diff --git a/pretraining/mathematica/algebra/parametric_equations/10628.txt b/pretraining/mathematica/algebra/parametric_equations/10628.txt new file mode 100644 index 0000000000000000000000000000000000000000..6f93d998009c094f55502e552b908a93bc2f0168 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/10628.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=4 t+23, x(t)=-4 t-15$ +Answer: +$y=8-x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/11755.txt b/pretraining/mathematica/algebra/parametric_equations/11755.txt new file mode 100644 index 0000000000000000000000000000000000000000..e727980128a733ae0a9d8e21ce11f3f272768061 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/11755.txt @@ -0,0 +1,5 @@ +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: +$y=5 x^2-20 x+20$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/12531.txt b/pretraining/mathematica/algebra/parametric_equations/12531.txt new file mode 100644 index 0000000000000000000000000000000000000000..495839d30ada18102d07247d5eba4c180fe9ec32 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/12531.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=4 (17-9 t)^2, x(t)=9 t-15$ +Answer: +$y=4 x^2-16 x+16$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/1274.txt b/pretraining/mathematica/algebra/parametric_equations/1274.txt new file mode 100644 index 0000000000000000000000000000000000000000..47fa5ef4bb4f4ac55430d6a895d16aa6266c23d4 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/1274.txt @@ -0,0 +1,5 @@ +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: +$y=16 x^2-64 x+64$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/1313.txt b/pretraining/mathematica/algebra/parametric_equations/1313.txt new file mode 100644 index 0000000000000000000000000000000000000000..6660b51b47a4e2c03a39ec1ebcccd94a2986420f --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/1313.txt @@ -0,0 +1,5 @@ +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: +$y=3 x^2$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/13596.txt b/pretraining/mathematica/algebra/parametric_equations/13596.txt new file mode 100644 index 0000000000000000000000000000000000000000..5c5712d6e66b5ca2818ccb0ce83e516e710b7cba --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/13596.txt @@ -0,0 +1,5 @@ +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: +$y=9-3 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/13854.txt b/pretraining/mathematica/algebra/parametric_equations/13854.txt new file mode 100644 index 0000000000000000000000000000000000000000..1cb8e5d0af4d49c804531441cd68f891d21659bf --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/13854.txt @@ -0,0 +1,5 @@ +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: +$y=6 \sqrt{2} x+\sqrt{2}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/14615.txt b/pretraining/mathematica/algebra/parametric_equations/14615.txt new file mode 100644 index 0000000000000000000000000000000000000000..ff9e414c6c6047e2b0ae0454b63115f25e59e26b --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/14615.txt @@ -0,0 +1,5 @@ +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: +$y=48 x^2$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/15056.txt b/pretraining/mathematica/algebra/parametric_equations/15056.txt new file mode 100644 index 0000000000000000000000000000000000000000..a6a4513fa81fe6d2b079120f6e6d41bbda5e2a02 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/15056.txt @@ -0,0 +1,5 @@ +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: +$y=49 x^2-28 x+4$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/15100.txt b/pretraining/mathematica/algebra/parametric_equations/15100.txt new file mode 100644 index 0000000000000000000000000000000000000000..da2acd3df7356f713ca96a3e0ffc878a8310c868 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/15100.txt @@ -0,0 +1,5 @@ +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: +$y=6 x-6$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/15827.txt b/pretraining/mathematica/algebra/parametric_equations/15827.txt new file mode 100644 index 0000000000000000000000000000000000000000..005b100efafd3492f411da843e28f99785d7874f --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/15827.txt @@ -0,0 +1,5 @@ +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: +$y=\frac{14 x}{3}-\frac{20}{3}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/16060.txt b/pretraining/mathematica/algebra/parametric_equations/16060.txt new file mode 100644 index 0000000000000000000000000000000000000000..9123f4c8ae18dff5301672b2d84719218bb84429 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/16060.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=32 t-119, x(t)=4 t-15$ +Answer: +$y=8 x+1$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/16336.txt b/pretraining/mathematica/algebra/parametric_equations/16336.txt new file mode 100644 index 0000000000000000000000000000000000000000..3f135c27d2c929fac9b89646295cbf65d8063687 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/16336.