoXUL9SW1dQjM6tC6hoUltXUIzA9K6hGb0aF1CM1aPyyUMNczXVSKxzemVq2LH0cf/NJk+PXCJptWcNnpMre6iaTU4TtPM+rMiGvNftzTQ9Npuo3y87Z5Rd4Y+3NIg+IHvtJozofEDL3x9PuLLAhEEgOX1tsnUOXaaxE4DUi6lv6q6hF6nVyvXNPsT/Td8yXZCKvvSLG3ohNsLPUKuSWVtofUV98HM+vOEYK5jdjU6Y3FGjdkxKcZ4VRf9vU6O+w837yXIyG3QSaeK8XyGpteq/dFFnx64SHf/ZjA9+OD9Yn7zVsZm4Kknlfb2ThmXcM6cOSLoIcLVI5y8miJv5DjdTQiu2LdvP7rjsedp8Kwv6cVpn9OL077QPl6avkzQ4BR0X5q2nB59dxI99ddZIp+4p8+vR5unLhN8Hn13Cr08HXJ9QeBnjOdUKR/z/e2EefSrEWPo5RnLtXXHbWXa3jY/P2kJPfjmX4UOE2W53zg1pNOpS+nBNz6kF6cuNSIXy8SpS7apy4RcL0xcEgov5il0Nm05PTRqLD03Zm58bCyNjw0z+mO5Xpr6heinx96ZQk9+ON34uAf9F+NjETxfnbWC+t3z7/SLX/yCzpw5p+DEaSWvjx/nzpyls91n6OjR41ReXk59ps/4lKprdlNdfYP72LNPnNfubiDdA7Rra/bQfffdRz/odyPdds//pVvuvJduuetndKuBA7QknXh6933UN+cW6nfrHXTb3eDB938m+cbLJ+oFb8ctd99LP7ztx4LfrXff58hjgjbrRqU14Pa76LobBpDKi8vpprfc+VOn/aB108B76Pv9B9Ct97j1Bn2i79R2afO++176l345xsYEt4fbCNmQFzLe8zP6l/4D6Oa73PJyHaPp3RjzA2jAj+9RxuG9dLMzZoOPPdlOyCTH9y333EfX33SrGPfoMxNyCL05czTBC+Pvn79/PT39m2epfvdeN3bU7xGYURdPdfAD2FG/ex8VF5VRWayK+rCFhXDQ3V0yxPTpzi7C4Q1BHeRcpbN69Te0YUMuFRQVUlGBPAoLC0nnkHSKqbiwhIqKiqiooFjQ+2LZl7T66zVUWIhzeQ18UEaHn1/dr79eQ0u/WE7FhaCNtsiU2+JXJ9NroAEZUR5t37h5Ey1YsICKikocWTOl5VeO9SHoFZW4dJOXl0fz5syVvONtUHXpzuv0Y7GQbdasWY6coM1y+7U782uJ/lfpzfl0NuXn57vkzZxmdrIuWrSENm7cKPoMPHhcyHGSHS2/NjI93Fv+xZeE8ehXTucaxkdBgZw7Qo/FRbR69Wravj2furq6BVac7uqg06c7BXbIvH7IekGnq4OOHTtBFRVlAKx5hDWsq0R0BetNSOmqSHt6ktlfuQqC8V91dS21trbS1auX4/Sv8K3A6RW67LRX9aN3795NTU1He9BFGS7HaY9CWV440thMDXv2xWtdEe1Bu6BJ3d9VhQba29HRQbFYuRHaatukXtwBdc+dO0eFJWWimBwTV2TfQYdxKVUaQfIYHmLMXblChUUlom+k7oJQ61kHtNBWmUpeKFVQHKMLFy70rBDClYqKCsIaDPcly6dMDU2uGGdyrO3Zs4eampris9jE+GNMkHOW+wudduRIEzU07I/3mcQMxg5zskk8amlpIeixz9y5c0XUHDF5eYFcU33JqldW1FJ7e6sxMPTyEUqKa3TPngZqbuwJWN462udXSfDZvXtvYjZoE01OoLOzk8rKKpIXMHgHgFVcXOovl8kRCdC6epUKC0oFDBoUwZ/UlavCort4PnzAglyVlZXiQeNqjGH9MW2Me78HNd8PnMaNGXXyNjY2UkNDg0KSAZJT5VbgrKTlvCWEhYWdFPAToKWkgXkoFdV+qaysFhaWcttIFu122h6nCABpbj5mhH46Ihgge3bvT1fMyP3O9g4qj1UZoeUlwjrk6+fPn6eiYmlh8TXTKfNECjeQz03zAT11LBYUlkZuYYUhU4KmnNjiQd3cmLhsMqcaNIqFBRZ+/eZ3LUhzQKelpY0trPkOYAUhlk2dqorwAMvbDgFYjUd9Fektq3vuAix1VugS9qkPl7A8Fo6F5R1gsLCKYGHFf977fN1ECtpewDKlSr92Q66oXUKhJ1NCOX3i1v5uYWHBJTT3823yVaLDh2FhRfOgdiysqOISQn1hWVh+XQPACsU09mEmAGuPahr7FDJ0CYAVpUuoApYhEXzJ+AGWb0FDF7Fedk0Ay1D7k5GRLqFZwErGi9ewkt03ed0ClkFtWsDSV6YFLH0dgoIFLDN6FFSshaWvTGth6esQFKyFpa9Ha2Hp69ChYF1CRxWBM941rMCEMqhoLawMlJRBEWthZaCkTItYCytTTSUvZy2s5LrJ5o61sLLRln9Za2H56yXQVWthBVKbq5K1sFzqCHzCH44GJpBFRWthZaGsdEWthZVOQ+nvWwsrvY4yKWEtrEy0lLqMtbBS6yeru9bCykpdvoWtheWrlqwvWgsra5X1qGA/a+ihkuAX7GcNwXXHNe2iO2tCL7UuoZ7+XLWtS+hSR6AT6xIGUluPStYl7KGSrC9YlzBrlSWvYF3C5LrJ9I51CTPVVOpy1iVMrZ9M7lqXMBMtZVjGuoQZKipFMesSplBOFresS5iFstIVtS5hOg2lv29dwvQ6yqSEdQkz0VLqMtYlTK2frO5alzArdfkWti6hr1qyvmhdwqxV1qOCdQl7qCT4BesSBtcd17QuIWtCL7UuoZ7+XLWtS+hSR6AT6xIGUluPStYl7KGSrC9cc5cQT7mwfqAtAeuUcRZ+7d5Tb/fD0lW0cAmLShwyfnp2bmpmQNu7gZ8myZTVeytg7d2NLZKj3w8rzLGBjnS5hO5Aqup+zGo+Zf9ndLMnYJmj71VY1ICFgSJ/5mTyUypbWAjkEfYPgCX2dPcEwgBfr7512+IGLHM6TKanaAGrTAahiBsEydoUTIduXZkGrGT9jOuwsPbtjWbH0ba2DqqoEGG+Enu6B1NY5rUAWG1tbZlX0CiZLGqOBsmkVaNdw+qKcMfRC1RcXJxUbpM3JGAVGgfCZG0sLC6i8xcuJbtt9DomGo/7ZABgimEiao4pisnpXBOXcP78hSLMF4cJEkF1nKc30NvMgY4SgNWquoQmaEOhXjpEsLAQLbbnPW9Z3XOi5qPHRZgv6VAzPb928b1sUjlg+Knc2dlO5eWVcblM8eDwXRyaTLbv3LkzwsJi3rIluIefmmYjj7dsghZcwsTPW073PMEHbYfleOkSoubo0k1XH1uDl1NHR5dHZyxpuvqZ3GdaRPv2NhCi2ST6LJP6qcpI2pIexkli2aixsZkO7DuYYC5yTIsv83nQVNKBhSUiP8+cOUv4h4ibJo620zJVz3Et4NHR1inqosMQiPHgwcOCPl8PStep195JHe3dsn1oc7ydxSUxqq/f45zz9TDS3XV7qKS0jDrbuwmK7WAdBtSZq43xfhAytnfSkcNHRfBKlAEvV1lNfo4e43ROHG+lbdu2JXiwfr2pDt+4fO3t7bRlyxZCirFiUi7WFfqFaYPXyVPtxvn0aHd7J+3cUSQCNoh78fEq+o71qKM/limux9JYOeGTnh7t0OERb2dba5eYu9z2mpo6ipXJmItCr5CN+RiSjeU4eKBRPKj7IKJrTU2NOBDolPNojMwj1TkkbdAoLS0ToXoSdHFPhzbX9ba/TrhNsETM0Gc+/in4IDBEQn9cTl8+SRP0JC3EuCspiTnnpuUDPxy1tfVCd7BEqqurFdlkO3DNBG9Jp4Zqa2uFXEj5Gsusz4f7IZFCh1VVVUZkSN2+GiotLRXehVuPPEb0Ui9NBNmV455l1aOfkE32UeK8TvABP/Wa7DOzvFlGWHT/D9+16KyFcyCAAAAAAElFTkSuQmCC[/img][br][br]Do you see a pattern? What predictions can you make about future rectangles in the set if your pattern continues?
The other day you worked with converting meters, centimeters, and millimeters. Here are some more unit conversions.
Use the equation [math]F=\frac{9}{5}C+32[/math], where [math]F[/math] represents degrees Fahrenheit and [math]C[/math] represents degrees Celsius, to complete the table.[br]
Is the relationship between temperature ([math]^\circ C[/math]) and temperature ([math]^\circ F[/math]) a proportional relationship? Explain why or why not.
