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pretraining/mathematica/algebra/parametric_equations/10338.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-3 t-50, x(t)=-t-15$
+Answer:
+$y=3 x-5$

pretraining/mathematica/algebra/parametric_equations/10464.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\left(147 t^2-630 t+673\right)^2, x(t)=49 t^2-210 t+225$
+Answer:
+$y=9 x^2-12 x+4$

pretraining/mathematica/algebra/parametric_equations/10833.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-32 t+\frac{3}{\sqrt{2}}-84, x(t)=-4 \sqrt{2} t-\frac{21}{\sqrt{2}}$
+Answer:
+$y=4 \sqrt{2} x+\frac{3}{\sqrt{2}}$

pretraining/mathematica/algebra/parametric_equations/11663.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=192 \left(30 t^2+135 t+152\right)^2, x(t)=48 t^2+216 t+243$
+Answer:
+$y=75 x^2+30 x+3$

pretraining/mathematica/algebra/parametric_equations/11865.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-112 \left(4 t^2+15 t+14\right), x(t)=64 t^2+240 t+225$
+Answer:
+$y=7-7 x$

pretraining/mathematica/algebra/parametric_equations/1219.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{592}{5}-\frac{1722 t}{25}, x(t)=\frac{41 t}{5}-15$
+Answer:
+$y=-\frac{42 x}{5}-\frac{38}{5}$

pretraining/mathematica/algebra/parametric_equations/12635.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-\frac{2 \left(49 t^2-364 t+670\right)}{\sqrt{3}}, x(t)=\frac{49 t^2}{3}-\frac{364 t}{3}+\frac{676}{3}$
+Answer:
+$y=4 \sqrt{3}-2 \sqrt{3} x$

pretraining/mathematica/algebra/parametric_equations/13260.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{1}{3} \left(162 t^2+936 t+1349\right)^2, x(t)=27 t^2+156 t+\frac{676}{3}$
+Answer:
+$y=12 x^2-12 x+3$

pretraining/mathematica/algebra/parametric_equations/1350.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-5 (t+15)^2-8, x(t)=t^2+30 t+225$
+Answer:
+$y=-5 x-8$

pretraining/mathematica/algebra/parametric_equations/13732.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{1}{729} \left(1400 t^2+12600 t+28251\right)^2, x(t)=\frac{100 t^2}{9}+100 t+225$
+Answer:
+$y=\frac{196 x^2}{9}-\frac{308 x}{9}+\frac{121}{9}$

pretraining/mathematica/algebra/parametric_equations/14746.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-t-10, x(t)=-t-15$
+Answer:
+$y=x+5$

pretraining/mathematica/algebra/parametric_equations/14813.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=78-10 t, x(t)=2 t-15$
+Answer:
+$y=3-5 x$

pretraining/mathematica/algebra/parametric_equations/14934.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{1}{343} \left(148257 t^2+610470 t+627445\right), x(t)=\frac{2601 t^2}{49}+\frac{1530 t}{7}+225$
+Answer:
+$y=\frac{57 x}{7}-\frac{20}{7}$

pretraining/mathematica/algebra/parametric_equations/15301.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{1}{9} \left(121 t^2+22 \left(5 \sqrt{3}-26\right) t-260 \sqrt{3}+751\right), x(t)=\frac{11 t}{\sqrt{3}}-\frac{26}{\sqrt{3}}$
+Answer:
+$y=\frac{x^2}{3}+\frac{10 x}{3}+\frac{25}{3}$

pretraining/mathematica/algebra/parametric_equations/15477.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{1}{9} (79-40 t)^2, x(t)=\frac{20 t}{3}-15$
+Answer:
+$y=4 x^2+\frac{44 x}{3}+\frac{121}{9}$

pretraining/mathematica/algebra/parametric_equations/15513.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=2 \left(20 t+\sqrt{3}+52\right), x(t)=-\frac{10 t}{\sqrt{3}}-\frac{26}{\sqrt{3}}$
+Answer:
+$y=2 \sqrt{3}-4 \sqrt{3} x$

pretraining/mathematica/algebra/parametric_equations/16335.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-42 t-101, x(t)=-6 t-15$
+Answer:
+$y=7 x+4$

pretraining/mathematica/algebra/parametric_equations/17045.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=20 \left(45 t^2+6 \left(35+\sqrt{5}\right) t+14 \sqrt{5}+246\right), x(t)=-3 \sqrt{5} t-7 \sqrt{5}$
+Answer:
+$y=20 x^2-40 x+20$

pretraining/mathematica/algebra/parametric_equations/18436.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{1}{4} \left(4 t^2-240 t+3605\right)^2, x(t)=\frac{t^2}{4}-15 t+225$
+Answer:
+$y=64 x^2+40 x+\frac{25}{4}$

pretraining/mathematica/algebra/parametric_equations/18477.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{4}{27} \left(162 t^2-936 t+1361\right)^2, x(t)=27 t^2-156 t+\frac{676}{3}$
+Answer:
+$y=\frac{16 x^2}{3}+16 x+12$

pretraining/mathematica/algebra/parametric_equations/21602.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-\sqrt{3} \left(12 t^2+216 t+977\right), x(t)=3 t^2+54 t+243$
+Answer:
+$y=-4 \sqrt{3} x-5 \sqrt{3}$

pretraining/mathematica/algebra/parametric_equations/21759.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{9 t}{4}+1, x(t)=9 t-15$
+Answer:
+$y=\frac{x}{4}+\frac{19}{4}$

pretraining/mathematica/algebra/parametric_equations/21937.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=4 (17-8 t)^2, x(t)=8 t-15$
+Answer:
+$y=4 x^2-16 x+16$