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=(3 t+8)^2, x(t)=-3 t-15$ +Answer: +$y=x^2+14 x+49$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/16922.txt b/pretraining/mathematica/algebra/parametric_equations/16922.txt new file mode 100644 index 0000000000000000000000000000000000000000..eed8f35521c5811b43bfa1b730be02548e65471b --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/16922.txt @@ -0,0 +1,5 @@ +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: +$y=\frac{7}{2}-\frac{13 x}{2}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/1708.txt b/pretraining/mathematica/algebra/parametric_equations/1708.txt new file mode 100644 index 0000000000000000000000000000000000000000..3233c68981fda50129dece6b31f0e4efe6abd784 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/1708.txt @@ -0,0 +1,5 @@ +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: +$y=36 x^2-\frac{288 x}{7}+\frac{576}{49}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/1820.txt b/pretraining/mathematica/algebra/parametric_equations/1820.txt new file mode 100644 index 0000000000000000000000000000000000000000..affc6d170cdf6c482fc603e9c9e8f8c228284efe --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/1820.txt @@ -0,0 +1,5 @@ +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: +$y=5-8 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/18794.txt b/pretraining/mathematica/algebra/parametric_equations/18794.txt new file mode 100644 index 0000000000000000000000000000000000000000..46cb2dc1e9251ee54f7c5bef7e66eb46ee9d099d --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/18794.txt @@ -0,0 +1,5 @@ +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: +$y=-7 x-8$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/20915.txt b/pretraining/mathematica/algebra/parametric_equations/20915.txt new file mode 100644 index 0000000000000000000000000000000000000000..cbc9732d2d899146940ddbd4d5d867bd9b7ae6b8 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/20915.txt @@ -0,0 +1,5 @@ +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: +$y=x^2-18 x+81$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/21074.txt b/pretraining/mathematica/algebra/parametric_equations/21074.txt new file mode 100644 index 0000000000000000000000000000000000000000..8e4b9655338316354c56d3f51f7ae78af3f275dc --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/21074.txt @@ -0,0 +1,5 @@ +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: +$y=\frac{49 x^2}{25}-\frac{378 x}{25}+\frac{729}{25}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/21277.txt b/pretraining/mathematica/algebra/parametric_equations/21277.txt new file mode 100644 index 0000000000000000000000000000000000000000..98c65ab3b638d14959e05f72a1f25e2ecb10ec01 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/21277.txt @@ -0,0 +1,5 @@ +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: +$y=-\frac{41 x}{7}-\frac{32}{7}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/21297.txt b/pretraining/mathematica/algebra/parametric_equations/21297.txt new file mode 100644 index 0000000000000000000000000000000000000000..f04131f9990b8fd372f5bc96a1810b635e8abca6 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/21297.txt @@ -0,0 +1,5 @@ +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: +$y=7 x-3$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/21566.txt b/pretraining/mathematica/algebra/parametric_equations/21566.txt new file mode 100644 index 0000000000000000000000000000000000000000..66f9dfabf020cd3df686b8ee9142bcf4d8e4c49a --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/21566.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=49 t+\frac{551}{5}, x(t)=-7 t-15$ +Answer: +$y=\frac{26}{5}-7 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/23122.txt b/pretraining/mathematica/algebra/parametric_equations/23122.txt new file mode 100644 index 0000000000000000000000000000000000000000..9553bfad88dc3e981f4cf047e433d36a079654f1 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/23122.txt @@ -0,0 +1,5 @@ +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: +$y=\frac{25 x^2}{2}+50 x+50$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/23380.txt b/pretraining/mathematica/algebra/parametric_equations/23380.txt new file mode 100644 index 0000000000000000000000000000000000000000..901e31891d72cc9d272c9ebefbe2a67610dbea56 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/23380.txt @@ -0,0 +1,5 @@ +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: +$y=-\sqrt{2} x-\sqrt{2}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/23654.txt b/pretraining/mathematica/algebra/parametric_equations/23654.txt new file mode 100644 index 0000000000000000000000000000000000000000..d04fa1b8bd7362336ba8756b5fb8cf04935047fc --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/23654.txt @@ -0,0 +1,5 @@ +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: +$y=7 x-2$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/24150.txt b/pretraining/mathematica/algebra/parametric_equations/24150.txt new file mode 100644 index 0000000000000000000000000000000000000000..15a93a4a2166fdae49030966e42746c7c4408074 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/24150.txt @@ -0,0 +1,5 @@ +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: +$y=-2 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/24258.txt b/pretraining/mathematica/algebra/parametric_equations/24258.txt new file mode 100644 index 0000000000000000000000000000000000000000..e53aaafe529ed0474188c66164aeba50e1547e51 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/24258.