Maths-
General
Easy
Question
How do you find vertical and horizontal asymptotes of a rational function?
What are the vertical asymptotes for the graph of ![f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJQAAAAmCAYAAAAiPrKqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAA51JREFUeNrtWz1oFEEUHiSEQ4IgIkFEhCASUoQDCxERCYhIsAgHKcRCRJAgQdJZiYVNSBFE7FJYpAiIBAlBAhJCCCEIEoJYBBsrERuLK8JxBM73yDtY1529md2Z2ZnM++Djkt3Z5d28dzPvZ54QDFWMAT8CD4At4HfgK+CZiuW6DnwPbALbwD3gfVaX/9gANoD9iWt14FrFcm0C7wEH6P8R4DZdYwSIpocyXQR+ZdWEhyHgfsb1R8DZjOsv6Z4LtFg94WAQ+JD8qHHJmF0a1wWOf+NIvmu07TE8RyfFmZyxd4Dz9Pct4LojGWvAz+SsMwLBaeAEKe5mzrhPdH9PIRrsKFBFrg/A26yiMDFARiXDDIXyo478OTSmS6yWsCFzfrv5oXkHIfwwcAF4MrTJeyKJXvIwS88dR4ySY561WqyQgnEV+yLsJUDR8X8H7PN5ok6kIpTu5O0UfN+2o2XfJjCBOEmKw/nBzPkP4IPUuLPiKKOeNKC7wEVLcq3SCuUtMDr5Q/yWsHw0inrBd14BbgVuUDdIeS3iBhlKEphFXwaez3h+iebWduSp48RbBxrPz4ThjNBn3UBeY4sMixERGvRLSmMOOF3y3U8L+F+MwPEC+Czj+hot+WnolBgwe7vOUxwPllP7bzLUbYp/q+xJqJYY+oW8kGoiqcfwEFjovJBx/bCHE69aYmjzFMcDDIUPJPcOezyrWmKwYVAdphf8D1cpFM5C3paHUCkx8JYXGdBnepuzAsmq16olBnbKI8Nr4GPJPVnaQKfEME3vYUQU5ckOi2UlNnVLDJzYjAxYaqnl3N9J+Ei6JQYfSy9d36xNPxY+9mEQuNr86jHmuBaHMbrF0xC7bAZmgL1lmH9SKYtMCf3yyVyOb+YT+FC/IeB21Ih8DjCHtsmmwDCBc7QlD1n003zNrV0GPhdHCekscFdygQldJaNyCTyot+DB918kd0Rm3NyVrLkyYdrjVMGVpygGKeKtWVoRbT8XXVey6pEaNKZhx4pDYCK4XkLuqg0qygBG5UhNGZ+mqOKmyGcpI3fVBhVlV7Ltrt0iisOtAnv4+izKbdugou5K1unaLRutqSgEHdwxw3KbOqXBXckKsNm1q7sSTJLPZltuWytU9F3Jtrt2dRSHpZ19odaCVlZuGwYVbFeyKbjo2tVR3IRQy8KbkNu0QQXRlWwTrrp2dRS3RNGaC7lNG5T3Xck2UUXXrgp+k0Pro9y9nHhtZ/8vCQWKffz/6YoAAAEddEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPmY8L21pPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1uPjM8L21uPjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4yPC9tbj48L21yb3c+PG1yb3c+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtbj43PC9tbj48bWk+eDwvbWk+PG1vPis8L21vPjxtbj4xMjwvbW4+PC9tcm93PjwvbWZyYWM+PC9tYXRoPlALcmEAAAAASUVORK5CYII=)
Hint:
A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =
where p(x) and q(x) are polynomials such that q(x) ≠ 0.
Rational functions are of the form y=f(x)y = fx , where f(x)fx is a rational expression .
- If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
- If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
- If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.
The correct answer is: From the graph we can analyze that the vertical asymptote of the rational function is x = -3 and x = -4.
- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .
- Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
x2 +7x + 12 = 0
x2 + 3x + 4x + 12 = 0
x(x + 3) + 4 (x + 3) = 0
(x + 3)(x + 4)=0
x= -3 or x = -4
The vertical asymptote of the rational function is x=−3 and x=-4
This function has no x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.
![](data:image/png;base64,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)
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zS7zzP21VRp3vPqe9NfH6qeDwO0zThdDrt1zpasnWu/+M4Dk1NTQiHw+jbt6+9PjqDEh5CCCHdnll/CMaeleCkJnB9J4AbMgcQXad9b+IFWVVVu6TASlxOnjyJ+vp6NDY2IhwOo7m5GeFwGLFYDIqi2KUxiT+tKiRBEJISEFEU7QTB6/Xaf/N4PPZP6+FwOOByueBwOOB0OuF0Ou3niX879aeVtCQmL5IkwTRN+P1+O4k59QEgKXnpyN8tVpWWrusIBoNpbz/E8zyOHTuGY8eOYcqUKSn5TEp4CCGEdGvGvtXQ1ywEGisAcOC2LwU/6irws++H6cyCrmmIRCI4ceIEKisrUVFRgXA4DEVR0NTUhMbGRvtnNBoFx3EQBMFOIqxSDVEUkZWVBb/fj7y8PPj9/qSHz+eDy+WC0+lM+mld/PPz85P+drpSklSxErCsrKy0xThVYnLHgrWNrCq0zmpTwuNwOFISrK1cLlfKvmBb8Dyf9p3zVIlFkaziORwOpttSEAS4XC6m6zXVrfrPhed5uFwupjGtfYfVMWLFY7nviA4HBJ5ntl55XoAopvbkei4cxzE/PoCW0g+W+2unL1rSSZifvgiu6RgMwdXSzkSWYX76d2w/eBIfNRfjxLFy1NfXQ1EUxONxSJIEwzAgCAK8Xi9CoRDy8/MxZMgQhEIhZGdnIy8vD7m5uUkJjVVCYyVAbaXrOuLxONxud8e+YwewTDwsVoLISpf00lqyZAn8fn/Kgp6NaZqIRCLIyspitmJ1XYcsy/B6vcxa2luN2bKystIek+M4KIqCQ4cOYffu3cjKymLSndH6jl6vl9m2jEajTC/OpmkiFosxTXpM00Q0GoXb7WYS0zAMHD58GKFQCHl5eUz2nf0NPI6d4LBerkDsoHHuf+gMjgOnxuEt2w5nw0nsev99qPn5gJHmuAAkSYIgCElVMOkWi8Xsm5F0EwQBW7duRXl5Bd566y04nc7T7j+JVShfnis4qPE4nHW7cUHtVoiaBMOU7Ia1AmfgwK5leG27DybHg/8igczNzUUoFEJOTg5yc3Ph8/ng9Xrh9XqRlZUFr9cLQRCgaRqqqqpw4sSJM/YwOt3z07EaGrMsbbHaB3k8HibxEqvRWMTkeR51dXWor6/HwYMH7ddvuOGGDn8mZ7bh7DV27FimdwSapjGNZzUoY1mqxDqmYRiQJAkej4dZ8mH1BGA5doOu6+2+O+sMazuyjAmw/Z5WQ0yWJYRmzlDohePB1+8BX12W3lgAXByHOS4HikQBH0oqynWdyaisVsNT1vsOk9IBjgfHC6iuqkSkuRkDBw0Bx/OAoQOAXZKi6zo0TUM0GkVTUxOi0ah9XKmajlF5HF642o9ePhG6CXu/d/DAhyd8+MOeUEu36YTQ1noVBKFVl+tzdYfuiK64hliNoFmWuFjrkNX3tHquJXZL37JlS4c/r00JT3l5OXJycjocpD0Mw0BjYyNCoRCzDalpGpqbmxEMBpnE5DgO8XicWUyO4xCLxVBWVoaRI0cyaXAGtJxYw+Ews/UKAI2NjfB4PEzuXoGW/bW5uRler5dZMmAYBpqamuDz+dIek+M46LqOzz77DL169UJxcXHS+BxpiQngk731WL6pArNG9cJXx/dOazxwHAxJRs3yf0ApL0ev678Bz5AhMHU9vXEBNDc3QxRFeL1eZoPIhcNhOByOlMa02sEALce9yfGA0gzs+AcOrH0T9bXVmDDvWjinfRti7iDAiKO8vNwudd6xYwdqamrsC5woisjLy0N+QS8M7J2Nqxyfond0NziHp2UHMQxwDjf0ix+GVnIxOD2etDzNzc3gOC5pvJh0sUo+FEVBMBhMa6xEsViMWQNi4MtGy4ZhIBAIMGm0XFlZiWPHjmHy5Mn26z6fr8Of2aZiFKuxFgvWeAY+n49pwsNxnN3anVVMAMxi8jxvN8ZjVexqjfPAclvqus48+QBg1/2zimkYBvx+P5M7LcMwkJWVZVcNsOD1ShAdDng9HibnHlMU0eRywXA4kOXLYlZNALSUdLBs+2GaJhwOR0pjapqGyspKeDwe5BcUgNMUYOOLMLa+jsFoRv9QHIH9y6HHKlHW61qs234IO8o+w/Hjx6HrOnw+H3JyclBcXIxRo0Zh2LBh6NWrF3Jzc1saBR/dCH3t72DWHwFggPNkgR8/H87SSwHBASD5BscqdWWV8Fg9t1hdJwHYpWMsq9FYx7TOOalar206Q6f7ju508VgPmW3FZFm0zDpm4gBTLCSOPcEK6+/Y1TFZJDwcx6GgoIDp3at5ytglaY9nmjCML6o7DDbnnlMHfWMl1efXxsZGPP300/j8888hiiKuvvbruG5yMfRd78DUdWgmBymuAxEJUtm/sO5YGd6v64XevfIxffp0DB06FCUlJRgyZMgZaxK4/lMhXP8scGIHoClAqBhcYSnAcaetslJV1e6okfYSyYQB8mRZTmssKx7Q0m7IKiBIHGMnnVjvrz6fD4WFhSn7POqWfh6orq6Gw+FAfn4+eJ6HpmnYsmULotEoJkyYgFAo1NWLSLqx2tpa7Ny5E7Isg+M4jBgxAkOHDmV6c0C6r48//hgA8Pzzz6O8vByLnvsLhsb8KIk1Q45GIcktjWvVuAqHQ8TcqWMxb/a96N+vH7Ky2l4ay/nygZKvJL1mJTjWhdhqD2QlHolteNIlMeFhVZVuxQRaStesEvTE8XR6OtM0cfDgQRw8eBBbt26Fz+fD9OnT01+lRXqu9evX4/e//z3uuecejB07FoIg4M9//rN9N/b+++/j3nvvTWkWTTLLO++8gzfeeANFRUV2m56SkpKMOKmSzonH49i1axdKS0vtHqc1NTX421trcffwBnjElmRDFEX4fX6IDifyplwAbszolMRPnMLB6o6uaZpdChGNRlMS51yseLFYjEk8K2ZiL1FrRGbWjeDTpbGxEb/97W+hqip8Ph/y8vIwYsQISnjI6S1duhTPPfec3evN7/dj27ZtOH78OH71q18hLy8Pv/nNb/Dvf/8b8+fP7+rFJd2QoiiIRCJ44IEHcPHFF3f14nRbHSlFON00AiykKib3RXUSz/M4cOAAHn30Uaxfvx579u7DyL4hyIEBKDArIcd1aJoOB2+C8+UCvcem7HsAX7b7jMVi4HkeeXl59oWfddMI1lRVRWNjIwzDsIf/sEq1enrSU1NTg+LiYvziF79IWdtBSngylNWo9Te/+Q3WrFlj7/wHDx6E3+9HdnY2eJ7HmDFjcODAAaiqynQsENIzxGIxnDhxAhUVLeOo9OvXD7fddhuVCOLMs0S39SJrDdtglZqxujjrum4/OhLTaqQrSRI+/fRTfPTRR6iurkavXr0wdOhQ5OTkYOasWRh81Wxw6/+M5rJ/QY43I9hnPISZPwTXPzXTBABftimxqltzc3OTLvQ9/aJ/Lta4Q3V1dYjH4/bAgJnwvauqqlBRUYHHHnsMR44cwfz583HllVd26jMp4clQPM/jkksuQTwex+rVq5NOxjk5OXZjV1EU0dTUBE3TKOEhrUiSBACYOXMmxo4di1dffRUvvvgi7r77bqY9mbqbUyd6PN0M0235DGsyRlVVmSU8qqoCaDn22xtTFEXIsoytW7fi/fffx7Zt23Dw4EGMHj0a9913H4YNG4bFixejZPBgCHmDgCt/g1WHHsG2vRvxyINPgAv1Ssl3OHXdq6qKQCCQERf69hJFES6Xy75pzZRSrYaGBhQVFeG73/0uqqqq8L//+7/Iy8vDtGnTOvyZbUp4WA4CSDqmubkZ77zzDioqKtC3b19ceeWVCAQCrU7AhmHYs/oCLSeOrhjennRP0WgU7733Hg4dOoSCggJceeWVeOyxx+xuvtdccw2ef/55VFdXY8CAAV29uF3KKqGxHlbbkfYkPNZIyyyrXyRJskuW2hPTNE18/vnnePfdd7F582aYpokxY8Zg5syZqKioAM/zWLVqFY4ePYqbbrqp5Z84EVVGCHub3TA92Sn/LolJJstB/7objuNaDazY05O/q6++Gtdccw00TcPAgQOxYcMG/Pvf/05/wvP0008jJycHbrfbfng8nqTf3W63PRJr4sOaOdaa8bUtMqVIjqVoNIp33nkHmzZtwsSJEzF79mwEAoFW7+vVqxd27doFWZaRlZWFyspKFBQUMOtdQLq3WCyG9957D+vWrcPo0aPh8/mwf/9+fOc730Hv3r3tQevO99KdxIaysizb3aDbm7Q4HA576hdWnE5nh2KapolQKISvfe1ruOaaa+zBAT0eD3bt2oW///3v0HUdt912G3r37m1fdHkYEDkTMFPbnTmxDQ/rrv3dUSatB8MwsHjxYuTl5eHqq6+2p9Pp06dPpz63TQnP2rVr7YZQiRm1tcNZyYl1IrQSotMlRdbDmtPE6/XC4/HY85y43W6oqgpRFO0DM3E2WyqJOL3CwkK8+uqrp/1bPB6370DHjBmDd999F88//zxyc3OxYcMG3HXXXZRgEgAtsz2/8MIL9u8nT57Ehg0bsGjRIkyaNAkffPABZs6ciYKCgi5cyq6TeA7UNM2epDI3N/e8qBIuKio67euFhYWYOnUqFEVBVlYWNE1jMhFrexJMRVEgimKPKwkyTROyLMPtdp/1PG39LROqtHiex5AhQ/Dss8/CNE3U1taisrISt912W6c+t00Jz5133gmXy5U0uJJ1V2M9rDudxMfJkyft5/F43M4+E5OYUx9WAz4rMUqc+M1KiqyHNWpw4t+t5MlKttrCaoSXiRd9QRAwYcIEFBQUoKGhAcFgEHfffTdef/117N27F3fccQfGjBnT1YtJuqmcnBw88MADePPNN/Hxxx/jqquuwpw5czLyWGkrK+nRNA2apiE3N5fpTPLdlc/ns3v1sRxdvS0qKirw3HPP4c4770SvXqlpR8SKpml48sknMWPGDFx00UVdvTjMzJ49G6IoYsWKFcjNzcVPf/rTTneWaFPC85WvfOWco6wahmHPg6Jpmp0EJf4ejUbP+ZAkCZFIxJ7NtqmpCfX19fbnWJ+pfzHPDcdxcLvdcLlc9k+n02k/93q9CAQC9iMYDNrP/X4/XC6XXbzLfTHbrlXMnAlEUcRll10GVVXx+eefw+l0om/fvnjggQe6etFID1FYWIgf/vCHGXNMdJZVwmPN+UTJzpc8Hg+amprsSYO7A9M08de//hUlJSVJyc6xY8dw8uRJDBgw4LTV/5a6ujpUVlaiV69erS64VVVVqK6uRp8+fZCXlwcAOHr0KBobG+3jRRAEBINB9O3b95zLWlNTgxMnTqBv377Izc0F0FJzMnfuXLzyyisYO3Ys0xHPu9oFF1yACy64IGXJc5sSHmvep7PheR4ul6vTbUEMw0BVVRU8Hg9UVbVLiKzJ2SRJsh+xWAyRSASRSATNzc1Jz60k6XTVcIlTOlilQS6XC9nZ2Xap0alJkvWwEiUrKepOdzFno+s6IpFIVy8G6YF0XcfWrVtRWFiI4uLirl6cLpXYbsSasZ58ied5uy0J6/GFzmTTpk3Yt28f7rrrLvu1FStWYPny5fD7/dB1Hffffz/69evX6n/Xr1+Pl19+GV6vF1VVVbjtttswe/ZsAMAHH3yApUuXwu/3o66uDnfffTcmTJiAt99+G59++qldfVZWVoYpU6bg2WefPety/uc//8ELL7wAv9+PSCSCBQsWYOzYljGLpkyZgiVLlmDZsmW45ZZbUrh2urcTJ06gvLwc06dPT8nndcvuVy6Xq10zbJ/aW8KqX49Go60SosTEKBaLQZIkRKNRNDU1IRwOo7q6GrFYDNFoFIZhQBRF++FwOCAIApxOJ4LBILKzsxEKhRAKheznPp8vqZrNmnTxdHc7oigyPWHSHTrpqEwZvTUVusuFvLtKbN/ZHbz33nsYMWKEPU/X0aNHsWzZMvz0pz/FkCFD8PLLL+Ovf/0rHn744aR9vLa2Fn/7299w++23Y8KECVi7di0WL16MqVOnora2Fv/4xz/wwAMPoKSkBEuXLsWiRYvw9PjWln4AACAASURBVNNP46677oKu6xBFEQcOHMDPf/5z3HrrrWddxoaGBvztb3/DbbfdhqlTp2LVqlX461//ioULF8Lj8YDjOFx44YV48803ccMNNzCbxLc7SOU1slsmPO09YDiOs5OSRG2ZI8owDESjUdTX18Pj8SAej9slSVZ12smTJ+1HQ0MDYrEYmpqaUFtbC0VRoCiKPZGbKIp2qZHVnsjr9cLv9yMvLw/5+fnIz89HdnY2HA4HevXqBY/HA6fTST2lCOkh2tP1vLa2Fjk5OT1+eA9ZltHc3Iz8/Pw2vb87JD0nT57E9u3b8b3vfc9+bfv27ejbty+GDBkCALjooovw8ccfo6amJqnK67PPPkNhYSGGDh2K/fv3o7S0FA899BDcbjfWr1+PMWPGoE+fPti/fz9mzpyJ8ePHJ7VHNU0Tr732GqZPn45JkyaddTkPHDgAt9uN8ePHAwCmTZuGt99+G0eOHMGIESMAAKNHj8YzzzyDffv2Ydy4caleVeeFnn0EpgDP8/B4PMjJyTlrPW4iSZIQDocRDoftkqGmpib70djYiIaGBjQ2NqKqqgqyLLcaI8Eakj03Nxc5OTn2Izs7O+mn9UhNN2AOoLt0QphZv3493n33XTz00EM9PuFpbGzEwoULsWDBAjtZ6O6qq6sRiUQwcOBA+7WqqqqkdjB+vx/xeBwNDQ1JCU9tbS2qq6vx+9//HuFwGPX19ViwYAE4jkNlZSUOHz6Mxx57DOFwGNFoFPfdd1/SNi4rK8OePXvw5JNPnnM5a2pq4PV67Z5+Ho8HgiCgtrbWTnhyc3Phdrsp4emEnn0EppBVFdaW4jOr9OZMrf0TG1erqopwOIy6ujrU1tairq4O9fX1dsmRqqqor6/HkSNHIEkSTNO0xy2yGmBbVXxFRUXo06cPevfujfz8fLtNUTAYPHvDydq9ELa+icGHdsB1vBDmqMvAjbgcACU/hKRLOBzGyy+/jBtvvNG+YYlGo9i0aRN4nsfkyZM7XDVRUVGBHTt2oLi4GKNHn30iTtM0ceTIEeTn5ydNvFhVVYWysjJkZ2dj/PjxcDgcqK6uxtatW+33WG0zx48fj8LCQkybNg2LFy/Gr3/96x7Rfqm+vh6xWCypx66iKK1Kn6w2WYkURcGePXtw5513orS0FB9++CH+/Oc/Y/jw4TAMA/v378dzzz2Hfv364c0338STTz6Jp556yt6mK1euxNSpU9vUs0hRlFZj6Fg9AS1utxuBQAANDQ3tXg+kBSU8aWBVr1knuby8PAwaNCjpPfF4HDU1NRBF0W4zZN1F1NbWora2FjU1NWhoaIAkSTh+/DgOHz5szwZsJUFWG6KcnBz06tXLTogKCgrg9fnhrvscwtrHwNXsRVDXwTftgH5sPfjmGvCTbgb47tGTgpBM8+6774LneXtk2HA4jIULF4LjOGiahjVr1uDBBx9EVlZWuz5369atWLRoEQYOHIgVK1Zgzpw5+MY3vnHG92/fvh2//vWv8dhjj9klMzt27MCf/vQnDB48GIcOHcKQIUNw//33o7q6GqtXrwbQ0ruovLwc+/btw6uvvopgMIhLLrkEb7/9NjZs2IALLrigg2uma1nd5y2GYdg9exMZhoGRI0di5MiRAIDp06fjjTfeQHl5OQRBwJQpU+yGzrNnz8a7776L6upqDBw4EPX19di5cycefPDBNi2TNdO8xRo5+nxqq8MCJTxdxOohFgqFztoYVNM0NDY2oq6uzi4lqq+vt5/X1NTg888/t0d6tT5LFB0ozM/BTUUVmOgsByc6YRiAkxcgqjFw25cCJbOA7IFnjE0I6RhFUfDhhx9i7ty5djXHsmXL4PV68bOf/QymaeLhhx/GypUrcf3117f5c1VVxSuvvILrr78eF198McrLy/HLX/4SU6dORf/+/Vu9/6OPPsJTTz2FcDhsL4eiKFi8eDHmz5+Pr3zlK6ivr8e9996LXbt2YcyYMfj9738PoOWi+9BDD2HOnDkYPnw4ACA7OxulpaV4//33e0TCk5ubC4/Hg1gsZr/Wp08f7N271/69oaEBPM8jOzt56ou+ffti48aN0DQNDofDHnfJ5XKhX79+qK+vt99r9Qi21vH+/fvhdrvbXPVXWFiI5uZmxGIxeL1eNDc3Q5blpAE+ZVlGY2Oj3V2dtB8lPF2oLXOeWMO3W2M8WKwZgq0G1lZ9c1VVFaqqqlB3sgF6cy08agMUToOhajBhQlF5iBwHKXYEn77xClwDp6K4T++kXmaEkM45evQoKisr7UE9TdNEWVkZ5s6dC6Dlhmfs2LHYtGlTuxKeEydO4OTJk3Z35eLiYgSDQezcubNVwnP48GEsXboUt9xyC9555x27yubw4cMQRREjR47EJ598gkAggCeeeKLVsb969WpUVlbixz/+cdLr48aNw+LFi3Hy5Em751N3VVhYiEAggIMHD6K0tBQAMH78eCxZsgSrV6/GlClT8NZbb2HkyJHIyclBOBzG4cOHUVpaismTJ+Pvf/87/vnPf+Lyyy/HsmXLkJOTg4EDB8Lr9WLZsmVYtWoVLrjgAixZsgTFxcX2SNT79u1DcXFxq9K748ePIxKJYOjQoUmvDx06FE6nEytWrMBXv/pVLFmyBAUFBUnbtKamBvF4HMOGDUvzWstclPD0UDzP2z3AsrOzWw35bgKINdYBqx4Gf2A1NOPLWZJh6miKSnj/wzXY0/ARRB5277GCggL06dMHAwcOxMCBA+07pJ7e4JIQliorKyGKot1+Q1EUxGKxpFKEnJwcRCIRxOPxNg9e2NjYaA+oCrQkTtnZ2airq2v13vz8fDz66KNQFAUrVqywXw+Hwzhx4gSefvppBAIBHDhwAOPGjcP3v/99+z2yLOPNN9/Edddd16ozR3FxsT2ER3dPeLKzszF58mRs3rwZV111FYCWJgbf//738fzzz+O1117D0KFD8d3vfhcAcPDgQTz11FN4/PHHkZeXhx//+Md47rnn8P777yM7Oxt33XUXRFFEnz598KMf/Qgvvvgi3nzzTfTp0wd33XWXPfyIoiinHWhw7dq12LJlC5544omk1z0eD374wx/imWeewapVq1BUVIQFCxYkDWfy2WefIT8/v8c0GO+OesRVLJ3dG60J/xIf6ZbOmFZpEQcgK5QHc+Ql0I9vhiiHIXAuiAIPDgYcpXPw3auuxZGqkzhx/DgqKytRWVmJvXv3wjAMCIJgly4NGjQIAwYMQL9+/dC3b18UFRW1u90BIeeTmpqapCqOUxugWto72aPVuaItn2OV2FidISymaaKiogILFizA9OnTUVVVhXvuuQeTJk3C1KlTAQDbtm2Doij2IHuJgsFgjxrI9PLLL8ejjz6K6upqu6PJ+PHj8dRTTyEej9vj3AAtpVfPP/+8nYAOGzYMv/3tb+25rBITkIkTJ2Ls2LFQFAUejyepEbeVQJ1q2rRpZ9zmgwYNsmOd+nm6ruPjjz/G1VdffV5P3NtZ3TrhSUwG0jXYlzV3l/VglfCkOqad6CS04+E4DlzpleBhQtvwV+h1FRCzfOCHX4bAhT/AVG8Opn7x/7Is2wMwHjlyBAcOHMChQ4dQV1eHzz77DB999BEEQUAoFEIwGERhYSEGDx6MkpISe1h1v9+fVD1HA9WR85Uoikn7vyiKcLvdSUmPdbE92xQM69atw0MPPQRN0zBjxgzceOON4Dgu6aIZj8fbXRVdXFxsV/EUFhaiT58+OHDggJ3wrFu3DqNHj4bf72/1v9YI0z2l1Hfs2LEoLS3FypUr8e1vf9t+3eoNm4jjuFavCYJwxhu8043/Zv3P6TQ1NWHixIlnXNYzxdq0aRNM08Rll112xv8l59Yt91hr+ofE5+kcqtya60tVVSZdLTmOS+q23tmYVpKTOCkrgC8mY+XBj7oaRuEEHNy0FkNGjoGv3yiAT9701mStubm5GDRoEL7yla/ANE2Ew2G7XdChQ4dw8OBBHDlyBDt27MDmzZuhqir8fj/69++P/v37o6SkBCNHjkTfvn3t0al7QvdVQlKpqKgIuq7b1VgOhwMFBQU4cuQIZs6cCaClLU1hYeFZj49BgwZhwYIFMAzD7oGpaRqqq6sRCAQgSRKqq6txxRVXtHnZevfuDdM00dTUhEAgAF3XIUmSPTaNLMsoLy/HN7/5zdP+f01NDXie7zFzOnEch1tvvRXPPfdcUilPV5gwYUK7/ycej+Ojjz7CN7/5zTaPFUdOr00JT1fdqVtTRGiaZhflpqMERtM0SJIEp9PJNOFJZUye5yEIgl0VdeodhpmVj0j2MBi5Ja2SnbMtpzWH2LBhwzBr1iyYpglFUXDs2DEcOXIEhw4dsh+ff/45Vq1aBafTiYKCAgwdOtS+kxw0aBCTg7UrpkDI9JiJCTUzCaWUjEOedXiqxHVxtmXr378/eJ7H0aNH0adPHwDAFVdcgUWLFqG0tBSapmHjxo249957AQBHjhzBvn37MHfu3KRjt2/fvpg/f37SZ0+dOhUvv/wyvve972H16tXw+XwYN24cdF3HBx98gNGjRyfNeWZVp1nnzn79+mHMmDF45plncMcdd2Djxo2QJMnuPl9XV4fq6uozzpt2+PBh9OrVC7179z7nOrJ+T/yZCqduh3N9dt++ffGzn/2sx5RKJRJFEffcc0+bRuJP97HK+jyQ6nht2vqyLENVVSbVPZqm2dUrVsJz6oBQqWaaZqvi5nQzTRMulwvxeDzlJwJrzi+rdEUQBCiKjLgcgyxF4XY5OrUteZ7HgAEDMHjwYMydOxfhcBgnT57EkSNHUFZWhn379qGmpgarVq2CLMvIzc1Ffn4+xo0bZ49dkZ2dDbfbnfJEVpZle1h3FqzectakiSxjnq5IPtWsMWMURYEsy4jH42n/nhxgT9WiqmrSmCnpCcjBUJSWc42hQ1VViJoG8zTnHWuAOmu5ztSeoqioCGPHjk0ar2bixIn4xje+gRdeeAE8z+M73/mOXa105MgRvPbaa5g5c+Y522jcfPPNePHFF/HII4+gqKgI999/P9xuNyRJwgcffIBQKJSUrDgcDgwePDhpnJkFCxbg5ZdfxmOPPYbc3Fz85Cc/sXuC6rqOoUOHtuqmbX3/jRs3Yvr06Wdczng8DlmW7WNQ0zR7n7XaL3aWVfKv6zpkWW7TubunTt3DcVyrMYJOx5ps20pwU33zznEcZFmGrutwuVxpP8fyPG9P3ZR4DujMdmxTwmNNsJnuL2hNAhqJRGCaJlRVhc/nQ15eXtpP7JnANE00NzejtrYWoijC6XTaJT6SJNmzzjscnUt4TmVNkZGXl4dJkyZBVVWcOHECR44cwc6dO3Ho0CFUVlbi7bffxltvvYWCggIMHjwYw4cPR2lpKfr162f3BLPaNXWUNd4Gq+TVMAw7ZjweZxZTkiTwPM8s4ZEkyT4PsEh4lC8SEFVVEY1G0xoPHAdTlqGq8ZYbLkmGGY2eNeGxLupnS06+9rWv4ZlnnkFjY6M9r9+8efMwb968Vu8dOnQo5syZc9b2PBav14s77rij1esejwd/+MMfWr2ek5ODhx9+OOk1n8+HH/zgB6f9/P79++PRRx897d8OHjyIEydO2CVTp7JKr2