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pretraining/mathematica/algebra/parametric_equations/10628.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=4 t+23, x(t)=-4 t-15$
+Answer:
+$y=8-x$

pretraining/mathematica/algebra/parametric_equations/11755.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=5 \left(80 t^2-280 t+243\right)^2, x(t)=80 t^2-280 t+245$
+Answer:
+$y=5 x^2-20 x+20$

pretraining/mathematica/algebra/parametric_equations/12531.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=4 (17-9 t)^2, x(t)=9 t-15$
+Answer:
+$y=4 x^2-16 x+16$

pretraining/mathematica/algebra/parametric_equations/1274.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=16 \left(9 t^2-90 t+223\right)^2, x(t)=9 t^2-90 t+225$
+Answer:
+$y=16 x^2-64 x+64$

pretraining/mathematica/algebra/parametric_equations/1313.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=27 (t-9)^4, x(t)=3 t^2-54 t+243$
+Answer:
+$y=3 x^2$

pretraining/mathematica/algebra/parametric_equations/13596.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-75 t^2+450 t-666, x(t)=25 t^2-150 t+225$
+Answer:
+$y=9-3 x$

pretraining/mathematica/algebra/parametric_equations/13854.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-72 t+\sqrt{2}-132, x(t)=-6 \sqrt{2} t-11 \sqrt{2}$
+Answer:
+$y=6 \sqrt{2} x+\sqrt{2}$

pretraining/mathematica/algebra/parametric_equations/14615.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=144 (9-2 t)^2, x(t)=2 \sqrt{3} t-9 \sqrt{3}$
+Answer:
+$y=48 x^2$

pretraining/mathematica/algebra/parametric_equations/15056.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\left(175 t^2-1050 t+1573\right)^2, x(t)=25 t^2-150 t+225$
+Answer:
+$y=49 x^2-28 x+4$

pretraining/mathematica/algebra/parametric_equations/15100.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=24 \left(9 t^2+45 t+56\right), x(t)=36 t^2+180 t+225$
+Answer:
+$y=6 x-6$

pretraining/mathematica/algebra/parametric_equations/15827.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-\frac{2}{9} (154 t+345), x(t)=-\frac{22 t}{3}-15$
+Answer:
+$y=\frac{14 x}{3}-\frac{20}{3}$

pretraining/mathematica/algebra/parametric_equations/16060.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=32 t-119, x(t)=4 t-15$
+Answer:
+$y=8 x+1$

pretraining/mathematica/algebra/parametric_equations/16336.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=(3 t+8)^2, x(t)=-3 t-15$
+Answer:
+$y=x^2+14 x+49$

pretraining/mathematica/algebra/parametric_equations/16922.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=101-\frac{117 t}{4}, x(t)=\frac{9 t}{2}-15$
+Answer:
+$y=\frac{7}{2}-\frac{13 x}{2}$

pretraining/mathematica/algebra/parametric_equations/1708.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{36 \left(289 t^2-3570 t+10997\right)^2}{2401}, x(t)=\frac{289 t^2}{49}-\frac{510 t}{7}+225$
+Answer:
+$y=36 x^2-\frac{288 x}{7}+\frac{576}{49}$

pretraining/mathematica/algebra/parametric_equations/1820.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-512 t^2+1920 t-1795, x(t)=64 t^2-240 t+225$
+Answer:
+$y=5-8 x$

pretraining/mathematica/algebra/parametric_equations/18794.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-567 t^2-1890 t-1583, x(t)=81 t^2+270 t+225$
+Answer:
+$y=-7 x-8$

pretraining/mathematica/algebra/parametric_equations/20915.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\left(25 t^2-150 t+216\right)^2, x(t)=25 t^2-150 t+225$
+Answer:
+$y=x^2-18 x+81$

pretraining/mathematica/algebra/parametric_equations/21074.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{16}{625} (165-28 t)^2, x(t)=\frac{16 t}{5}-15$
+Answer:
+$y=\frac{49 x^2}{25}-\frac{378 x}{25}+\frac{729}{25}$

pretraining/mathematica/algebra/parametric_equations/21277.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{1}{343} \left(-68921 t^2+353010 t-453593\right), x(t)=\frac{1681 t^2}{49}-\frac{1230 t}{7}+225$
+Answer:
+$y=-\frac{41 x}{7}-\frac{32}{7}$

pretraining/mathematica/algebra/parametric_equations/21297.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=12 \left(21 t^2+105 t+131\right), x(t)=36 t^2+180 t+225$
+Answer:
+$y=7 x-3$

pretraining/mathematica/algebra/parametric_equations/21566.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=49 t+\frac{551}{5}, x(t)=-7 t-15$
+Answer:
+$y=\frac{26}{5}-7 x$

pretraining/mathematica/algebra/parametric_equations/23122.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{25}{4} \left(9 t^2+6 \left(2 \sqrt{2}-21\right) t-84 \sqrt{2}+449\right), x(t)=\frac{3 t}{\sqrt{2}}-\frac{21}{\sqrt{2}}$
+Answer:
+$y=\frac{25 x^2}{2}+50 x+50$

pretraining/mathematica/algebra/parametric_equations/23380.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-\frac{25 t^2+210 t+443}{\sqrt{2}}, x(t)=\frac{25 t^2}{2}+105 t+\frac{441}{2}$
+Answer:
+$y=-\sqrt{2} x-\sqrt{2}$

pretraining/mathematica/algebra/parametric_equations/23654.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=175 t^2-1050 t+1573, x(t)=25 t^2-150 t+225$
+Answer:
+$y=7 x-2$