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=-35 t-111, x(t)=-5 t-15$ +Answer: +$y=7 x-6$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/24771.txt b/pretraining/mathematica/algebra/parametric_equations/24771.txt new file mode 100644 index 0000000000000000000000000000000000000000..41a5ad1771fb0c1eaf173063b99d2c195e7aeb1a --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/24771.txt @@ -0,0 +1,5 @@ +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: +$y=2 x^2-8 x+8$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/2602.txt b/pretraining/mathematica/algebra/parametric_equations/2602.txt new file mode 100644 index 0000000000000000000000000000000000000000..02914b07533ab5a4ca54a172cd117b9bb8c7f2a0 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/2602.txt @@ -0,0 +1,5 @@ +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: +$y=-6 x-8$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/26992.txt b/pretraining/mathematica/algebra/parametric_equations/26992.txt new file mode 100644 index 0000000000000000000000000000000000000000..fec9797b4c06853cdf9446324473f63d67686fbd --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/26992.txt @@ -0,0 +1,5 @@ +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: +$y=\sqrt{2}-\frac{11 x}{\sqrt{2}}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/29499.txt b/pretraining/mathematica/algebra/parametric_equations/29499.txt new file mode 100644 index 0000000000000000000000000000000000000000..42e858ee58167c22cf1be32de3f2b5e59807047c --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/29499.txt @@ -0,0 +1,5 @@ +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: +$y=7 x+3$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/29749.txt b/pretraining/mathematica/algebra/parametric_equations/29749.txt new file mode 100644 index 0000000000000000000000000000000000000000..de39dcc4b53dc0591f80ee96ae9807c0fb7cd62d --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/29749.txt @@ -0,0 +1,5 @@ +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: +$y=3 x-1$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/29994.txt b/pretraining/mathematica/algebra/parametric_equations/29994.txt new file mode 100644 index 0000000000000000000000000000000000000000..1043fdfac4d9def05569b6e2aacff7d4ca8de4dd --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/29994.txt @@ -0,0 +1,5 @@ +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: +$y=4 \sqrt{5} x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/3241.txt b/pretraining/mathematica/algebra/parametric_equations/3241.txt new file mode 100644 index 0000000000000000000000000000000000000000..556417c7628fb822cccd6758aa1768ddcbc528b0 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/3241.txt @@ -0,0 +1,5 @@ +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: +$y=8-7 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/32760.txt b/pretraining/mathematica/algebra/parametric_equations/32760.txt new file mode 100644 index 0000000000000000000000000000000000000000..0296e88895b2deeefbcf5d9fa08168ad01adaacc --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/32760.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=4 (14 t+27)^2, x(t)=-7 t-15$ +Answer: +$y=16 x^2+48 x+36$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/32786.txt b/pretraining/mathematica/algebra/parametric_equations/32786.txt new file mode 100644 index 0000000000000000000000000000000000000000..ca193024793c91a25870a9f69c173b9d1f99c231 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/32786.txt @@ -0,0 +1,5 @@ +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: +$y=\frac{256 x^2}{25}+\frac{608 x}{25}+\frac{361}{25}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/33456.txt b/pretraining/mathematica/algebra/parametric_equations/33456.txt new file mode 100644 index 0000000000000000000000000000000000000000..4b700c34e7c4f2835ceebad48aa8b641379e2580 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/33456.txt @@ -0,0 +1,5 @@ +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: +$y=25 x^2+50 x+25$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/34731.txt b/pretraining/mathematica/algebra/parametric_equations/34731.txt new file mode 100644 index 0000000000000000000000000000000000000000..9fc6de3f7777d9c20174bb04cd544f59a75cf141 --- /dev/null +++ b/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: +$y=-7 x-1$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/34846.txt b/pretraining/mathematica/algebra/parametric_equations/34846.txt new file mode 100644 index 0000000000000000000000000000000000000000..c708c8659a6b26a061bd12baecc74f2acc91940e --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/34846.