OxmH0sq6pqV++l6ubGat+p6zoURWF27HVXHMfZzSOsNlbpSHis7SqKIpOEJxaL2QUglrQnPNZs4OlmZaaapsHtdiMejyM/P5/agLQRx3F2tZEsy/D5fHA6nXbCEwgE7EbH6Zabm4vS0lLMmDEDLpcLdXV12L59O3bt2oV9+/ahrKwM27Ztg9frRVFREcaNG4fS0lKUlJR0qo7dGtCR1d2cNWFsVlYWs6TcmgLF7/czianretKo3iz4fXE4nU5kZWUx6fpsyDIiHg84pwuBQADeMxwjiSU851r3U6dOxbvvvosPPvigVbXUqWRZxuTJk+25lLqrFStWYPbs2RgwYMBp/26aJjweDwKBAFwuF1wuFzweDxwOh12qmwrWxdbaFuFwOO01Ad2ZYRj2OGpWyX46qp6cTid0XWfWligajSISiaTsHNDtKjStokpVVeF2uynZ6QCv14tIJJJUXdQVMxdbPdBcLheKi4tRXFyMK664Ag0NDaioqEBZWRnKyspQWVmJt956C0uWLEFRURFKSkowbdo0jB49Gnl5eW266+1q3WFmaNK9CIKA733ve1i6dCmam5tP2+PJcurUM93RsWPHoGkavvOd73T1oiRVjVklndYoxedb71Cryjmxez05vW6V8FgXZqtXFm28jrG6raarkXd7nBqf4zh7BvixY8fCMAxUVFRg79692LlzJ7Zs2YJ///vfWLt2LQoKCjB27FiMHz8eEydObDXaNCHd3YABA3Dfffd19WKkRN++fds8NxTApsG5VXXjdrsRjUZRX1+PQCAAh8ORsvZC3ZmiKGhqakrqEUvXzTPrVglPokzfUVlIVzf+VOJ53u7SfvHFF6OhoQE7d+7Ep59+ip07d+Jf//oX1q5di9zcXIwaNcou+cnPz+/qRSfnMbqodD0robHGBPJ6vZAkCfX19fbcgqxKh63SdJZtTa0bWp/PB5fLBUEQ7BoR2j9Pr9slPO2pfmlqaoIgCOfV/E+apqGhoQG5ubltqu7rzsnOqazSn4suuggzZ85EXV0d9u7di/Xr12PHjh1Yt24d1qxZg+LiYowbNw6zZ8/G0KFDaeRRwlTimFekNavUhcVFN3E7WAmOpmloamoC0DILebrPgRzHQZIkKIrCbHZzKybQ0oTB6o1L++TZdbuEp62amprwyCOP4KabbrIn6DsfaJqGP/zhD5g3b95ph33PFBzH2fN7zZgxAw0NDSgrK8P69euxefNmLF++HCtXrkRpaSkuvPBCTJ8+Hb1794YoinTQk7RJHOfEuriSL1ndoVkmPEBLeykr+RFFEYqigOM4eDye9Pcq/KKkqa3dx1MRD/iyvas1qjdVZ51bj0143njjDeTk5Jwz2YnFYqiursbAgQPt13Rdx7Zt2xAOhzF+/PgO90BrbGzEtm3bkJWVhQkTJpx2UKu9e/fi8OHD9kVYEAQEg0GMGzcOoigiEolg27ZtAFrmd7FKq0zTxN69e3H06FEUFBRg9OjR9vD0V111FRYvXoxx48Yx6zXT1bKzszF79mzMnDkTx48fxyeffIINGzZg9+7dKCsrw5IlSzBu3DhMnDgRU6ZMoWEMSFpZDWUVRYEkSVTKiJYqlmg02mow1XRfhBOrtqzSHCsJYNF92hq6Qdd1pucdK8nrCZ06uosemfCUl5dj7dq1+OUvf3nO9y5evBhHjx7F7373OwAtyc6zzz6LAwcOIBQKYdmyZXjwwQdPO7Pt2Zw4cQK/+93vEAgE0NjYiP/85z+48847WyU9O3fuxEcffWSPfvzpp58iLy8Pr776KsLhMB577DG7V9Xy5cvxi1/8An6/Hy+//DLWrFmD0tJSHDx4EIMHD8bdd98Np9OJyZMn47XXXsM///lP/Pd//3e7lrunEwQBxcXF+K//+i9cddVV2L17Nz755BNs3rwZq1atwr/+9S+MHz8el112GSZPnnxeVXcSNqwLqyiK8Hg8aGpqsofS6Ko77MQLn9VhgaV4PI7m5mbwPN+qPQkLiaM5W8mPVc3DIuGxRrlnmXxQe53265EJz+rVqxEIBDB48OAzvicWi+GFF17ASy+9hLlz59qvb9q0Cbt378bChQvh8/nw/PPP47XXXmtX7wMAeP311zFkyBDccccdiMVi+OlPf4r169fb8+RYrrvuOlx33XUAgOrqatx3332444474Ha78ac//QklJSW4/fbbYRgG7r//fqxbtw6TJ0/G+++/j1/+8pcoKSlBQ0MDfvjDH2LLli2YPn06OI7DjBkz8M9//hPz58/vsSOIdlZWVhYmTZqESZMmoaamBh9//DE++OADbN68GVu3bsWIESNw6aWXYubMmTQHDUmJxOoLq/TAGpCtubm53YmGNVhcZ6Y8sAb727p1K6qqqjBq1CgMGTLkjMuiKEpKB620qlOcTifcbneriVNZO9PUFixjskCJTvv1uIRH13Vs2LABI0eOPOtJYsWKFaisrMStt96KY8eO2a+XlZVh8ODB9p3/1KlT8cQTT5xznIxEkiRh9+7duP322wG0NBobNmwYNm/e3CrhSfTSSy9h+PDhuOCCCxAOh3Hs2DH84Ac/QFlZGTRNw09+8hN4vV44nU48+eSTKCgoANAyKqrb7bYb4gFAaWkp/vKXv+DAgQP28PTns4KCAlx33XWYMmUKdu/ejXXr1mH79u34wx/+gOXLl+Piiy/GRRdd1KUTB5LMkNhQ1uoK7HA47JKVtg6pYY2Mbg1c2dGSCEEQsHfvXrz++uswDANTpkyxJwU9Has3UWcb9FrJnlWakjifHzXqJt1Rj0t4mpubcezYMVx55ZVnfd/cuXNxww03YMWKFaioqLBfP3nypD2ZHwD4/X6YpolIJNLmhCcajULTtKT2M7m5udi1a9cZ/+fgwYPYunUrHnnkEQBAJBJBOBzG4sWLEQwGcfz4ceTk5ODBBx+E0+lMujBv3boVDQ0NSYlNXl4eRFHEoUOHKOFJEAgEMHfuXMyZMwe7d+/GqlWrsHHjRixatAjvvfceLr/8csybN4/J6L0kcyU2ErXmUUvsYdqWRMKaPkcUxQ7PTWSNubVx40Y0NTXh2muvRWlp6VlLjVwuF5xOZ6fnQ0pM6hLXBZU8kO6qxyU80WgUDQ0N56zGsQapO7UXhaZpSQekdcJoz4FvDS9/utfPZOXKlRg5cqQ9oirHcSgvL8esWbNwyy23QFVVPPjgg1i+fDluvPFG+//27duHJ598EjfffHPShIDW9AmNjY1tXu7zgTXhrMvlwpgxYzBmzBgcPnwYK1euxOrVq7Fo0SKsXr0aV111FWbNmkVtfEinJPYSAto3DIRpmnA4HPagcR1JPgRBwIEDB7Bx40YUFhZizpw58Hg8Z51mwZp0NpVz6qVzZnRCUqXHlTlaxaaJli5dihkzZmDmzJlYuHDhWf8/KysLqqrav2uaZt9hncnRo0fx9a9/HTNmzMBNN92Eurq6VrOrq6p6xjEYJEnCtm3bMGPGjKTXQ6EQJk+eDKBljpLRo0dj79699t+3bNmChx56CNdffz2uueaapP+1krTO1P2fLwYOHIgf/OAHePTRR3H55ZejpqYGf/zjH/HQQw9hzZo19ngWhLRH4ng8ic9ZPQRBgK7r+Pjjj1FbW4tp06Zh2LBhSY12WT1OXQ+EdEc97mrp9/uRl5eXVLJRWlqK22+/HRzHYciQIWf9/759++Lzzz+3fz927Bi8Xu9Zq7NCoRBuvPFGRKNRhEIhFBUVwefzoaKiAiNGjADQ0nPsTD29ysvLIctyUtWTNYlnfX29/VpiO6L169fjiSeewPe///2kRteJ75UkiaZbaCOO4zBs2DCUlJTg0ksvxbJly7Bx40YsXLgQEyZMwPz58zF27Fg6WZMO6eh+09nGtZWVlVi/fj2ys7MxZ86cNn0G6wa9hHQXPS7h8fl8GDx4MPbt22e/Nnz4cAwfPvy077eqOCwzZszAmjVr8OGHH2LQoEF46623cNlll8HpdKKxsREbN27EjBkzkJWVZf9PMBi0e1pZLr74YqxYsQIDBw7EsWPHcPjwYdxyyy0AgN27d6O+vt4u0Tlw4AC8Xm/SeD8ejweXXHIJXnrpJRQUFKChoQFbt27Fgw8+iIaGBjzyyCOYMWMGiouLsWPHDgBAv3797JnOjx8/Do7jMHTo0M6szvMOz/MYPXo0RowYgS1btuDtt9/G5s2bsWfPHlx++eW49tpradoK0mNs374dFRUV+OpXv4qSkpKuXhxCurUel/AAwLx58/DKK6+0qWdVdnZ2UslLnz59cMcdd+Cll15CLBbDnDlzcPnllwNoGUhw8eLFGDp0aNJAhadz2WWXIRKJ4IknnoDH48GCBQvsODt27MDu3bvthMfhcGDMmDGtuoHecMMN4Hkef/zjHyGKIm699VaMGjUKW7ZsgdPpxM6dO7F7924YhgGe53H33XdjwoQJAFq61w8ZMgT9+vVr38ojAFoGJps6dSpGjRqFNWvWYNmyZXjrrbewefNm3HDDDZg1axacTmdXLyYhZxQOh/F///d/8Pv9mD59OlVvE3IOPfIIufDCC/H3v/8dW7duxaxZs8763nnz5mHevHlJr40dOxaPP/54q/cWFhbiiiuuSCrdOROO43DDDTfghhtuaPW3b3zjG0m/X3LJJbjkkktavY/n+dN+xsSJE/GPf/zjjLGj0Sg2bdqEW265hYqkOykrKwtf+9rXMHHiRCxfvhwffPABHn/8cWzYsAHz58+nEjTSbe3evRv79+/HiBEjMHLkyK5eHEK6vR7XaBloacdz7bXXYsWKFUkNkDsrEolg+PDh9vg33dXq1avRq1cvXHjhhV29KBmjqKgI//M//4Nf/epXmDRpEj755BP8/Oc/x9KlSyHLclcvHiFJVFXFf/7zH8iyjAsuuICmtiCkDXpkwgO0VCn169cvqQFyZ+Xl5WHq1Kkp+7x0iMVi2LNnD7797W9TlUuK8TyPMWPG4Gc/+5ndCP4vf/kLFi5ciIMHD3b14hFiO3r0KLZs2YL+/ftj7NixXb04hPQI3a5Kq61VNE6nE3fddVfa50npbrxeLx544AGqykojj8eD6667DsOHD8cLL7yAdevW4cCBA/jWt76FefPm0cSkpEsZhoFPP/0UJ0+exOzZs1FUVNTVi0RIj9AtS3jaczE/Hy/8tH7YKC0txf/7f/8P119/PZqamvD000/j6aefxsmTJ5PfyPEtD0IYaG5uxubNm+H3+zFt2rSuXhxCeoxuV8IDJM9VQzqG1mFq5OTk4Pbbb8fIkSPxyiuvYOXKlaivr8dtt93W0pPPNABNBgwHuunhRDLM/v37UVFRgWHDhqF///5dvTiE9Bjd6gydOOOs2+11XgAAIABJREFUNT8NaT9d11uNgEo6ThAEzJo1CyUlJfjb3/6GtWvXorq2Dguuno4x/EG4G6vAubwwRl4BftglAJWqkTQxTRM7d+5EOBzGuHHj2jz/HyGkmyU8wJclE06nE4qiIB6PU5uJdrJmYE6cyI+qtjqvqKgIP/rRj1BQWISDa1+D8K8PIYU4OJwumDChV2wConXgJ3yLkh6SFg0NDfjss89QUFBAkwYT0k7dNuGxJrarr6+H3+8/52ShqYjLugF0qmPquo5IJAJN05CVlWUnPSR1PB4Pbp7/dTQ6NoHbtQsRmYfL5OH1esHJYRh7VoIbMgdckBqSktTbt28fKioqMGbMGHsiYkJI23SrhCexNEIQBLjdbnAch+bmZjQ2NqYtITEMA/F4HE6nk1lJiGEYUFUVLpcrJTETE8XEZIdKdlLPaUjIE6KQfT7EZBWKosA0TWR53BDlMKBGu3oRSQYyDANbt26FqqqYNGlS2m8CCck0bUp4WF40rVmArWosnufhcrlgGIY9Q3iqaZqG5uZm+Hw+JiUiHMchHo/DMIyUxTx1FmVBEFolPKxnMu6KmZOZxBTdMF1+OEQRPp8TsVgMqqrC1OMIFTrBOdN/IWK5bhPb1jHTBVWxdihGIdu7XquqqrBr1y7k5+d3qjqrK84DiT9ZxmQpI891XRwz1fHalPBEIhG43W4mVT6GYSAajcLhcNgNl03TtBswpyvh0XUdmqYxS3g0TbMfnY3JcRx0XU9q8J14MuU4DrFYDLFYDNFoFKIonnE9Jr7e2XWtaRrC4bCdiLHQ3NwMTdNSevd7atIIzgH0ngTx8AbwmgS32w0YOmRJwpr9YfQ+UouS4YXQtHjKliGRdYxwHJf29m3WvmrtO5Ikpb0zAQdAliTomgZZlhGNprnEjONgSBIURYWmaZBiEiDLMHU9rWFN00w6Hs92vPE8j127duHQoUOYMWMGQqEQYrFYh47RSCQCp9OZthvIRKIoQlEU6LqOaDQKXdeZXEcikYh9Hkx3PI7jIEkSFEVhOp9ZLBaDrusQBIHJOuU4DtFoFJqmMYnJ87x9zkk8B7Rl6qczadPWOXXG8XQ6U4KTzruExNIRVglPOmJa68Y6eSauM13XYRgGdF0/40nHeu3Udd/RHdtKIlVVZZbwxONxiKLY6f2kVZID2N+B43lg5DUQRCf4sjfAN5QjUDgAu5py8adPwsitehZ3/OD7KC0tRTye+qQncTume71yHGeXrlpxWSQ8hmHABGAYJvQ0Jx7gOBi6AdNsOffoxhfHCIOEx7pROVsiwHEcVFXFzp07IQgChg8fDpfL1eF9K3FbskgGrPPR2c49qWZdR1h9R+u7pX1fTZAYk1XCk3gdSXdMKw9I5XptU8ITCAQQCARSEvBcrC8YDAaZXSQ1TYMoisxjCoKAUCjEJKYoivD5fAgEAmfsypqYbFrPz3XneTZWsuPxeJitV0VR4Ha7U1LCc2qJWWJXfwDA5P+CMXwepNoKOEJ5GMv7cWnOm1ixfBmef/553HnnnRg1alSnl+NU1rbx+/1M7iitqle/3w+fz5f2eADgzZIhiiK8Xg+Tc4/hcCDsdsN0OODz+eDtxF1ke/A8D1EUzzkXVmNjI44ePYqcnBxMmDABHo+nU/NnOZ3OlpJJBtxuN0RRRCAQYNbuyDpOO1Ma0B4OhwOKojC7TgIt53Rd15kOTSAIAtOY1jknVeu1TWdL1r2XOnORJWd2uvWaWKpjleRZj87ezeu6jlgsxrS3WDQatRuhp0JimzJRFO22UXbik5UHA17oHjcCooDv3PLfcDsdWLJkCR5//HHce++9GD16dEqWJRHLY6SziW8Hg9qxGYcEGIVsz3o9dOgQqqqqUFJS0unJjVlvy86WFHc0Juv2LefDdbIr9p1