pretraining/mathematica/algebra/parametric_equations/2239.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=9 \left(3 t^2-90 t+673\right)^2, x(t)=t^2-30 t+225$
+Answer:
+$y=81 x^2-108 x+36$

pretraining/mathematica/algebra/parametric_equations/24177.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=243 t^2+810 t+667, x(t)=81 t^2+270 t+225$
+Answer:
+$y=3 x-8$

pretraining/mathematica/algebra/parametric_equations/24193.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-2 \left(256 t^2-960 t+901\right), x(t)=64 t^2-240 t+225$
+Answer:
+$y=-8 x-2$

pretraining/mathematica/algebra/parametric_equations/24562.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=25 t-77, x(t)=5 t-15$
+Answer:
+$y=5 x-2$

pretraining/mathematica/algebra/parametric_equations/25230.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=2 t+27, x(t)=-t-15$
+Answer:
+$y=-2 x-3$

pretraining/mathematica/algebra/parametric_equations/25588.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=39-17 t, x(t)=\frac{17 t}{3}-15$
+Answer:
+$y=-3 x-6$

pretraining/mathematica/algebra/parametric_equations/2676.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=4 t+\sqrt{3}-52, x(t)=\frac{2 t}{\sqrt{3}}-\frac{26}{\sqrt{3}}$
+Answer:
+$y=2 \sqrt{3} x+\sqrt{3}$

pretraining/mathematica/algebra/parametric_equations/27823.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{9}{25} \left(128 t^2+480 t+453\right)^2, x(t)=64 t^2+240 t+225$
+Answer:
+$y=\frac{36 x^2}{25}+\frac{108 x}{25}+\frac{81}{25}$

pretraining/mathematica/algebra/parametric_equations/29440.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=9 (6 t+43)^2, x(t)=-2 t-15$
+Answer:
+$y=81 x^2+108 x+36$

pretraining/mathematica/algebra/parametric_equations/30070.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=35 t+76, x(t)=-7 t-15$
+Answer:
+$y=1-5 x$

pretraining/mathematica/algebra/parametric_equations/30343.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-8 t-21, x(t)=-4 t-15$
+Answer:
+$y=2 x+9$

pretraining/mathematica/algebra/parametric_equations/30823.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=49 (3 t+14)^2, x(t)=-3 t-15$
+Answer:
+$y=49 x^2+98 x+49$

pretraining/mathematica/algebra/parametric_equations/3089.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=25 (16-3 t)^2, x(t)=3 t-15$
+Answer:
+$y=25 x^2-50 x+25$

pretraining/mathematica/algebra/parametric_equations/31225.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\left(63 t^2+630 t+1573\right)^2, x(t)=9 t^2+90 t+225$
+Answer:
+$y=49 x^2-28 x+4$

pretraining/mathematica/algebra/parametric_equations/32233.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{5 (t-24)}{9}, x(t)=\frac{5 t}{3}-15$
+Answer:
+$y=\frac{x}{3}-\frac{25}{3}$

pretraining/mathematica/algebra/parametric_equations/32921.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=4 t+6 \sqrt{2}-44, x(t)=\sqrt{2} t-11 \sqrt{2}$
+Answer:
+$y=2 \sqrt{2} x+6 \sqrt{2}$

pretraining/mathematica/algebra/parametric_equations/33244.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-12 t-\frac{61}{2}, x(t)=-8 t-15$
+Answer:
+$y=\frac{3 x}{2}-8$

pretraining/mathematica/algebra/parametric_equations/33277.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=40-15 t, x(t)=5 t-15$
+Answer:
+$y=-3 x-5$

pretraining/mathematica/algebra/parametric_equations/33568.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\left(8 t^2+240 t+1801\right)^2, x(t)=t^2+30 t+225$
+Answer:
+$y=64 x^2+16 x+1$

pretraining/mathematica/algebra/parametric_equations/33649.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=3 \left(75 t^2+450 t+677\right), x(t)=25 t^2+150 t+225$
+Answer:
+$y=9 x+6$

pretraining/mathematica/algebra/parametric_equations/34079.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=23-10 t, x(t)=5 t-15$
+Answer:
+$y=-2 x-7$

pretraining/mathematica/algebra/parametric_equations/34115.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=4 \left(25 t^2+150 t+227\right)^2, x(t)=25 t^2+150 t+225$
+Answer:
+$y=4 x^2+16 x+16$

pretraining/mathematica/algebra/parametric_equations/34272.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-\frac{13}{3} (t-26), x(t)=\frac{t}{\sqrt{3}}-\frac{26}{\sqrt{3}}$
+Answer:
+$y=-\frac{13 x}{\sqrt{3}}$

pretraining/mathematica/algebra/parametric_equations/34508.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{4}{49} (341 t-1645), x(t)=\frac{22 t}{7}-15$
+Answer:
+$y=\frac{62 x}{7}-\frac{10}{7}$

pretraining/mathematica/algebra/parametric_equations/34828.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{4}{625} (161 t+895)^2, x(t)=-\frac{14 t}{5}-15$
+Answer:
+$y=\frac{529 x^2}{25}-\frac{598 x}{25}+\frac{169}{25}$

pretraining/mathematica/algebra/parametric_equations/36395.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=(44-21 t)^2, x(t)=7 t-15$
+Answer:
+$y=9 x^2+6 x+1$

pretraining/mathematica/algebra/parametric_equations/36405.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-245 t^2+1050 t-1117, x(t)=49 t^2-210 t+225$
+Answer:
+$y=8-5 x$