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=4 (t+15)^2, x(t)=-t-15$ +Answer: +$y=4 x^2$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/35369.txt b/pretraining/mathematica/algebra/parametric_equations/35369.txt new file mode 100644 index 0000000000000000000000000000000000000000..7d0269d53ce43c52dd67e8174cea87f93c940366 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/35369.txt @@ -0,0 +1,5 @@ +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: +$y=\frac{9 x}{5}-\frac{18}{5}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/36032.txt b/pretraining/mathematica/algebra/parametric_equations/36032.txt new file mode 100644 index 0000000000000000000000000000000000000000..4cf9d4d6af7210951ef254a742544c768c977df3 --- /dev/null +++ b/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: +$y=\frac{676 x^2}{25}-\frac{416 x}{25}+\frac{64}{25}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/37748.txt b/pretraining/mathematica/algebra/parametric_equations/37748.txt new file mode 100644 index 0000000000000000000000000000000000000000..7358de61d9c846aa8812db2cc0875b8fe24ca16d --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/37748.txt @@ -0,0 +1,5 @@ +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: +$y=x^2-9 x+\frac{81}{4}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/38426.txt b/pretraining/mathematica/algebra/parametric_equations/38426.txt new file mode 100644 index 0000000000000000000000000000000000000000..39edf53b221882dc44bf6cd83f45ebd3f5ae4734 --- /dev/null +++ b/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: +$y=-\frac{13 x}{2}-\frac{33}{4}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/39102.txt b/pretraining/mathematica/algebra/parametric_equations/39102.txt new file mode 100644 index 0000000000000000000000000000000000000000..b9f4d6783a2122ef20af81192c7ce0025d5e08af --- /dev/null +++ b/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: +$y=-x-6$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/40337.txt b/pretraining/mathematica/algebra/parametric_equations/40337.txt new file mode 100644 index 0000000000000000000000000000000000000000..7f8b61d1b3aefd6e28fc8236c2fe971cc37f25b9 --- /dev/null +++ b/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: +$y=x+9$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/40705.txt b/pretraining/mathematica/algebra/parametric_equations/40705.txt new file mode 100644 index 0000000000000000000000000000000000000000..4fe61846f705c40c770cd61578450df15fd803a2 --- /dev/null +++ b/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: +$y=\frac{9}{2}-3 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/40868.txt b/pretraining/mathematica/algebra/parametric_equations/40868.txt new file mode 100644 index 0000000000000000000000000000000000000000..e164d71f015919aef6782dd6e4349d94685c1b35 --- /dev/null +++ b/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: +$y=-\frac{x}{\sqrt{2}}-\frac{5}{\sqrt{2}}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/41195.txt b/pretraining/mathematica/algebra/parametric_equations/41195.txt new file mode 100644 index 0000000000000000000000000000000000000000..f43b78b9e5b6db6d0e63b6e7c2324646b360ec9a --- /dev/null +++ b/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: +$y=-9 x-9$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/41453.txt b/pretraining/mathematica/algebra/parametric_equations/41453.txt new file mode 100644 index 0000000000000000000000000000000000000000..fd01bb024ecfbcc4e6bd919a1588547c358daa5a --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/41453.txt @@ -0,0 +1,5 @@ +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: +$y=3 \sqrt{2} x-5 \sqrt{2}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/41544.txt b/pretraining/mathematica/algebra/parametric_equations/41544.txt new file mode 100644 index 0000000000000000000000000000000000000000..3aa993b57e64443c41254916215aa8e1d88c61af --- /dev/null +++ b/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: +$y=16 x^2-24 x+9$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/41913.txt b/pretraining/mathematica/algebra/parametric_equations/41913.txt new file mode 100644 index 0000000000000000000000000000000000000000..2341aef1619bef5310eeed63597bbb5ec24555ae --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/41913.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=4 \left(25 t^2-150 t+229\right)^2, x(t)=25 t^2-150 t+225$ +Answer: +$y=4 x^2+32 x+64$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/41919.txt b/pretraining/mathematica/algebra/parametric_equations/41919.txt new file mode 100644 index 0000000000000000000000000000000000000000..8716ef3b5993f0c15e999de614c137513f3dfb92 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/41919.