UxqM+y8Qu1YnH45BlGZFIBPF43D5pdPRhlZoJgtCpz2nPIxgM2j3fUvEwTROqqiISiUBRFGiadkrbBxPQ44DRUuTq8Xhw880346abbkJ1dTX+9Kc/Yd++fV23cUlG2L9/P5qamjBq1ChmpRaEZJpu1S2dsJdYT6qqKmRZRnZ2NrPi7p7ANE3EYjGEw+Gkqq0z3Xk4HA5cf/31iMViWLp0KZ555hncc889GDBgAOMlJ5kgEolgz5498Pl8GDJkSFcvDiE9FpXwnMcSi5p1XYcsy/D7/ZTsnMJqC+DxeCDLclKDvTMlPU6nE9/61rdw6aWXYs+ePXj66adx7NgxlotNMkRdXR3279+PPn36UNJMSCdQwkOSGipTsnNmbrcbmqa1ue2F1+vFt7/9bVx00UXYvn07Fi1ahNraWkZLSzLFnj17EI1GMXjwYOTk5HT14hDSY1HCc56zLtxWuxSaiuLMrHGh2tMlMxQK4dZbb8WkSZOwceNGvP7665BlOc1LSjKFpmnYuXMnDMPAqFGjumRAPUIyBV3dSNf0wunB/j97dx4dV3neD/z73mWWO4t2yZIXWcbGOMaAhR0M2CasZWlI4KQQQtMkBEjbkLYhTdOkWU6anKb9Jelp05aSnqRJ04SYhuRQEgKGJkAgBowNBEzwii0Z2ZIlS7Pembu99/eHuDeSJVkja+a945nnw5ljYY3v895l7n3mXed6vBYsWICPfvSjWL16NbZu3YqHH36YjjUpydDQEA4ePIiWlhbqv0PIPFHCQ0rGOcfu3buRy+WCLkrZWZaFV199tWK1L4sWLcLtt9+OtrY2bNmyBdu2batIHFJbBgcHMTAwgOXLl6O1tTXo4hByWqOEh5Ts2WefxTe/+c2Kz7QbBFmW8cgjj+CBBx6oWIzVq1fjfe97HyzLwn/9139h3759FYtFasOhQ4dgGAa6u7vnNdEgIYSGpZMSZbNZfP/738ctt9wy7ayXr7zyCp588slJyzDE43HccMMNpzRLpuu6ePbZZ3HWWWfN2FHz4MGDeOyxx5BMJnH11Vejqalp0u9N08T27dtx/vnnIxqN4vDhw3jooYf86fy91eWvueYaLF68GDfddBM+//nP4+KLL0ZPT8+cy1yKyy+/HAMDA7j//vvx3e9+F5/4xCeoIyqZVrFYxN69exGPx2l0FiFlQDU8pCSPP/44OOe48MILp/39xJmZZVnGs88+i/vuu++UZzx+6qmn8Dd/8zcYHR2d9vcvvvgiPv3pT8NxHAwPD+PLX/7ylBFQP/7xj/HVr34VhmEAgF8+zjkkScK+ffvwrW99C5lMBgCwdOlSrFixAj/60Y9OqcylkGUZ73nPe7Bx40bs3LkT3//+96HresXikdNXNptFX18fEolExRJwQuoJ1fCQWXHO8eijj6K3t3fG1bl7e3vR29sLADh+/DhefPFFfPazn0VLS8ucYtm2jZ/85Cf44Q9/6K8EfCLXdbFlyxZceeWV+PCHPwwA+PrXv47/+Z//wUc/+lEUCgV85zvfwcMPPwxN0/xap6VLl+JjH/uYv43PfOYzuOuuu7B69Wp/25s2bcI3vvENjIyMVKzPRCKRwPvf/34MDQ1h69atWLp0Ka6//vqKxCKnr76+PqRSKaxcuXJK7SUhZO6ohofManBwEP39/Tj33HNLev99992Hrq4ubNq0ac6xBgYG8PLLL+MTn/gElixZAtu2p7xH13WkUimcf/75/t+tWbMGv/3tbwEAr7/+Oo4ePYpPfvKTaGpqmrbP0datW3Hs2DHccMMNk/5+xYoV0HUde/bsmXPZ56K7uxsf+MAHEIvF8OMf/xi7d++uaDxy+unr60M2m8WZZ55J82MRUgaU8JBZHTlyBI7joKOjY9b3DgwM4Nlnn8XNN998SrG6urrwxS9+EStXrpw22QHgr4be39/v/11fXx+KxSJs28aaNWvwt3/7t+js7ITjOFP+fbFYxE9+8hPceOONU1b9bWxsRCwWQ19f3ymVfy7OP/98vPvd78bIyAjuv/9+pNPpisckpwfDMHDo0CEoioJly5bR/DuElAE1aZFZjY2N+f1ePLquw7ZtMMYQjUahKOOX0hNPPIGFCxfibW9726zb5Zwjn88DGO/krGnajE1mE8myjOuvvx7/+Z//6U+Y+MQTT6ClpQWu6/rbmGk02UsvvYRCoYDNmzdP+V04HEY0GhWSfDDGcN1112H37t147rnn8Mgjj+Cmm26iyR8JxsbG8MYbb6CjowNdXV1BF4eQmkB3VjIrb/Vxj2ma+MhHPoJzzjkHGzZswOOPPw5gvP/Ntm3bcPHFF5f0jXT37t3YuHEjzjvvPNxwww04duxYyWW68sor8Wd/9mfYuXMnisUibrnlFsRisZKShWeffRZr1qyZUrsDjHdsdhxH2BDghoYG3HzzzWhra8NDDz2EV155RUhcUt2Gh4cxODiIzs5OLFiwIOjiEFITqIaHzGrhwoVgjCGVSgEYXw3885//PDKZDCRJ8ofMDg8PI5vNYs2aNSVtt6enB9/73vfgOA7C4fCchmd/97vfRU9PD770pS8BAP71X/8VZ5555rSdnCcyTRNvvPHGlL47nmw2i1QqJfQhs3r1atx444341re+hS1btmDx4sVz7uxNasvBgwfBOUdPTw/C4XDQxSGkJlDCQ2bV1dWFtrY27N27F+eddx4YY1ixYsWU97355ptgjKG9vX3S3+/duxe//OUv8cEPfnBS58toNDpjR2jOOQzDmLQEw4MPPghVVXHdddehvb0d3/3udyHLMg4ePIi9e/fic5/73KRtuK4L0zQnbWN0dBQDAwNYsmTJtHG9vjtnnXXWLEelvK688krs2rUL27Ztw9atW3HLLbdQv4065TgO+vr6IEkSDUcnpIyoSYvMKhqNYtOmTXjuuedO+r5EIoFLLrlkSnOQYRh4+eWX57RsQzQaxWWXXTZp0kJd11EoFAAA1157Lf7wD/8QjzzyCEZHR/HXf/3XaGtrm7SNhoYGbNq0adI3ZEVRcNlll015r+e5557DqlWr0N3dXXJZyyEWi+Fd73oXmpub8eijj2Lv3r1C45Pqoes6jhw5AlVVsWjRIgCT128r16uS2yWkGlENDynJddddh09/+tPYt2/ftLU7wHityHQ1I21tbbjooovmNLQ2mUz6c+Z43ve+9036/8svvxyXX375jNtYuHAh7rzzzkl/19raOmW7nkwmg+3bt+OOO+4IpHZlzZo1uPLKK/HDH/4QDz30EO666y5aTqAOHTt2DMPDw+js7PQTfq9zfjl4/dQcxylrgsIYA2MMruv6PxNSTaiGh5RkyZIluPzyy3H//ffP+SbJGMPmzZurfi6RRx99FN3d3diwYUNgZbj66quxcuVK/PrXv8YLL7wQWDlIcI4dO4Zjx46hq6sLkUgEpmnCsqyqftm27f/pzWZOtT2k2lANDynZH/zBH+CBBx7AyMjIjE1C0yll/p6gGYaBbDaL2267zR9iH4SOjg68613vwje+8Q389Kc/xerVq6kDcx1xXRdHjhxBoVBAe3s7VFVFoVAoawJRLBb99eTKtU1vbTpZlv0XMD6FBCU+pFpQwkNKlkgk8KEPfSjoYlREOBz2l6kI2sUXX4ydO3fiiSeewGOPPYb3vve91DxQJwqFAg4dOoRoNIrW1lbkcjmYpgkAZUscJEkC57ysa7hNXDRYVVVEIhG4rjvrqElCRKKEh5AqEw6Hcf3112PXrl3YunUr1q1bN2O/KVJbdF3HgQMHsHjxYrztbW9DMpksaTLOufCSk0rUvJimiXQ6DV3XEYvFqHaHVBXqw0P8DoZUi1AaEcfpzDPPxCWXXILBwUH88pe/nHGZDVJbhoeHoes6fu/3fg9Lly5FKBSa9Pksx8tT7u0yxhAOh9HS0gLOOUzTpL48pKqUlPCIfhAG8fCth5jT3fAkSfLb3iVJopvTSXhV9Iqi+P0UKpUsMsZw2WWXYdGiRXj66aenLGYq8toJIiFmjIFB7L2HMQDeS0i8qce1v78fjDGsX7/+tP0CIssywuFwoEl6EMeu1p8fQcQsd7ySmrQymQwURRHyMOSc+zP4ilpTyLZt5HI5AGIuWsYYLMtCNpsVcgExxlAoFJDL5fw1orxzyTmH4ziwLAuFQgG6rk+75AIB8vk8CoUCGGNQVdXvkJnNZmFZVlmbHhhjaGpqwgUXXID7778fDz/8MDo7O6EoChzHQTqdhuM4ZW/umK4cjuMgm81C0zQkk8kZ1ygrW0yMH2vLsqDreuXXNWMMbrGIYrEIy7SQy+Vg53Jwp1l4ttyy2SwURYFhGACA/fv3I5vNVv2IxtnIsozR0VFwzlEoFGBZFjKZzJSJQCsll8tBkqSyD72fjnd/9fpaiaLrur9/Io4pYwz5fF5YTEmSkMlkkM1mJ90DGhoaTnmbJSU8kiQJTXhO7OlfSV6y4cUTkWR5oyNExWSM+XEURZl0Lr1FQb3jkM1m/U6HZJzruv6kh5qmIRQKQVEUv0bMO4/lHt0lyzIuvfRS7NixA8899xw2btyItWvXTjqPlR5RduLnQ1EUIQkPkyTgrRrIio+aYwxclsHY+OdAlsb3063wF5GJNYaqqiKXy2FoaKhmalkn3ne8n0U9Rybe70QkPIqiwLZtoSM8FUXxY4tKeLxnsoiYE0f9leu4lrSVeDwOTdPKEnA2XttvPB4XWsPjui7i8biw6jpvvgpRMRlj0DQNsVhsyrl0Xdev5SkWixgbG/Oba+bD+xYgcvVvb9KzcvL6IcTjcYTDYb9JizHmzzlS6krvc7V8+XJcddVV+M53voNf/epX6O3tRTweh2VZiMfjQm6w3v7FYjFhEyFGo3koioJIJIJYLFbxeFySEA6HwBUFUS0KTVDC77ouFEVBNBpFJpNBKpVCY2Pjaduc5XFdF9FoFPF4HKFQCLIsIxaLCfsi5d0HRD23vORKxLXq8WpfRe2jR2RM73lVruNa0pNI9DeOIKYor4eY08Xz/t/7phCJRBCPx6Gqql8TdaqviU0vlZjCfrpXOp321+Aqx4sxhlAo5Cc70yWClT6PmzdvxvLly7F9+3Z/NXWR104gywa4v1v6QHBIQFDIE49rLpfD8PAw4vH4rP82n8/j17/+tfBmFGD8gbdt2zaMjo6e9H1BLjdRDzHr9Zk1HzQsvc5NnD8DgN83RVXVed+wbNuGbduIxWLCanksy0I0Gi3LCtNe/yqvSt7rVya6415bWxuuuOIK3HPPPXjmmWewZs0aobVmRIzR0VFks1mcccYZs15f9913H3K5HC666CJBpfsdWZbx2muv4fnnn8fHP/5x4fEJOVWU8BAAvxux5f08cYbUU014JElCKBRCKBQS9oD24oVCoXlt58TRbAAmHR/R1q9fj56eHuzYsQMHDhyYcbV3cvrxmkaPHDkCAGhpaTnpNfb666/jmWeewVe+8pUZ37dz505s3boVnHNcdtll80qMXNfFQw89hOXLl2P16tUAgBtvvBGf+tSnsGPHDqxbt+6Ut02ISPQ1kfgmPtgnviZ2Iq/2V7nKe+IxCDLZAYD29nZs3rwZ6XQaTz/9NEzTPO37eZDfcRwHR44cgSzLsy7F8qMf/QhnnXUWurq6pv39E088ga9+9atYtWoVent7ce+99+Lhhx8+5bLt3LkTn//853H48GH/71paWrBu3Tps2bKl4p3YCSkXSnjIJBPnBpnuoV+PryDmoZnuvGzYsAGLFi3Cs88+i0OHDlGzVo3wOp96Cc+CBQtmfO/Q0BBefPFFbNy4ccb37N+/HzfffDNuuOEGXHvttbjpppvws5/9DM4pDLPPZDJ44IEHsHjx4imd8jds2IDXXnsN/f39c94uIUGgOyYhp4nu7m68/e1vx8jICF544YVTeoCR6sMYw9jYGMbGxqBp2kkXi92/fz8Mw8AZZ5wx43vuuOMO3HDDDf7/FwoFfxDCXP3whz/EypUrceGFF06ZSHDJkiVgjGHXrl1z3i4hQaCEh5DTyMaNG9Hc3IwdO3bg6NGjQReHlMno6CgymQw6OjoQjUZn7DfX39+PRCJR8uRrg4OD+PGPf4yrr756zjWCO3fuxIEDB/Ce97xn2marWCyGpqYm9PX1zWm7hASFEh5CTiM9PT244IIL0NfXhxdeeCHo4pAyYIxhZGQE6XR61oQnnU6Dc+7X1jiOg4GBARw8eBD9/f2ThqkfPXoUX/jCF7Bx40Zce+21Jy1DPp9HX18fDh48iOHhYaTTaTz44IO49dZbkUgkJk065/Hm1snn8/M8AoSIQaO0CDmNhEIhbNy4EU8++SSefvppvOMd7zhpEwipbt4IrePHj6NYLKK9vR2RSGTGhCcWi01qmjp27Bg+8IEPYM+ePWhpacEPfvADrF69Gvv37/eTnY985COzluOpp57C3XffjWw2i6uvvhrveMc7sH37djQ2NuL//u//8MILL+Dw4cNoaGjA+vXrAcBfNkL0xHeEnCpKeAg5zaxcuRIrV67Eb3/7W+zatQuXXHJJ0EUip4gxhmKxiCNHjiASiaCtre2kTU9LlixBPp9HJpOBpmlob2/HD37wA1iW5Y/w6u/vxxe/+EVcf/31uPnmm0sqx6WXXopf/vKX/qza6XQaXV1d/qShr732Grq7u9Ha2ur/G13XMTY2hkWLFs37OBAiAiU8hJxmNE3D+eefj9/85jd44YUXsGHDhrJMtEiCUSwWcfToUSQSCbS0tJx03qszzzwTiqLg4MGDWLBgwbTD2P/t3/4NfX19yOVy+Pa3vw3LstDd3Y1rrrkGjz32GA4dOoTbb799UmIVjUYnLRvS3NyMnp4e//+feeYZrF27dtLf9fX1wbIsrFmzphyHgZCKoz48hJyGVq1ahUWLFuE3v/kNdRo9jTHGYBgGhoaGEI/H0dbWdtKEp7OzE2vXrsUzzzwz7e8dx8F5552H6667DiMjIxgZGcHx48f9fjbRaBRHjx6d82Sil1xyyZSRYdu3b8fKlSvR3d09p20REhSq4SHkNOO6Lrq6utDb24uHHnoIL730ElasWEETEZ6mUqkUdF3HwoUL0djYOOt0A+9+97vxj//4jxgeHkZbW9uk38myjFtuuWXGf5tIJHDuuedO6YA8myuuuGLS/2cyGTz33HP44Ac/KHSFcELmg2p4CDnNeCvQX3DBBWhoaMDzzz+PsbGxoItF5shLUIeHh2HbNtrb2yct6TKTtWvX4txzz8WDDz4455jt7e24/PLLT6m8Ez388MPo7u4+