pretraining/mathematica/algebra/parametric_equations/24150.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-18 (t+5)^2, x(t)=9 t^2+90 t+225$
+Answer:
+$y=-2 x$

pretraining/mathematica/algebra/parametric_equations/24258.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-35 t-111, x(t)=-5 t-15$
+Answer:
+$y=7 x-6$

pretraining/mathematica/algebra/parametric_equations/24771.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{1}{2} \left(4 t^2-84 t+437\right)^2, x(t)=2 t^2-42 t+\frac{441}{2}$
+Answer:
+$y=2 x^2-8 x+8$

pretraining/mathematica/algebra/parametric_equations/2602.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-2 \left(108 t^2-540 t+679\right), x(t)=36 t^2-180 t+225$
+Answer:
+$y=-6 x-8$

pretraining/mathematica/algebra/parametric_equations/26992.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-\frac{396 t^2+2772 t+4847}{2 \sqrt{2}}, x(t)=18 t^2+126 t+\frac{441}{2}$
+Answer:
+$y=\sqrt{2}-\frac{11 x}{\sqrt{2}}$

pretraining/mathematica/algebra/parametric_equations/29499.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=63 t^2-630 t+1578, x(t)=9 t^2-90 t+225$
+Answer:
+$y=7 x+3$

pretraining/mathematica/algebra/parametric_equations/29749.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=48 t^2+360 t+674, x(t)=16 t^2+120 t+225$
+Answer:
+$y=3 x-1$

pretraining/mathematica/algebra/parametric_equations/29994.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=20 (2 t-7), x(t)=2 \sqrt{5} t-7 \sqrt{5}$
+Answer:
+$y=4 \sqrt{5} x$

pretraining/mathematica/algebra/parametric_equations/3241.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-112 t^2-840 t-1567, x(t)=16 t^2+120 t+225$
+Answer:
+$y=8-7 x$

pretraining/mathematica/algebra/parametric_equations/32760.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=4 (14 t+27)^2, x(t)=-7 t-15$
+Answer:
+$y=16 x^2+48 x+36$

pretraining/mathematica/algebra/parametric_equations/32786.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{169}{625} (48 t+85)^2, x(t)=-\frac{39 t}{5}-15$
+Answer:
+$y=\frac{256 x^2}{25}+\frac{608 x}{25}+\frac{361}{25}$

pretraining/mathematica/algebra/parametric_equations/33456.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=100 \left(18 t^2-90 t+113\right)^2, x(t)=36 t^2-180 t+225$
+Answer:
+$y=25 x^2+50 x+25$

pretraining/mathematica/algebra/parametric_equations/34731.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=7 t+104, x(t)=-t-15$
+Answer:
+$y=-7 x-1$

pretraining/mathematica/algebra/parametric_equations/34846.txt

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

pretraining/mathematica/algebra/parametric_equations/35369.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-\frac{9}{25} (16 t+85), x(t)=-\frac{16 t}{5}-15$
+Answer:
+$y=\frac{9 x}{5}-\frac{18}{5}$

pretraining/mathematica/algebra/parametric_equations/36032.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{4}{625} (416 t+995)^2, x(t)=-\frac{32 t}{5}-15$
+Answer:
+$y=\frac{676 x^2}{25}-\frac{416 x}{25}+\frac{64}{25}$

pretraining/mathematica/algebra/parametric_equations/37748.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{1}{16} (78-29 t)^2, x(t)=\frac{29 t}{4}-15$
+Answer:
+$y=x^2-9 x+\frac{81}{4}$

pretraining/mathematica/algebra/parametric_equations/38426.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\frac{3}{8} (39 t+238), x(t)=-\frac{9 t}{4}-15$
+Answer:
+$y=-\frac{13 x}{2}-\frac{33}{4}$

pretraining/mathematica/algebra/parametric_equations/39102.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-7 \left(7 t^2+30 t+33\right), x(t)=49 t^2+210 t+225$
+Answer:
+$y=-x-6$

pretraining/mathematica/algebra/parametric_equations/40337.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-3 (t+2), x(t)=-3 t-15$
+Answer:
+$y=x+9$

pretraining/mathematica/algebra/parametric_equations/40705.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-3 t^2+90 t-\frac{1341}{2}, x(t)=t^2-30 t+225$
+Answer:
+$y=\frac{9}{2}-3 x$

pretraining/mathematica/algebra/parametric_equations/40868.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-4 t-\frac{5}{\sqrt{2}}+\frac{21}{2}, x(t)=4 \sqrt{2} t-\frac{21}{\sqrt{2}}$
+Answer:
+$y=-\frac{x}{\sqrt{2}}-\frac{5}{\sqrt{2}}$

pretraining/mathematica/algebra/parametric_equations/41195.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=-18 \left(8 t^2-60 t+113\right), x(t)=16 t^2-120 t+225$
+Answer:
+$y=-9 x-9$

pretraining/mathematica/algebra/parametric_equations/41453.txt

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+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=\sqrt{2} \left(54 t^2-396 t+721\right), x(t)=18 t^2-132 t+242$
+Answer:
+$y=3 \sqrt{2} x-5 \sqrt{2}$

pretraining/mathematica/algebra/parametric_equations/41544.txt

@@ -0,0 +1,5 @@
+Problem:
+Solve for $y=f(x)$ given the following parametric equations:
+$y(t)=9 \left(12 t^2+120 t+299\right)^2, x(t)=9 t^2+90 t+225$
+Answer:
+$y=16 x^2-24 x+9$