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=-24 (t-5), x(t)=3 t-15$ +Answer: +$y=-8 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/43299.txt b/pretraining/mathematica/algebra/parametric_equations/43299.txt new file mode 100644 index 0000000000000000000000000000000000000000..1a2f43c987ea6e3e243c4810ff15932a282f39f8 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/43299.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=32 t^2-480 t+1807, x(t)=4 t^2-60 t+225$ +Answer: +$y=8 x+7$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/43504.txt b/pretraining/mathematica/algebra/parametric_equations/43504.txt new file mode 100644 index 0000000000000000000000000000000000000000..be8d66186922092ab144ad7130bfd164b97e99ab --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/43504.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=\frac{1}{729} \left(6647 t^2-35190 t+46521\right)^2, x(t)=\frac{289 t^2}{9}-170 t+225$ +Answer: +$y=\frac{529 x^2}{9}-\frac{92 x}{3}+4$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/44590.txt b/pretraining/mathematica/algebra/parametric_equations/44590.txt new file mode 100644 index 0000000000000000000000000000000000000000..81017375103b2c92874e1ed6765a49b5f8b28436 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/44590.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=5 \left(5 t^2+\left(6 \sqrt{5}-70\right) t-42 \sqrt{5}+254\right), x(t)=\sqrt{5} t-7 \sqrt{5}$ +Answer: +$y=5 x^2+30 x+45$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/44859.txt b/pretraining/mathematica/algebra/parametric_equations/44859.txt new file mode 100644 index 0000000000000000000000000000000000000000..cb989287b0248abf7728fe94f7a76f8d37f89707 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/44859.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=30 t-73, x(t)=6 t-15$ +Answer: +$y=5 x+2$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/45910.txt b/pretraining/mathematica/algebra/parametric_equations/45910.txt new file mode 100644 index 0000000000000000000000000000000000000000..5c2c018d90ee4912406fcd90023e7f4394cc2249 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/45910.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=\frac{1}{16} \left(-845 t^2+7800 t-17924\right), x(t)=\frac{169 t^2}{16}-\frac{195 t}{2}+225$ +Answer: +$y=\frac{19}{4}-5 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/46063.txt b/pretraining/mathematica/algebra/parametric_equations/46063.txt new file mode 100644 index 0000000000000000000000000000000000000000..ba6fccae51a2f591f28cb3bf40b3fff98a335717 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/46063.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=-5 \left(-5 t^2+\left(6 \sqrt{5}-70\right) t+42 \sqrt{5}-254\right), x(t)=-\sqrt{5} t-7 \sqrt{5}$ +Answer: +$y=5 x^2+30 x+45$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/46407.txt b/pretraining/mathematica/algebra/parametric_equations/46407.txt new file mode 100644 index 0000000000000000000000000000000000000000..c24e7df87080b445440e215e4613aa73a55719a9 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/46407.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=-81 t^2+270 t-229, x(t)=81 t^2-270 t+225$ +Answer: +$y=-x-4$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/46881.txt b/pretraining/mathematica/algebra/parametric_equations/46881.txt new file mode 100644 index 0000000000000000000000000000000000000000..a722848bb146424565ab77f78606cd3eba5ee066 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/46881.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=-\frac{4}{3} \left(153 t^2+765 t+958\right), x(t)=36 t^2+180 t+225$ +Answer: +$y=-\frac{17 x}{3}-\frac{7}{3}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/47001.txt b/pretraining/mathematica/algebra/parametric_equations/47001.txt new file mode 100644 index 0000000000000000000000000000000000000000..722fd052f0124914113e9818970c662f10f3aec6 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/47001.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=\frac{7 t}{2}, x(t)=-7 t-15$ +Answer: +$y=-\frac{x}{2}-\frac{15}{2}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/47151.txt b/pretraining/mathematica/algebra/parametric_equations/47151.txt new file mode 100644 index 0000000000000000000000000000000000000000..9943241b6bd3b72c3a38bf1605352d156f220a9b --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/47151.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=-216 t^2+1080 t-1345, x(t)=36 t^2-180 t+225$ +Answer: +$y=5-6 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/47458.txt b/pretraining/mathematica/algebra/parametric_equations/47458.txt new file mode 100644 index 0000000000000000000000000000000000000000..0c24bb421be56b782db0c1f6f0ad257341792def --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/47458.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=-\frac{51}{343} \left(384 t^2-3360 t+7301\right), x(t)=\frac{576 t^2}{49}-\frac{720 t}{7}+225$ +Answer: +$y=\frac{51}{7}-\frac{34 x}{7}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/47785.txt b/pretraining/mathematica/algebra/parametric_equations/47785.txt new file mode 100644 index 0000000000000000000000000000000000000000..49b3e193bafa65536fef348742a5cdf950ae4db4 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/47785.