6QSIhFQbSngIOQ1xztHT04NVq1bh4MGDeO2114IuEjkFruvi+PHjcBzHT3hK8aEPfQitra0oFotzitfV1YVEInEqRfU5joNYLIbbbruNahXJaYUSHkJOQ5xzJBIJbNiwAZZlYefOnZPmYCGnj+HhYViWhY6OjpITnpaWFtxwww2IRCIVLt1Usizj+uuvp9FZ5LRDCQ8hpynXdXHOOeegp6cHL730Et58882gi0TmyDRNjI6OgjGGlpaWmuoPE/T6c4SciBIeQk5Truuio6MDZ599NlKpFH7zm98EXSQyR/l8Hul0Go2NjUgmkwBQM4vCUsJDqk1tfLIIqUNe59b169dDVVW8/PLLyOVyAZeKzIWu60ilUmhubp60hINt23MeOl5NLMuCoiiQJAmSJFHiQ6oCJTyEnOa6u7vR09ODPXv24NChQ0EXh8zBxBoeL+FRVRW2bZ+2a1Tpug7TNBEKhSjZIVWldhqMCalTLS0tOPvss7Fr1y689tprWL16NT1kThOZTAb5fB5NTU1IJBKwbRuqqkLTNORyORiGgVAoVNaY3rVRiRoky7JgGAai0ShUVa2Z5jlSGyjhIaQGnH322Ugmk9ixYweuvvpqNDQ0BF0kMgsXwODIGDiT0dwyvkaVJEmQZRnhcBiSJMEwDOi6Ds552RIUXdf9GOXi9ddRFAWxWAyhUGjOkxsSUmmU8BBSA1asWIHFixfj8OHDOHDgAHp7e4MuEpkFH96P5qO/xoUtOfS0ja847vXhYYxBkiSoqgrOeVkTHs45QqEQNE0r2za9hEeWZb/fjle7Q7WNpFpQwkNIDUgkEjj//PPx2muv4ZVXXqGEp5pxC3zXQ+DPfBPrRt7AmkUmkm9ugTuwFGzheQDg932RJMlPSsqVnITDYYRCIYTD4bI2a3lJz8QXIdWkpIRH9IUbxIelHmLWerx6jskYw9lnn42mpia8+uqrGBkZQWtra1ljCd3Ht2KJvV69Hyobx933JJwnvga3mAVcF6osQR58Gc7//R2Ud/4/sOalU/a7nImJqqr+q9z9eKY7XyyQcyk+2Qr6HlCLMcsdr6SEJ5fLlb3j3Ew458jlclAURUgbMGMMlmUhm81OqoYVFdOrAq50PF3Xoes6crlcSev1lINt28L20ZPL5eA4Tln7J5yMd71yzqGqqtCYAPyYjDG0t7dj4cKF2LNnD/bv349YLDbrQpSzYYzBcRzk83nk83m/P0klMQCFQgG2baNQLFZ+qD1j4IUiTNOEbdvQ8zrcQgHuPI/ddHFgm1AOPgfJyIFDgsM5AAZICnj6KPQju8GjnYBjlTf2BPl8HpZlwXXdit8HFEVBsViE4zjI5XLChtt793OgMp2zJ2KMoVAowDAMof2WdF2H4ziTagEriTGGfD4P27aFxJQkyb/vTLwHxOPxU95mSQmPiA/GibEoZmXjBRFThFo/jzPFdF0X8Xgca9aswe7du/Hqq6/6o7XmW64grh14MURfq6jkfjKAO4BVAAC/X47XZweuC9d5KyGo8D6LOpcTt1/L9x7R94ATY9bi/e7E+1s5lJTwJBKJeS84VyrOOWzbRjKZFFYrYNs2GGNIJpPCquts2wYAYTFlWUYsFkMikZhXhjwXXu1CIpEQdi4dx4GmaUJrJAFA0zShNTzeWlonLkWwfv16PPzwwzh06BAYY2U515xzxONxxONxxGKxeW+vFFGtAEVREI1Ghdx7uKIgHQ6DKypi8Rg0TatQpBjcxefC3vNzuNb42meKooABkKIJxDp6AC0CoHJrZLmui1AOd9n4AAAgAElEQVQoJGwdrkgkAlmWkUgkhNW8ek0hoq5XRVEQCoWEPSeB8Xu64zjC7ufAeK2LyJjePadcx7Wkp5DoGT9FZ8r1ErPW41FMYMGCBejp6UFfXx/6+/vLGkvoPpb5m90cQo6PF6+kFZdDWnUNGDhk14Hs2mCROKS17wM63lbh4MHcByb+KTKmSNVyD6ilmOWOR7NCEVJDmpqasGrVKhw/fhwHDx4MujhkGizWCumyT+G1Be/Gw4MNOLrwKqjv/HtI626d0HOaEFJulPAQUmNWrFiBWCyGV155BYVCIejikGlYahy/LizB9wd7cHj5LcCySwBGt2NCKok+YYTUmBUrVqCtrQ379u3D8ePHgy4OmYZZLCIzOoKGWATJeKX6CxFCJqKEh5Aa09jYiLPOOgupVAq7d+8OujhkGqZpYmxsTFinbEIIJTyE1BxVVXHOOefANE3s3r274vPmkLkzDANjY2PQNI0SHkIEoYSHkBq0dOlSdHZ2Yt++fRgeHg66OOQE2WwWxWIRmqYJGzpNSL2jhIeQGtTV1YXu7m709/fjyJEjQReHnGBsbAyO46ChoYFWFSdEEEp4CKlB4XAYPT094Jxj7969gcxLQmY2OjoKzjmam5uFTcpJSL2jTxohNWrlypVQVRV79uyBaZpBF4dMMDY25ic8tKo4IWJQwkNIjVq8eDFaW1vx5ptvYnBwMOjikAm8Gp7Gxkaq4SFEEPqkEVKjGhoasHz5cgwNDeHw4cNBF4e8xTRNpNNpMMbQ1NRECQ8hgtAnjZAaFYlEsGzZMhiGgYMHD1I/niqRz+eRzWaRSCQQi8XovBAiCCU8hNSwpUuXorGxEXv27EEulwu6OAS/S3gaGxsRjUYp4SFEEEp4CKlh3d3daG1tRX9/Py0zUSW8hCeZTFLCQ4hAlPAQUsOSySR6enqQz+exf//+oItDMJ7wZDIZNDQ0QNM0SngIEYQSHkJqmKqqWLVqFQzDoISnSmQyGRiGgYaGBkQiEUp4CBGEEh5CatzSpUuRSCTQ19eHsbGxoItT99LpNGRZRjKZpBFahAhEnzZCatyCBQuwZMkSHDlyBKOjo0EXp645joN0Og1FUWjRUEIEo4SHkBrX3NyMRYsWYXR0lCYgDJiX8KiqikQiQc1ZhAhECQ8hdWDJkiVQFAUHDhyA4zhBF6ducc79Gp5kMhl0cQipK5TwEFIHenp6EA6HceDAAViWFXRx6hY1aRESHCXoAhBCKq+zsxONjY0YGhrC6Ogourq6gi5SXTIMA7lcDqqqIplMwnXd037x0EKhgPvuuw8vvPACGGPo7OzEHXfcgc7OzqCLRsgklPAQUgfi8TiWLl2KF198EQMDA5TwBCSbzcKyLMRiMYRCoaCLUxaDg4PYtm0bzjnnHDQ3NyMajdbMvpHaQgkPIXUgGo2ip6cHTz31FAYGBrB+/fqgi1SXcrkcTNNEZ2cnFEWpiRqe0dFRLFu2DNdeey00TUNnZycNtydVqaSER/TFK0mS8JtAPcSUJEnouWSMBXLtUMzpLVq0CJFIBP39/TBNs+Rv4d55FHrtvPXZEBVzPBYDYwxMqtxnMp/Pw7IsNDY2QlVVOI5z2t9fDx8+jB07diCbzaKvrw/r1q3Dn/zJn0DTNADjx9Z7iSL63hrUvU70KD/RMct93ykp4dm5cycaGxvLFvRkOOfIZDJIJBKQZVlITNu2oes64vG4sIvWtm3k83kkEomKx2SMoVgs4vXXX4dhGMKGwzqOg1wuJ2QfPZlMBpFIRFiVOucc+Xwe0WgUiiKmwtR1XWQyGcRisZJjyrKM4eFhcM7x/PPP4+yzz0ZjYyM457P+W845du/ejcHBQRw9elTItbN3oIixsRwOHDCwAxUeSs8YYBiw3nwTGD2O9K5dYGMpoIRjMxeyLOPFF1/E0NAQRkZG8NJLL8EwDMiyLHRNrVwuB0VR5hxTkiQsWbIEra2tk/6+vb0df/RHf4TrrrsOx48fx9e+9jU88cQTePvb346BgQH09/djbGwMO3fuRDgcFrKf+XwekiQJWbqDMYZCoQDTNIWOvCsUCuCcIx6PCzmmjDHoug7HcYQ8QyRJwtDQEIaGhiYlr+vWrTvlbZZ0t2xpaUFTU9MpB5kLzjlUVUVDQ4Pw5COZTAr7VmDbNiKRiJDZVr0PZGNjI1paWvzOkpXmOA7C4bDQGWVVVRXah4Bzjkgkgmg0ClVVhcVUVRWxWKzkmIwxaJqGxYsXo6+vDwDQ1tZW0hB1zjkaGxvR1NSEtra2kpKk+WAAktkswiETiUQCra0VvvcwBrdYREbT4ITCSDY1QWltA3h5h+8riuJ/DhYuXIgFCxYgn88LT3jC4bD/OZlLTFmWoWkaHn30Ufz93/89LMvC+9//ftx00004//zzEQqF0NHRgTPPPBN9fX3YvHkz2tra/P5KLS0twpbSiEajYIwhFosJSXiKxSIMwxCa8Oi6Ds65sC+wjDHk83lhMSVJgmVZMAxjSpJ9qkpKeHp6eoTX8DQ0NAhLPhzH8RMeUbwkq6GhQUi8QqGAVCqFnp4exONxITE5534Nj6hzmclkoGma0NoWr4ZHVI2kV8MTj8fnFJNzjnPOOQdDQ0NwXReLFy8u+d+l02l0dHQI6+x8uDgC7YCO9vY2LF26qOLxXMPAQEsLCtkMFi1chMiS0o7NXCWTSYTDYZx55plYunQpdF2HLMsIh8MViTedXC6HUCh0yl8K2tvbcfHFF8NxHCxZsgT/8R//gXA4jI9//OPIZDI4dOgQNm/ejEQi8VbC2opYLIaenh5hX0R0XQcAv1mt0kzThGmawu6tAFAsFuE4DmKxWM3GDIfDkGUZS5cuLcv2SnoqiJ6ozLZtcM6FPkAcxwHnXGg7rOiYjuMIPZecc9i2LbRjprePIhMe27bhOE4g1+tcYkqShJ6eHliWhQMHDuDyyy+fczxRuOPAdV1hMcf3kYPzysV0HAepVAqKovgPYtu2KxJrtnLM5z7Q29uL3t5e//+7u7vx9a9/HX/5l38J27bR0dGBTZs2+b/nnAs9lwCE943y7nUiib6fBxHTu7eWC43SIqSOLFq0CKqq4ujRo9B1Xdg3YDJeC5DJZBCNRmvquK9evRp/93d/h+3bt6OlpQXr1q0TWmNFSKko4SGkjjQ2NmLBggU4duwYRkdHa+rBW+1M00Q2m625hAcYX6D2+uuvD7oYhJwUTZZASB1paGhAR0cHjh07hrGxsaCLU1csy6rJGh5CTheU8BBSRzRNQ0dHB/L5PIaGhoIuTl0xDAPZbBaapgntaEoIGUcJDyF1ZuHChQiHw+jv7w+k02y9MgwD+XwekUiEangICQAlPITUmYULFyISiaCvr49WThcok8nAtm1omkadegkJACU8hNSZzs5OxGIxDA4OIpvNBl2cupHJZACMdxyntaYIEY8+dYTUGU3T0NXVhVwuh8HBCi/bQHzpdBoAhE02SgiZjBIeQupMJBLBkiVLkMvlcPTo0aCLUxe82bEBSngICQolPITUGUVRsGjRIhiGQTU8griu6zcfilx+gBDyO5TwEFKH2tvb0dDQgIGBAeTz+aCLUxdyuRxc16WEh5CAUMJDSB1qa2tDc3MzJTyC2LYNXdchSRISiQQACFsdnRAyjhIeQupQW1sbWlpaMDIyglQqFXRxal6xWESxWISqqohEIkEXh5C6RAkPIXUoHA5jwYIFsG0bAwMDQRen5hWLRRQKBcRiMYRCoaCLQ0hdooSHkDrEGMPChQsBAEeOHAm4NLXPq+GJxWJQVTXo4hBSlyjhIaROdXZ2gnOOwcFBcM6DLk5NMwwDxWIRmqZRwkNIQCjhIaROtbe3IxKJYGRkBLlcLuji1LSJNTzUpEVIMCjhIaROxeNxtLe3Y2xsDKOjo0EXp6Z5fXiohoeQ4FDCQ0idisViaG9vx+joKI3UqrBisQjDMKiGh5AAUcJDSJ2KxWJoa2tDNpulGp4Ky+fz4JxD07Sgi0JI3aKEh5A61t7eDkVRcPToUeq4XEHZbBaKolDCQ0iAKOEhpI61t7cjGo3i6NGjME0z6OLUJMdxkMvloCgKYrFY0MUhpG5RwkNIHZuY8FiWFXRxapKX8KiqSgkPIQEqKeFhjFW6HFPiUUyKRzErH7O1tRXxeBypVArpdPqksYRfOxB772EMgPcqo5kSniCO68S4IuNN/FNkTJFq/TwGEbPc8ZRS3pTNZhEOh4Usdsc596t/ZVmueDzGGCzLQjabhSRJkKTKV3p5MXO5HGRZrnhMxhh0XYeu635MEefStm1ks1kh++jJ5XJwHAfhcFhIPM45stksHMcRNvrG+4wAmNcQZ0mSYFkWmpqasGfPHhw6dAgtLS1wHMd/D2MMtm0jn88jl8tB1/WK9/VhAPRCAZZto1AsVn6OIMbAC0WYpgnbsqHndbiFAtwJx+FUSZLkdwp3XReu66JQKMBxHLiu69/rOOfCFhPNZrMIhUJ+GSpJURQUi0U/6bNtW8h+evdzoPKLtDLGUCgUYBiGkGeWR9d1OI4DSZKEHFPGmH9/FRFTkiTkcjn/3uOJx+OnvM2SEh4Awj6QXhzXdYV1ohQdkzEGzrkft+IPEMb8/fPiiTiXXgyRnWFFHdMT4wUR07uGTpXrulAUBZ2dnXj55ZcxNDQ0ZT+mu3ZEJDyuF0PEcWUMnI8//L3/OOe/K8M8eYm/oiiIRqOTjqH3s8iER+R9wNvPideOqHuPqHgT7+ei73Uij+nEe4HI81jOe2tJCU8ikUAikShLwNlwzuE4DpLJpLBaAdu2IUkSksmksOo627bBGBMW0+swKfJcejUFIs+lN/RXZG0LY0zohHLezSaRSEBRSv7OMqNly5aBc458Pj/tKCLOOeLxOBKJxLy+Xc2FFiv6CUIymax4PK6qyITD4Mp4s5NWxr42hmH41+WCBQumNGt5+ylSKBQStmp7JBKBoihIJpPCal4lSQJjTFifKVVVYRiGkGvVoygKHMcRdj8HAFmWhcb07jnlOq4lPYVEffOYGI9iUjyKKSZma2srwuEwhoeHYRjGjLGE7uNbscRer94P5d1uLpeDZVmIRqOTEvFAjiuCuQ9M/FNkTJFq/TwGEbPc8WiUFiF1rqGhAY2NjRgZGYGu60EXp+bk83nYto14PC6sppMQMhV9+gipc8lkEg0NDTh+/Djy+XzQxak5uq7Dtm0kEgmhnVoJIZNRwkNInWtoaEAymcTY2BjV8FSAl/BQDQ8hwaJPHyF1LhqNorm5GbZtY2RkJOji1Jx8Pg/HcRCPx6mGh5AAUcJDCEFbWxsYYzh27FjQRak5xWIRtm1D0zSq4SEkQPTpI4Sgra0NkiTh2LFjtIhomXkTDdKyEoQEixIeQgja29v9Gh5KeMqrWCzCdV1aKZ2QgFHCQwhBc3MzwuEw0uk0jdQqI8dxUCgUIEmS8MkFCSGTUcJDCEE0GkVLSwuy2SxSqVTQxakZtm2jWCwiHA4Lm/2bEDI9SngIIYhGo2htbUUmk5lx1XQyd5ZloVAoUMJDSBWghIcQQjU8FWLbNgqFAkKhECU8hASMEh5CCGRZRktLC0zTxNjYWNDFqRlek1YkEhG2cCYhZHqU8BBCAIx3XI5EIhgeHoZt20EXpyZYloVisUg1PIRUAUp4CCEAxhMeTdMwPDwM0zSDLk5N8Jq0wuEw1fAQEjBKeAghAMYTnmg0imPHjlHCUyYTOy1TwkNIsCjhIYQAGE94YrEYUqkULSJaJqZpwjAMGqVFSBWghIcQAgAIh8Nobm6GaZoYHR0Nujg1Qdd1cM4RCoWgqmrQxSGkrlHCQwgBMD5Sq62tDZZlUcJTJrqugzFGy0oQUgUo4SGEAPjd0HTLsmhoepl4TYOU8BASPEp4CCEAAEmS0NzcTAlPGVENDyHVgxIeQoivubkZjDGk02laNX2eXNelhIeQKkIJDyHEF4vFkEgkkEqlaNX0eXJdF4VCAYwxWimdkCpACQ8hxBeLxZBMJpFOp1EoFIIuzmnNdV0/aaQaHkKCRwkPIcQXj8eRSCQo4SkDL+GhGh5CqkNJCQ9jrNLlmBKPYlI8iik+plfDk8lk/ITHiyV0H9+KJfZ6Le/2XNdFsVicsQ9PIMcVwVyvXtxajBVUzHq4dsodSynlTel0GrIslzXwTDjnyGQykCQJkiSmAsq2bWSzWbiuKyQmYwyWZSGbzQJAxWMyxqDrOrLZLNLpNIDxm3GlOY6DTCYDoPL76Emn07AsS9istpxzZLNZWJYlbGI5zjnS6TQcxyl7TMYYVFVFPp/HwMAAFi1a5F+rmqYhmUxWvDMzA5DP52FZFvJ53b9mKxeQgRcKKBaLMC0T2VwWdi4H13FOeZOSJCGbzSKTyYBzDsdxkM/nJy3K6roucrkcFEWBZVlCPpMAkMlkEAqFYJpmxWMqioJisQjbtpFOpxGJRITsZy6XA2MMjuNUPB5jDIVCAYZhVDTOiXRd9/dPxDFljCGfzwuLKUkSMpkM8vn8pHtAQ0PDKW+zpIRHURSEQiEhB5VzDkVRoCiKkCTLy1hVVYWqqsISHmD8uIqI6e2fd1xVVRX2ARG1jx5vP0UmHxOPq6iY3vVa7piSJKG1tRWyLGNsbAySJE25dkQkPLIsQ5IkyIpc+ePKGLht+1+yVGX8uLrzuGYlSQLnHLZtIxKJIBKJQFXVSd9YXdf1j6mozyQAofcB7z4+8R4rYj8VRfGvXREJj23b/udSFO++Kvp+7p1LEQmPd/2U67iWlPDEYjFhbdCccxiGgVgsJvQhyTlHLBYTVl2nqiocxxEaMxqNCj2XjuPAcRxomibsXJqmCU3ThNbwePsoMuGxLAuxWAyKUtJHeE4WLFiAUCgEXdcRiUQAjF87mqb5/19pkUgEsiwjEg4L6fDLGUMoFIIjK4hEI4iWYaFPWZbhui4SiQQSiQRCodCU69JLmEX28bFtG6FQSNi5DIVCkGUZmqYJW0CVcy607xRjzN9HkRzHEXrtuK4rNKamaf69pxxKegqJ+uYxMR7FpHgUM5iYTU1NkGUZIyMj/oND+D6+FUvs9er9UJ7tFYtFGIaBaDQ6bWLqHdNaunZmijfxT5ExRar18xhEzHLHo1FahJBJmpubIUkSRkdHafLBeTAMA6ZpzpjwEELEooSHEDJJQ0MDwuEwstms3/mTzJ1hGLAsixIeQqoEJTyEkEnC4TAaGxuh67o/yo7MnWEYfpOWqFGuhJCZ0dcOQubgxPbkif0wRLVtVyqmV5MTCoXQ3NyMkZERSnjmYWKTlsjRO4SQ6VHCQ8gsTux0OTHR8EZpeS8RJsYs1+g3b3oGSZIQCoXQ1NSEfD5PCc88mKYJy7IQDoephoeQKkAJDyEnMbEmhXM+6U9gfFioaZpC+2hwzmGaZlkmjps426+X8KiqiqamJhSLRUp45sE0TXDOhQ3/JoScHCU8hMzCm3vCcRzYtu3/7CU/3orYE2fRrSQvZrkm5PIm3PMmpItEImhoaIDrukilUv7QdDI3hmGAMSZs7hlCyMlRwkPIDLyExnEcWJY1vvSAaU55+HuTcIlKeAD4E1aWO6Y34Z83SVwqlYJpmmWNUS+KxaJfY0YICR4lPIRMY2Izlm3bKBQK4JyjtbW1Zh9guj6+bpWiKP6syt7aZFTDMzeO46BYLEJRFKrhIaRKUMJDyAy8pMe2bViWhba2tpqeT0XTNLiui0KhgGg0ikgkgkwmA8uygi7aaYdzTgkPIVWG5uEhZAYTa3hkWa7pZMcTjUb9tXImNmlRDc/ceAmPLMuU8BBSJSjhIWQaJw47r5cHPmMMnHO/D08ul4NhGEEX67QzsYZH1EK2hJCTo4SHkBkEsehhtQiFQojFYrBtG+l0OujinHY45zAMg2p4CKkilPAQchKlJjuu62JgYKDqRzQNDQ3NmsC4rgtJktDY2AjHcWgunlPgOA4KhQLV8BBSRSjhIaQMnn/+efzLv/xL1Xfw3b59O/75n/951uHsXsLDOUc6na7LWq758Gp4qNMyIdWj9nthElJhuVwO3/ve93DzzTcjFotN+55XX30Ve/bs8fvI9PT0YN26dXOONTAwgB07diAWi+Giiy6CpmlT3mNZFrZt24bh4WEwxuC6LtavX4/u7m5cffXVePLJJ/HYY4/h2muvnTGOJEloaGiA4zhIp9Po7Oycc1nrGfXhIaT6UMJDyDw98sgjcBwHF1544bS/dxwH9957L3Rdx+LFi/0lIeaa8Lz++uv46le/irPOOgsjIyN44okn8JnPfGZKkjU4OIh/+qd/wrJly6BpGhzHwdKlS9Hd3Q1VVXHVVVdhy5YtuOSSS6ZN0E5s0qI+PHPnLTkSDoephoeQKkEJDyHzYJomHnvsMVx00UUzfpNPp9OQJAlf/vKXsXDhwlOOtWXLFrz97W/HH//xH8OyLPz5n/85tm3bhiuvvHLS+w4fPozly5fjK1/5yrRD6Xt7e3HPPffgxRdfxKZNm6aN5dXwAEA2m6XJB+fIMAzYto1YLEYJDyFVgvrwEDIPAwMD6O/vx5o1a2Z8z/DwMDjn6O/vx9atW3Hw4MFTitXa2opUKgVgvBnNcZxpa2gOHz6McDiMHTt24Be/+AXGxsYm/b6lpQWLFy/Gc889N2Msxpg/23Iul/PXCyOlMQwDnHNaKZ2QKkIJDyHzcOTIETDG0NXVNeN7+vv7sXPnTjzzzDN48cUX8alPfQqPP/74nGO9973vRV9fH26//XZ89KMfxfLly3HBBRdMed+BAwfw8ssvY+fOndi6dSvuvvtuHDp0yP+9JEno6urCnj174DjOtLFc10U0GkUikfATHlK6iQkPJYqEVAdq0iJkHkZGRuA4zklnYV60aBG+8IUv4KqrroIsy3j00Ufx7W9/G+vXr0djY2PJsf73f/8XoVAId955J44fP44HHngAL7300pS+QBdeeCGuueYarF27FgDwpS99Cf/93/+Nz33uc/57mpubsWvXLliWNW0NhOu6iEQiiMfjyOVyKBaL9OCeAy/hiUajdNwIqRJUw0PIPIRCIUjS7z5G+Xwed955J3p7e3HhhRdi27ZtWLVqFa655ho/sVi3bh0URcGxY8dm3O7LL7+Myy67DOeddx7e//7344033sAzzzyD2267DWvXrsUVV1yBCy+8ED/96U+n/NtLL73UT3YAYOPGjTh69OikGZO9RGdi2Sfyani8hIeatOamWCyCc45IJDLjMSaEiEU1PITMw4IFC+C6LnK5HNrb2xEOh/HBD34Qv//7vw9ZlrFy5Uo8+OCD4JzjxhtvBDDep8d13ZPW7ixZsgR/9Vd/BcMw0NLS4vfVmfjwDIfD4JxP+nfFYhH//u//jquuugqrV68GABw9ehQtLS2TOs8ODg6ira3tpEOmI5GI36Sl6/rcD04d82p4IpEIJYqEVAlKeAiZh8WLFyMSieCNN97AsmXLoCgKLrrooknvaWhowNe+9jU0NTWhvb0d99xzDzZt2oT29na88cYb2Lt3L6644opJzWLNzc24+uqrJ21n/fr1uPfee/Gnf/qnSKVS+PnPf44Pf/jDAIAnn3wSyWQSvb294Jzj61//Oj75yU9icHAQDz74IP7iL/7C306hUEBfX9+U0V0TeTU8sVgMlmVRH545mljDQwkPIdWhpIRH9AeWMUYxKV6gMb3tzLa91tZWrF+/Hs899xyuuOKKad/zjne8A6FQCA899BCKxSI2b96MG264AcB47ctDDz2EzZs3z7oa+x133IEf/ehH+OY3v4lQKITbb78dmzdvBgDs2rULHR0d6O3txV133YWf/OQnuPfeexGNRnH33Xdjw4YN/nb6+vqQTqdnnDfI239ZlpFMJiHLMvL5/JTapEpijIFB7L2HMQDea568uZai0eiMTVqlXF+VEMR9YOKfImOKVOvnMYiY5Y5XUsIzOjoKQMwiipxzpFIpcM6FtX3bto1cLgfbtoWcTMYYLMvyhxZXOiZjDIVCAel0GqOjo7BtW8i5dBwH2WwWtm0LO5fpdBqFQmHes9t6q6R7tRsna3565zvfiX/4h3/A0NAQOjo6pvyeMYaLL74YF1988ZTfLVu2DOvXry+pvKFQCLfeeituvfXWKb+76667/J/D4TBuueUW3HLLLdNu5xe/+AV6e3tx5plnTltWy7Jw/Phxv6My5xzDw8M4fvw4otFoxRMfBiCdycA0TeRyORw/fryi8cAY3GIRuq7DNAykU2kUUym4M4xgm40kSRgZGUGxWIRlWRgdHfVnvJ7IdV3k83koioJoNCps+Y5MJoNQKCQkpqIoyOfzME0Tx48fRyQSEbKfuVwOkiTBMIyKx/Pur6ZpzrpkSznpug7OOSzLEnJMGWPI5/P+fbHSMSVJwtjYGFKp1KR7QEtLyylvs6SER9M0xONxYQmPZVmIxWJC5q/wbvCu6yIWiwl5MHsxOedCYjLGIEmS30Qh6lzatg3HcRCPx4UlPJZlQdO0eU/25iU8pmnO+i3jvPPOw5o1a/Czn/3Mb2Iqla7r2LRp06y1O+Vy5MgRvPrqq7j77run/b3rupBlGZFIBLFYDB0dHYhEIjBN0x+mPtNQ9nJhAKLRAuS31qGKx+MVjQfGwGUZmVAIXFEQ1aLQ4vFTTni8+5Y3W3UikZj28+a6LlzXhaqq0DRNWMLjOA5CoZCQmN7SGoqiIB6PC0t4vNnCRdzrvNrQYrFY+Wt1AkmS/PurqIQHgLCYkiRB0zQ//yiHku6y4XBY2How3twVIkc3SJIE0zSFtrdLkuTvp4iYjuNAVVWEQiFh51JRFBiGgXA4LOxcRiIRRCKRee+j67pwHAeSJJX0re22227Dli1bkEql5jTU/IwzzphPMeds586duOKKK6at3fFMvDZbW1sRCoVgGAZUVYWiKEKSM1VRIUmSsMU3OeeQZQWyJCOkhhBSFGAe++klhYlE4qTXojdaTuR6W979XOR9QJIkoQkJW7QAABoDSURBVDG9mcFFPrcACJ1V23EcP3kVJRKJCI0ZDoehqmrZjmtVdlr2vvkEEVd0m2gQMUUJ6hyWI663nVK3tWDBgkkdg6vVO9/5zjm9P5lM+s0SIvvwnO5M0wQw/oCYSVD3uXoQ1L1cdLxaj1nuWDRBBCEnUavJaKlisRhCoRBM05w0jw+ZmW3bME3TrykjhFQHSngImYHXd6feJo7z9tlrEvCGpheLxaCLdlqwbRuGYSAUCkFV1aCLQwh5S33dyQkp0cRkR5bluml+8EYqegmP19mUEp7SeTU8lPAQUl0o4SHkJBhjUFUVjuPUxWzD2WwWsiz7I40URUEikYBlWXWx/+VANTyEVKeq7LRMSDWQJAmu60JRFGia5s8pVIsLQjqOg3w+D9u2EYvF/JE1qqpSDc8cWZbl1/CImm6AEDI7+jQSMg1vojivSSsUCoExhmKxOGnEkuu6ME0TqqoK6+vjuq4/TLxcc1XJsgxVVSclO16TVjKZhGlZKFDCUxLHcfwaHpFDhgkhJ0cJDyEz8GpxvPlgvASAcw7OOVzXBeccmUwG0WhU6JwfXk1MOZpMJEma9PJWUfcmIdSSTXDeaqYhs/NqeDRNoxoeQqoIfRoJOYmJHXi9JMBLdIDxb/PhcFj45JyRSMSflGs+TlwzzKul8meXNjJYZ7+EL5xzDCuP/hD8NyFIb7sWUKPl2JWa5NXwNDQ0UB8eQqoIJTyEzOLExQ+9mg+vyUtVVf8lAucciqKULeZ0izsyxoBCGs7jX0Ln3p+isc2Cmn4VzqNfAIZeh3TpJyjpmYFlWX6TFtXwEFI96NNISAkmJjsnJggTm4NEqUTMEztiu3sfh7v/KbiSDMuVwJgCl0nge/8PbMVlYD0XlS12LfFGaYms9SOEzI4SHkLm4MSk4MQmIVFlqHhMboMf2wOXW2BvNen5HbXtIpAfqUzcGmBZFmzb9tceI4RUB5qHhxAyFZPBYq0Ak8DATqjhkuEqM68RVe8sy/JXQS/XKDpCyPxRwkMImYoxsDMuAUt2AdwEA+ByDjgW0LQEbMGqoEtYtQzD8BMeQkj1oISHEDIt1nEW5Ms/BbnrPFiQUXAY3CUbIF/x12CNi4MuXtUyDMNfh4wQUj0o4SGEzIgt2wTc9B/4z8I78LcHzkTf2o+DdZ0bdLGqGiU8hFQnSngIISfFQjGk1TYM6CrGcjTb8sl4M29TwkNI9aGEhxByUowxxLUowB1kM5mgi1P1KOEhpDpRwkMIOSnGGDRNg+u6yOVyQRenqnnrnDHGEA6Hgy4OIWQCSngIIbPSNM1fN4zMbGLCQ6O0CKkulPAQQk6KMYZoNArOOdXwzIJqeAipXpTwEEJOykt4ACCfz/szLpOpqNMyIdWLEh5CyKwikQgURYGu69B1PejiVDVKeAipTpTwEEJmpaoqotEoCoUCDMMIujhVi2p4CKleJSU8ohZFnBiPYlI8ilk9MVVVRSQSQbFYFJPwnLAivQh+qHmEnNiHZ7aER/SisyfGFRlv4p8iY4pU6+cxiJjljlfSUr6pVAqSJKYyiHOOdDoNxpiwmLZtI5fLgXMuJCZjDJZlIZvNwnXdisdkjKFQKCCbzSKVSsF1XbiuW9GYAOA4jrB99KTTaZimKezbNecc2WwWpmkKG5XjjZbyVuSuJG+V9GKxCEmSkMlkMDw8jEQiAcdxKhMTQC6Xg2VZyOfzSKVSFYnzu4AMvFBAoVCEaZnIZrOwslm4c9w/SZJQKBSQyWRgWRYMw0A2m53xOHnD/