Use the equation [math]C=2.54n[/math], where [math]C[/math] represents the length in centimeters and [math]n[/math] represents the length in inches, to complete the table.
Is the relationship between length (in) to length (cm) a proportional relationship? Explain why or why not.
Here are some cubes with different side lengths.
[img]data:image/png;base64,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[/img][br][br]Complete the table. Then explain how the total edge length of [b][i]any [/i][/b]cube is found.
Complete the table. What is the surface area of each cube?
Explain how the surface area of [b][i]any [/i][/b]cube is found.
Complete the table. What is the volume of each cube?
Explain how the volume of [b][i]any [/i][/b]cube is found.
Which of these relationships is proportional? Refer back to the tables you completed if you need help.
[i]Explain [/i]how you know that relationship is proportional.
Write equations for the total edge length [math]E[/math], total surface area [math]A[/math], and volume [math]V[/math] of a cube with side length [math]s[/math].
A rectangular solid has a square base with side length ℓ, height 8, and volume [math]V[/math]. Is the relationship between [math]\ell[/math] and [math]V[/math] a proportional relationship?
A different rectangular solid has length [math]\ell[/math], width 10, height 5, and volume [math]V[/math]. Is the relationship between [math]\ell[/math] and [math]V[/math] a proportional relationship?
Why is the relationship between the side length and the volume proportional in one situation and not the other?
Here are six different equations.[br]Select [b]all [/b]of the equations that you predict will represent a proportional relationship.
Complete the table using the equation: y = 4+x
Complete the table using the equation: y = ˣ⁄₄
Complete the table using the equation: y = 4x
Complete the table using the equation: y = 4ˣ
Complete the table using the equation: y = ⁴⁄ₓ
Complete the table using the equation: y = x⁴
Do the results in each of the tables change your prediction from the first question? [i]Explain [/i]your reasoning.
What do the equations of the proportional relationships have in common?
Close

Information: IM 7.2.8 Lesson: Comparing Relationships with Equations