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=76-25 t, x(t)=5 t-15$ +Answer: +$y=1-5 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/47802.txt b/pretraining/mathematica/algebra/parametric_equations/47802.txt new file mode 100644 index 0000000000000000000000000000000000000000..2a579e48bf5746a5c208a30d2d98256886148579 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/47802.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=\frac{9 (110 t+371)^2}{2401}, x(t)=-\frac{30 t}{7}-15$ +Answer: +$y=\frac{121 x^2}{49}+\frac{132 x}{49}+\frac{36}{49}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/48091.txt b/pretraining/mathematica/algebra/parametric_equations/48091.txt new file mode 100644 index 0000000000000000000000000000000000000000..4a642d1176d1815986f78873abc9b2738bf18215 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/48091.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=\frac{1}{25} \left(900 t^2-4500 t+5653\right)^2, x(t)=36 t^2-180 t+225$ +Answer: +$y=25 x^2+56 x+\frac{784}{25}$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/48390.txt b/pretraining/mathematica/algebra/parametric_equations/48390.txt new file mode 100644 index 0000000000000000000000000000000000000000..d75c11f70f7fd2cde811e1dae39e9777732ce5df --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/48390.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=196 (t-2)^2, x(t)=7 t-15$ +Answer: +$y=4 x^2+8 x+4$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/48484.txt b/pretraining/mathematica/algebra/parametric_equations/48484.txt new file mode 100644 index 0000000000000000000000000000000000000000..895603238cb6dc30ea1a5dd24ed296a2863daeb6 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/48484.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=\left(45 t^2+450 t+1123\right)^2, x(t)=9 t^2+90 t+225$ +Answer: +$y=25 x^2-20 x+4$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/48703.txt b/pretraining/mathematica/algebra/parametric_equations/48703.txt new file mode 100644 index 0000000000000000000000000000000000000000..9faae3626bb0142979eb62a5e8a7d18305332e8c --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/48703.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=\frac{1}{16} \left(1125 t^2-4500 t+4504\right)^2, x(t)=\frac{225 t^2}{4}-225 t+225$ +Answer: +$y=25 x^2+10 x+1$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/49006.txt b/pretraining/mathematica/algebra/parametric_equations/49006.txt new file mode 100644 index 0000000000000000000000000000000000000000..05d915f8a8be09111902ba87ef4f857455f704c2 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/49006.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=(31-2 t)^2, x(t)=t-15$ +Answer: +$y=4 x^2-4 x+1$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/49910.txt b/pretraining/mathematica/algebra/parametric_equations/49910.txt new file mode 100644 index 0000000000000000000000000000000000000000..5c92ef274983812d9e2264093dee36b3d63af828 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/49910.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=\frac{4}{729} \left(352 t^2+3960 t+11151\right)^2, x(t)=\frac{64 t^2}{9}+80 t+225$ +Answer: +$y=\frac{121 x^2}{9}+\frac{22 x}{3}+1$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/7782.txt b/pretraining/mathematica/algebra/parametric_equations/7782.txt new file mode 100644 index 0000000000000000000000000000000000000000..55ef19222f9b346dbeac7b7d19fb5eb8980b614c --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/7782.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=46-15 t, x(t)=5 t-15$ +Answer: +$y=1-3 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/8058.txt b/pretraining/mathematica/algebra/parametric_equations/8058.txt new file mode 100644 index 0000000000000000000000000000000000000000..42e8b9442d79fba3d46722f739c5396611c75015 --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/8058.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=20 t+63, x(t)=-5 t-15$ +Answer: +$y=3-4 x$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/8593.txt b/pretraining/mathematica/algebra/parametric_equations/8593.txt new file mode 100644 index 0000000000000000000000000000000000000000..5262e62da7e6ab5aa61c502636b1d0deac6800df --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/8593.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=12 \left(3 t^2+54 t+241\right)^2, x(t)=3 t^2+54 t+243$ +Answer: +$y=12 x^2-48 x+48$ \ No newline at end of file diff --git a/pretraining/mathematica/algebra/parametric_equations/9700.txt b/pretraining/mathematica/algebra/parametric_equations/9700.txt new file mode 100644 index 0000000000000000000000000000000000000000..f4c4c5c865c4bebddc5ae2697294d4f7ec4184fe --- /dev/null +++ b/pretraining/mathematica/algebra/parametric_equations/9700.txt @@ -0,0 +1,5 @@ +Problem: +Solve for $y=f(x)$ given the following parametric equations: +$y(t)=54 \left(338+15 \sqrt{3}\right), x(t)=-9 \sqrt{3}$ +Answer: +$y=75 x^2-90 x+27$ \ No newline at end of file