BVFgWmaQj6TAJDJZBAKhRCNRiseU1EUFAoFWJaFVCqFSCQiZD9zuRwkSYJt2xWP591fRZ5DANB1HY7jgHMuJC5jDPl8XlhMSZKQTqeRyWQm3QMaGxtPeZslJTyhUEjYhco5RygUQigUErLSsJd8mKaJcDgsLOGRJAmGYQiJyRiD4zhQVRWhUAjhcFjIufQeyKKOK4BJ+ygC5xyGYfjXrKiY3nEVlfBEo1FEo1Houg7XdRGJRGDbdmViYvw8SpIERVEqfy7f2kdFkeFIsn9sTyXhmbhwaDweP+lx8pq/vH0U9bD0rlURMRVFgSzLkGUZ4XBY2H6apglJkoTE8z4jrusKHZln2zYcxxF2TL1npaiYkiRNulbLoaSER9M0RCKRsgScjfdtUtM0YQ9JRVHgOA40TRNWXacoCmzbFhbTe0iJPJeO48C2bUSjUWHn0jAMaJomNPnwzqPIGh7TNKFpGhSlpI/wvLiui3g8jng8jkwm488xU8n9DYfD/kPSGyFWSRzjSZYty4hEIoic4vWjKIrfnJVIJGY9To7jQFEUYZ9JALAsy/8SK0IoFIIkSYhGo8ISAsdxwBgTely9fRTFdV04jiN0HznnQmNGo1FEIpGyHdeSnkIiq+m8eBST4lHM6ojpuq7/UC4UCigWBayn9da+ib1evR9OfRuWZfk1m7N9kfHOYS1fO168iX+KjClSrZ/HIGKWOx6N0iKEzMprdnEcB4VCIejiVK2JVf4imuQJIaWjhIcQclJep/NIJAJJkpDP54MuUtXy+lV4zTiEkOpBn0hCyKxc10UsFoMsy8jlcoE0GZwOvCYtSngIqT70iSSElCQajUJRFFpe4iS8Ji1KeAipPvSJJISUxKvh8ebiIFNNrOGhPjyEVBdKeAghJfFqeLxJOslUE2t4gpjtlxAyM0p4CCEl0TTN78NDCc/0qNMyIdWLPpGEkFm5rusnPN6U9mQqatIipHpRwkMIKUksFoOqqigWi7AsK+jiVCXqtExI9aJPJCGkJN4aU5ZlQdf1oItTlWhYOiHViz6RhJBZua4LWZYRj8cp4TmJiTMtU6dlQqoLJTyEkJLIsoxYLAbbtml5iRlYluWvlk4IqS6U8BBCSuLV8Ni2TTU8M/D6NoVOcbV1QkjlUMJDCJmVt56WpmnUpHUSpmlClmWq4SGkClHCQwgpycQaHmrSmopzDsMwKOEhpEpRwkMIKYnXh8eyLEp4psE5h2maUBQFiqIEXRxCyAko4SGEzMobpRWLxeC6LiU80+Ccw7IsyLJMfXgIqUKU8BBCSsIYQzQa9WdbpuUlJqMmLUKqGyU8hJCSRSIRRCIR6LpOsy2fwHEcatIipIpRwkMIKYnrugiHwwiHw5TwTMPrw0M1PIRUJ0p4CCElm1jDY9t20MWpKhM7LVMfHkKqDyU8hJCSuK6LSCRCNTwzmFjDU8tNWgMDA7jvvvswNjYGYLwp7+c//zk+8pGP4DOf+Qx2794dcAkJmR4lPISQkkxs0ioUCpTwnKAemrRefvll3Hnnnbjvvvv8TusvvPACHn74Ydx6660466yzcM899+DYsWMBl5SQqaryawhjLJCF9+olpihB7Vu9nMcgYobDYYRCIYyNjVGT1glc1/WHpZeS8AR1nztVQ0ND2LJlC3p7eyFJkp/wbN++HRs2bMDmzZuxbt06HD58GK+//jra29sDK2s9fB7r4f5a7lhVWcPjui5c1w0kbj3EFCWofauX8xhETFVVEQqFUCwWKeE5gTcPjyRJJTVpBXWfK8V05WpqasKnP/1p3HbbbYhGo3BdF7ZtI5/Po6WlBcD49ZFIJDA4OCi6yJPUw+exHu6v5Y5VUg3PM888g4aGBiE76rouMpkMEokEJElMPuY4DnRdRzweF5a9Oo6DfD6PRCJR8ZiMMRSLRezbtw9jY2OIx+NCzqW3j/F4XNi5zGaziEQiwpoUOOfQdR2RSERYvw3XdZHL5RCNRoXE5Jxj3759aGlpQUtLCwYGBjA4OIhf/epXOHz4cNnn42EAdg05GBkpYvfuDJL5A2Xd/tSADDBNsINvQB4ZweCOF8DffBOYw35JkoSRkREcPnwY8Xgc27ZtQ0NDw0mPjeu60HUdiqIgEokIe5Dk83koioJwODzt72VZxhlnnIGFCxdO+nvbtsEYg+M4cF0XnHPYtg1FUSDLMvL5vP9ey7Jw5MgRvPHGG9i/fz9GRkbwq1/9CqFQSMh+6roOxhg0Tat4PO/+alkW4vF4RWNNZBgGHMfxJwOtNMYYCoUCHMcR8gyRJAnDw8M4duzYpLX7Lr300lPeZkl3y7PPPhvNzc2nHGQuOOdIpVJobGwU9pC0bRu5XA7JZFJITMYYLMtCNptFQ0NDxWN6FyoArFq1Sljy6jgOstmssOMKAKlUCtFodMabeblxzpHNZqFpmtAkK51OIx6PVzym94BjjGHBggXo7OzE008/jePHj2PJkiU477zzKpLw6PvGsGt0AEuWtOG8czvKuv2pARl4oYCRQ2/AtG20rVyJyLIz4DpOyZuQZRmHDx9GY2MjWlpasHbtWiSTyVkTnlwuB0VRhDyYPZlMBqqqzhiTMYZ4PI5f/OIX+NjHPobh4WHccccd+OxnP4tYLOa/T5IkqKoK27aRyWQQi8X8h3BzczPa29uRTCbx1FNPoa+vD+ecc46wxC6Xy/n7ISLhKRQKMAwDDQ0NFY01ka7rcBwHyWRSWMKTy+XAORcSU5IkDAwMoKHh/7d3L0mOE2sYhr/UXbKrqquiGRBBBCMigBELYAEwYRNM2AMbYHMMGdMb6CrfqmzdUmdQlWr3oTlt+dhplf0+EUQTBO1fFyv9KTOVutEPP/xwkM/cKfDc3d3p9vb2IAU/x1orY4z3wJMkia6vr7318DRNoziOdXNz46Vmmqa6ubnR3d2drq6ujl5Peg48URR5DTzujd4+w4f78fDVw2OtVRiGurq6UhiGXuq9efNGb9680e3trd6+faskSZQkydEa+Kur52tyMpl4aXu6PNdTUcikqa6vr1VcXw/+jKurK8VxrMlkoi+++EJZln327yRJ0vfw+BJFkeI4/mzN77//Xn/88Yc2m42++eYbZVn2j+s4DEN99913+uuvv7TZbPTu3Tv9/fff+umnnxRFkabTqSaTiZIk0e3trbcbkSRJ+h4eH/I8V1mWut7je7OvLMv63hZf0jT1WvPp6Umr1epgbcBOLbTvJeSttd7HJ11NnxOyfNe01no9l67b2yff+3jqmj4CjzuP7pp0d+nbQxgHr/lSz1c78LyPL/X2LFlVVX9Odgn47riOtX398ssv9csvv3z2M3788Uf9+eef+vXXXxUEgX7++Wd9++23/f/rzqPPNt1a6+0mS6KtO2a9Q35vRvmUFoDxyvNckniB6H+p61pd153tI+nO119/rd9++63v3Xv79q1+//13vXv3TkVR6KuvvnpVT5/hchB4AAziAs/2REJ8CDxuOOVcxXHcP5XlZFn2Ua8OMEajfCwdwPi4rmU3L2K9Xo/2sepT2O7hOefAA7xWBB4Ag2wPaRF4PnArT5/7kBbwWhF4AAzCkNanNU1DDw8wYgQeAIMURdEvtub7KZEx257DA2B8CDwABsmyTGEYqixLlWV56s0Zje0hLXp4gPEh8AAYJI5jpWmquq5VVdWpN2c0mLQMjBuBB8AgbmVgeng+dinr8ACvFYEHwCBRFCnPc9V13Q/j4HLW4QFeKwIPgEHcm7bp4fnY9lNaAMaHwANgENfDU1UVc3i2sA4PMG4EHgCDuDk8VVXRw7OFOTzAuBF4AAyyHXjo4fmAIS1g3Ag8AAZxQ1plWRJ4ttDDA4wbgQfAIEEQKMsytW2rzWZz6s0ZjaZpJImVloGRIvAAGCxN0/71EpDatlXTNDLG0MMDjBSBB8Bg7vUST09PvDFdHwJPGIaKoujUmwPgEwg8AAZL01RRFOnp6YkXiOp5OMsFniCgWQXGiCsTwGB5niuKIt6Y/sJaq6ZpFEWRwjA89eYA+AQCD4DBtoe02rY99eacnBvSiuOYwAOMFIEHwGBZljGktcUFHnp4gPEi8AAYLE1ThWHIkNaL7cDDHB5gnHa6Mn2/+dcYQ03qUXMkNV2t7XpFUfQ9PMcY0jLGyMhv22OMJPfPQNZatW07qIfnU8fVh1O0A9t/+qzp07mfx1PUPHS9nZ6fnM1mCoLAy+On1lrNZjNJ8nan1DSNVquVrLVeTqYxRnVda7lcquu6o9c0xmi9XmuxWOjh4UHWWi/nsm1bLZdLWWu9ncvZbKayLL0t/mat1XK5VFmW3tZfsdZqPp+rruuj1zTGqG1bzedzZVmm6XTaf5/cf7+/v+//v4PUlLRcrVTVtVarlR4eHg7yuf9e0KjbbLRer1VVlRaLharFQt2O+xMEgd6/f6/Hx0cZY7RcLrVYLHY6HsvlUlEUqSxLb4/3LxYLJUmiPM+PXjOKIj0+Pqquaz08PCjLMi/7uVqtFARBv/r1Mbnroaoqr72d7majbVsvx9QYo8fHR281gyDQbDbTfD7/qA24vb3d+zN3CjxJknj7olprlaZp32V+bC581HWtNE29/DAbYxSGoaqq8lLTGCNrbX8efZ3LpmlUlqWyLPMWeNx3J01TL/WstarrWlmWeQ087rj6CDxN0yhJEqVpqizLZIzRzc2N0jRVXdcyxvQrLx+kpqQ4fh4act/ZozJGtusURZHaIFSaPO/nroHHrb3TdZ2yLFNRFErT9LM/fl3XqaoqxXHs7ZqU1N8Q+KgZRVE/kdtn21PXdb8iuI/A42oc/bu6xfUq+jqmri3wVTMIgr4tP9Rx3SnwFEXh7URaa7XZbFQUhbcfySiK1LatiqLw1l0XRZGapvFW0zXGeZ57O5duXkOe597OZVmWKorCaw+P20efgaeqqn5YyUe9PM+V53kfJK+vrzWZTDSbzWSMOfjxTtPnp8BcT8SxWUlxHKsJw+cGduD+uOOSZZkmk8nOgdsNg/n8oazr2k+QfJEkiYIg+Oj7c2xt2/ZB3Be3j750XdeHD1+2Q5YP7vfqUMd1p18h3yupdl1HTepRcyQ1Xa3tetu9Okd5vcRLLb/f1/3/rlt4cMgcnk8dVx9O0Q5s/+mzpk/nfh5PUfPQ9XicAMBgbrjADa9dOhYeBMaPwANgMNfDQ+B5tt3Dw2PpwDhxZQIYzPXwtG2rqqpOvTknRw8PMH4EHgCDbffwHGUOzyvDSsvA+BF4AAy2PYeHHp4PgYe3pQPjxZUJYLDtp7SYw/M8h8day8tDgREj8AAYjKe0PlbXtSR5WRcJwH4IPAD2ctR1eF4ZAg8wfgQeAHtxq626H/tL5l6xQeABxovAA2AvaZrKGKOqqk6ysu2YVFUlY4y314sAGI7AA2AvcRwrjmOVZammaU69OSdFDw8wfgQeAHtxgaeqqosOPF3XqWkaeniAkSPwANhLHMdKkuTie3i6rlNVVQqCgMADjBiBB8BetgNP27an3pyT6bquH9Ii8ADjReABsBeGtJ65Hh7m8ADjRuABsJcoihjSekEPDzB+BB4Ae9nu4bn0IS03aZkeHmC8CDwA9pIkCT08IvAArwWBB8BeeErr2fakZQIPMF4EHgB7YdLyB23byhjDm9KBESPwANhLFEWK41ht26qqqlNvzskwpAW8DgQeAHsJw1BJkqjruot/YzqBBxg/Ag+AvWVZJmOMyrI89aaczHYPD0NawHgReADszQWe9Xp96k05GSYtA68DgQfA3tI0lSQCT11LEj08wIjtdDsym81kjDn2tkiSrLWazWaSpCDwk8eaptFqtVLbtl5qGmNU17WWy6WstUev6e7AF4uFHh4eZK1V13VHrSk9P7niax+d+XyusiyVJImXetZaLZdLlWXpbZVda60Wi4Xquj56TWOM2rbVYrFQnueaTqey1kp6vj6bplFd17q/v9f79+8VBMH//d0ykparleqq0uPjo+7v7w+wJ/+roFG32Wi9XquqSs0Xc5XzubodFlMMgkDL5VLr9bpvR+bz+U4LMXZdp9VqpSiKVJall2tSkpbLpeI41mazOXrNKIr09PSkuq718PCgLMu87OdqtVIQBKqq6uj1XPtaVVV/bfjw9PSktm3Vtq2XY2qM0ePjo7eaQRBoNptpsVh81Abc3d3t/Zk7BZ6iKHR1deXloFprVde1JpOJl7slFz66rtN0OvUaeKy1XmoaYxQEgfI812Qy0XQ69XIum6ZR27bejqurmed53/NwbNZaWWtVFIXXkOWOq4/A445pURT/CDw3NzeKouij6+cQgSfL1gqjSGmaajqdHmBP/ldBIxuGmiexbBSpKAoV0+nOgaeua4VhqDiOdX19rel0unPg6bpOcRyrKApvgadtWyVJ4qVm9HIOwzDUdDr1Fni6rlMQBF7aOjd3qyzL439XtwRB0LcDvgKPJG81gyDQZDLpb7QOYafAk6ap17vXJEmUpqm3H0ljjNI0VZqm3nqyfNd0q+L6PJdhGCpNUyVJ4u1cun30GT7ceTzFNeJjzoh7GitJkn/Um06nCsNQbdsqjuODnWf3WW5xw2OzbasoihQGz8ElDkNpxxuuMAz7+Tt5nisMw51v1qqq6h/v98VdH75qRlGkIAi81nTtqq96rsfDV7sjfbih9P3d8VnTtTuHOq47tU6+7jy261GTetQcR01X61P13A/Ler0+7Pa8fJbf76v7l2F/r2kaWWv74LN7vX8/rsd0inZg+0+fNX069/N4ipqHrsekZQB7c09p+ZgPMlYu8LieDADjxNUJYG9ZlknSRQeetm37wONrSBzAcAQeAHtzQ1o+nzIaGzdxfeiQFgC/CDwA9uYm6dZ13a9Fc2nckFYcxwQeYMQIPAD2FoahoihS0zQX+wJR94QOPTzAuBF4AOwtDENlWXbRPTzM4QFeBwIPgL25tZYuvYeHwAOMH4EHwN7c4oBN06hpmlNvzklsP5ZO4AHGi8ADYG9uFWb3Tq1L5Hp4mMMDjBuBB8De3CsD2ra92B4e9zJeeniAcTPdpS6eAQAALgY9PAAA4OwReAAAwNkj8AAAgLNH4AEAAGePwAMAAM4egQcAAJw9Ag8AADh7BB4AAHD2CDwAAODsEXgAAMDZI/AAAICz9x8wHETwlVdipgAAAABJRU5ErkJggg==)
From the graph we can analyze that the vertical asymptote of the rational function is x= -3 and x = -4.
Related Questions to study
Maths-
Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....
Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....
Maths-General
Maths-
Write an explicit formula for the arithmetic sequence.
an = 12 - 5n
Write an explicit formula for the arithmetic sequence.
an = 12 - 5n
Maths-General
Maths-
Write an explicit formula for the arithmetic sequence.
an = 8 + 3n
Write an explicit formula for the arithmetic sequence.
an = 8 + 3n
Maths-General
Maths-
Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.
![straight F left parenthesis straight x right parenthesis equals fraction numerator x over denominator x minus 6 end fraction](data:image/png;base64,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)
Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.
![straight F left parenthesis straight x right parenthesis equals fraction numerator x over denominator x minus 6 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Write an explicit formula for the arithmetic sequence.
![a subscript n equals a subscript n minus 1 end subscript plus 2.4 semicolon a subscript 1 equals negative 1](data:image/png;base64,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)
Write an explicit formula for the arithmetic sequence.
![a subscript n equals a subscript n minus 1 end subscript plus 2.4 semicolon a subscript 1 equals negative 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALUAAAARCAYAAACb3u1RAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAkFJREFUeNrtWr9LAzEUDkVExMVBHDociIg4iJuIu0Nx6FocC+Lg7iAdxMXZTRykiAhSpENxK+LgUBAREfEfcChCBxEREc4X+oTzyLW5XH7e3YNvyJE2X768e3l5OUJy022rgAbgHfANeABsxPyPdYCfcR3nADXULzfDdgOoACawvQC4xWc8Rn/3nDs1OQVs5jqotSTieoBHzr5HgGq+mHy6FwB7gG5gW/QMEbWJiw6npvbFmbq0BcZzUU8purcAh4BJFOECUE442DDo4mK7U69gCjLIRjGaewPGO8fnZYvXVpvuFZxo0OqAkgHnsImLDqceA3QwCg+yA8D2kPFYTu2qnol1v8ZoET7QmNiibOKiOlrRyNkErA3pt8iI5L7jesqK9pH9PnFbCuZgH4ZIq+BiY6SeQYee5ejbYfTjHc+mtdWq+xvjQHJvyDlMcxGtf8ZZyHnAMWBckhPJ0tPF2m/k/F8xt/szOrGGIZKmuYjWP3n7T2OOO6JpZ4ijp4u130iu+6Rf/yxgrnUGuIro+0L6N1p3WB7akUzSFi6qnLqFkZo3OscZj3VQjKOnjEqOVWnfLkaQGr7ZXUbZhwrzg290EbAE6CkgagMXX+Ei8KQRspyaV0/XnFooj59iPFvGqBjMz9oaJpCEi2gu6uqNHXXskoCeaZi7kNGaZz3UPkkpFxcXlu5WTxrz9VQYvZXaCrWrKeXi4sIW8SBKcqfmt8vQ1tYk5m6mVHPJ8gdDmZp7j/wvD4XbaeBi8iLBycOXbfYLk7UPgKAaNAEAAAEZdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPmE8L21pPjxtaT5uPC9taT48L21zdWI+PG1vPj08L21vPjxtc3ViPjxtaT5hPC9taT48bXJvdz48bWk+bjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1Yj48bW8+KzwvbW8+PG1uPjIuNDwvbW4+PG1vPjs8L21vPjxtc3ViPjxtaT5hPC9taT48bW4+MTwvbW4+PC9tc3ViPjxtbz49PC9tbz48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21hdGg+1catWwAAAABJRU5ErkJggg==)
Maths-General
Maths-
Write an explicit formula for the arithmetic sequence. ![a subscript n equals a subscript n minus 1 end subscript minus 3 semicolon a subscript 1 equals 10](data:image/png;base64,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)
Write an explicit formula for the arithmetic sequence. ![a subscript n equals a subscript n minus 1 end subscript minus 3 semicolon a subscript 1 equals 10](data:image/png;base64,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)
Maths-General
Maths-
Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.
![straight F left parenthesis straight x right parenthesis equals fraction numerator 6 x over denominator 2 x plus 1 end fraction](data:image/png;base64,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)
Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.
![straight F left parenthesis straight x right parenthesis equals fraction numerator 6 x over denominator 2 x plus 1 end fraction](data:image/png;base64,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)
Maths-General
Maths-
The cost to rent a bike is
28 for the first day plus
2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?
The cost to rent a bike is
28 for the first day plus
2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?
Maths-General
Maths-
The daily attendance at an amusement park after day x is given by the function
f(x) =
. On Approximately which day will the attendance be 1125 people ?
The daily attendance at an amusement park after day x is given by the function
f(x) =
. On Approximately which day will the attendance be 1125 people ?
Maths-General
Maths-
Graph each function and identify the horizontal and vertical asymptotes
![straight F left parenthesis straight x right parenthesis equals fraction numerator 3 x squared minus 11 x minus 4 over denominator 4 x squared minus 25 end fraction](data:image/png;base64,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)
Graph each function and identify the horizontal and vertical asymptotes
![straight F left parenthesis straight x right parenthesis equals fraction numerator 3 x squared minus 11 x minus 4 over denominator 4 x squared minus 25 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ4AAAAqCAYAAABC3uIYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAA+xJREFUeNrtnEFnHVEUgK+nIqpKVFVlUSKqquJRWURUlYqoLip08URFlagnqrrvorqpt4guuqkusyhRURURqqIi6hERWVSU6D/o4i3qecL0nM4ZJpM78+ZO7rv3TN75OMTMnZh773nnnnPu3KOU0I2ApAOyBTIqQyK4pAJSB9mRoRB80JYhEFxzG+S7DIOQ5A7IGshfsky/QN6CXLDwvy+TjzfSw/e/CvISZNdSO1/cJ7+4b9gAmQEZiF2rgqxbUIhVUr5esgQyn2PS8rbzwTmQn/2meGm0Tmjp0IqedxxJ22znkvcgT0TxwqVxX3MdB+eN5vpruheBSnfN8TvbULy8/bPJJMg3xj8KJ1wCeUx+3r2UNjvULgLbv9NMblLKYvHy9M8W6N7sgVzpV8VLKsnzjLbTIIv0993Yr5VDH2y0c9k/tK4LzN0AJwyBPABpUhokja90f9dC9BvkENc+nkn/ir7/GEX8ShTvaJTVzLiPFrFDg8fJattq56J/OL6jonjHaWc4w59oOaqdQsVz1T8bVr4r9ZRoKWvtr3ucxDEKMHTR7heQs2QVt5WdRDMXxfPdv8D2JP4o8NyWo6UMt7MegpxR4aY+7mT8BplLtLtIaZL4RGC2femUKB6H/gUmDbuZSVSgaoGXuAmy6aCzt1S4w9Am2aABT4b9KyDDmuc/UiTIJSIPCrTj0r/AVsOqJnIxYZMUUBCMFK+RyNOY8szQNxRE8f6zTktZxCD5e8Ma/2Kb7seZUHwStEKJFK+ljn71gdwgJzYO+lhTmucHVPpmva3Eq1BSxcua7MOU5xZi6ZK5LpFTR4ZZMLV4hxn3llW4LXOgsnNFHUc/GBG+YmWpjacxUKnmM56XpVYoZPFws3lSc71CqZJZ8u/SkOBCsJpOeaXC77yQRyo845DmCzZkmAVTxdMlkMfJv4uzSAqYRBLIQiHFQzBvF+25DtLyO6Rpt0ZLa4SrLbOyZA6kKoEh3D8SKAtSlaAAT5XZ1lejS7Tbz0hVAsE5UpVAyIXN0/G9rEoQfXXcIl8Sz1rMZvibkjNljM3T8b2uSoBWtEbvjFwnJa8VCCYFz9g6He+jKgGCZ133RPHKRZ7T8ZyrEqQFMqJ4jDE5Hc+1KgEyoeTca6kwOR3PtSoBJvqb6vg+e5TIbpElfhHzCwWPFDkdz60qAe4qfVb6D3Mj8EQe7ixhvb19j66AQBQ5Hc+pKsEIKZ3JttyUktyid0ytDaeqBGi1PqjwMPdJgxCBiTKmWRcuVQkwwFmmJdQUPENzINNcDsXjVpVgNaeftkLRboVkmpRuRqaZv+JxrEqQ1z3AUh9YUwbP0vwhKznu6iX/AbTjy6L9yIGNAAABd3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj5GPC9taT48bW8+KDwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtbj4zPC9tbj48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtbj4xMTwvbW4+PG1pPng8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjQ8L21uPjwvbXJvdz48bXJvdz48bW4+NDwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+MjU8L21uPjwvbXJvdz48L21mcmFjPjwvbWF0aD5YK6m2AAAAAElFTkSuQmCC)
Maths-General
Maths-
Graph each function and identify the horizontal and vertical asymptotes
![r left parenthesis x right parenthesis equals fraction numerator 2 x squared plus 7 over denominator 1 plus 2 x plus x end fraction 2](data:image/png;base64,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)
Graph each function and identify the horizontal and vertical asymptotes
![r left parenthesis x right parenthesis equals fraction numerator 2 x squared plus 7 over denominator 1 plus 2 x plus x end fraction 2](data:image/png;base64,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)
Maths-General
Maths-
Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3
Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3
Maths-General
Maths-
Graph each function and identify the horizontal and vertical asymptotes
![straight F left parenthesis straight x right parenthesis equals fraction numerator 3 over denominator x minus 2 end fraction](data:image/png;base64,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)
Graph each function and identify the horizontal and vertical asymptotes
![straight F left parenthesis straight x right parenthesis equals fraction numerator 3 over denominator x minus 2 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Graph each function and identify the horizontal and vertical asymptotes
![straight F left parenthesis straight x right parenthesis equals to the power of x 2 minus 1](data:image/png;base64,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)
Graph each function and identify the horizontal and vertical asymptotes
![straight F left parenthesis straight x right parenthesis equals to the power of x 2 minus 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFsAAAAQCAYAAAB5qQM2AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAdBJREFUeNpjYCAdZAFxBwnqO6B6aAUOA7EelM0ExDuAWJ5hGACQp46Toe8oUoBQG/gA8XIouw+Ig4ZCQP7HgdEDzYAMs42hKZBW4AIQFwDxbDRxayBeA8SfgPgXVF00jcNRDYhroXbhDWx8wAAa2JRkd2MaeXASEN8AYjY08YNAHAnEPFC+FtQPkTQM7MVAnEYoPAkFdhcQ51DgiDwSy3pigQu0GLkGxKJEqAeV55foVFKQHdigiscWic8BLb+l0dSBPHwGKo8MLIF4L5U9JAtNvTzQSriZSH0/Bntgf8KSTXWAeBua2BYgdsOinw1qBin1Ba66A2beYWgZCePfRSoycAFLCotDqgU2Pg/+waEvB6lpFw8ts3CBXwPcCADltpPQinNQp+w/eORWAbE9NGUJD9LAFgTiDThyHaW5jC7FCAzYQgMyDY9+ahcjpAAlaECr0LkpTXZg78aR/ZigZWc0tLzGV1buHYAUrQFtf3MNQL+F6k2/RiBOhLJjgXgCnrK9i84eFocWcSwD1EmkaqfGFOoZZNAHDXR6dmpwgS3QlM0w1AKbAdqu1kOq2XdDKx50sA1abNCru05OZUdPO4fNQNSwBhkkdru7CLRSRgwAAK1RklyX+LDXAAAA13RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj5GPC9taT48bW8+KDwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbz4pPC9tbz48bXN1cD48bW8+PTwvbW8+PG1pPng8L21pPjwvbXN1cD48bW4+MjwvbW4+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tYXRoPp9tyDIAAAAASUVORK5CYII=)
Maths-General
Maths-
Write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to
.
Write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to
.
Maths-General