messages listlengths 1 1 | ground_truth stringclasses 23
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3e^(1((-2(-1|(-2x)|) - 2)/(-2(-1|(-2x)|) - 2))) - 2 and g(x) = 4(-2(3|x + 1| + 1)^2 + 4(3|x + 1| + 1) - 3) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(-1((1x + 2)/(2x + 2))^2 - 1((1x + 2)/(2x + 2)) - 3) + 3| and g(x) = -1e^(-1(4x - 2)) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (3(1(-1(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) + 3) - 1) + 1)/(-1(1(-1(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) + 3) - 1) - 3) and g(x) = (-3(4(2|x + 3| - 2) + 2) + 1)/(-2(4(2|x + 3| - 2) + 2)) intersect in the interval [-10, 10... | -2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (1(1(3cos(2πx + 3) + 2)^2 + 2) - 3)/(-2(1(3cos(2πx + 3) + 2)^2 + 2) - 3) and g(x) = -1|(1x^2 - 1)| + 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{You... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1(-1|((-2x - 1)/(-3x + 4)) + 1| + 1) - 3 and g(x) = (-2(2x^2 - 3x - 5) + 1)/(-3(2x^2 - 3x - 5) + 2) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your a... | 1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (1(-4(2|(-4x^2 + 5x + 3) - 1|) - 5) - 2)/(-2(-4(2|(-4x^2 + 5x + 3) - 1|) - 5) + 1) and g(x) = 2(2|((1x)/(3x + 1)) - 2| - 3) - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 3e^(-1(1|((-1x + 2)/(1x - 3)) + 2| - 3)) - 1 and g(x) = 5(2|x - 3| + 3) - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-1(-3(3|x| - 2) + 2))/(1(-3(3|x| - 2) + 2) + 3) and g(x) = 3e^(-2((2x + 3)/(1x))) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1|(1((-1(5x - 4) - 1)/(-1(5x - 4) + 2))^2 + 2) - 1| + 1 and g(x) = -5((-2(2e^(-1x) + 1) + 1)/(-1(2e^(-1x) + 1) + 3)) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2e^(2((3(1x - 4) - 1)/(-2(1x - 4)))) + 2 and g(x) = 1(2|x - 3|)^2 - 4(2|x - 3|) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2e^(-1((1(-3|(1x^2 + 3x + 3) + 2| + 1) + 2)/(1(-3|(1x^2 + 3x + 3) + 2| + 1)))) - 1 and g(x) = -5(-4((-2x + 3)/(-3x))^2 - 5((-2x + 3)/(-3x)) + 2) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex fo... | 3 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -3|(-2((-1(3x^2 - 2x - 2))/(-3(3x^2 - 2x - 2) - 2)) - 5)| + 3 and g(x) = -2cos(2π(-1|(3x + 2) + 2| - 2) - 2) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3(1|(-3((-3x)/(1x))^2 + 1((-3x)/(1x))) - 1| - 2) - 2 and g(x) = 1(1((2x + 2)/(3x - 2))^2 + 3((2x + 2)/(3x - 2)) - 5) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -5(-2|((-2(3x^2 - 1x + 2) - 1)/(1(3x^2 - 1x + 2))) - 2| - 1) - 1 and g(x) = 5(1(2|x - 2| - 1)^2 + 4(2|x - 2| - 1) + 5) - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 3 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (3(3(-3|(1x^2 - 2x)| - 3) - 3) - 2)/(1(3(-3|(1x^2 - 2x)| - 3) - 3) + 2) and g(x) = 1|((2(3x - 2) - 3)/(-1(3x - 2) + 2)) - 3| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your ... | 3 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -4(-4(2|((-2x + 2)/(1x)) - 1| + 1)^2 - 4(2|((-2x + 2)/(1x)) - 1| + 1) - 1) - 2 and g(x) = 5(2e^(-1(3x^2 - 1x - 5)) + 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-3(-3|(-3(1x^2) - 4) + 2| + 1) - 1)/(-2(-3|(-3(1x^2) - 4) + 2| + 1)) and g(x) = (3(-2|(-1e^(-1x) + 1) + 1| + 1) + 2)/(3(-2|(-1e^(-1x) + 1) + 1| + 1) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaT... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -4((2(3|x + 3| - 3) + 3)/(2(3|x + 3| - 3) + 1))^2 + 4((2(3|x + 3| - 3) + 3)/(2(3|x + 3| - 3) + 1)) - 2 and g(x) = -2e^(-1((3x + 2)/(1x + 2))) + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format:... | -1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3sin(2π((1(-2|x - 2| - 2) - 1)/(-3(-2|x - 2| - 2) + 2)) - 3) and g(x) = 1((2x - 3)/(1x + 2))^2 - 5((2x - 3)/(1x + 2)) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | -4 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-2(-1(-1|(4x^2 + 2x - 1) - 3|) - 5) + 3)/(2(-1(-1|(4x^2 + 2x - 1) - 3|) - 5) + 1) and g(x) = 4(2(1|x + 2| - 3)^2 + 1(1|x + 2| - 3) + 3) - 5 meet in the interval [-10, 10]?\n\nPresent the answer... | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (2(1|(1(3x - 1)^2 + 4(3x - 1) - 4)| - 3) + 3)/(-3(1|(1(3x - 1)^2 + 4(3x - 1) - 4)| - 3) + 1) and g(x) = -1(-2((3x + 3)/(1x)) + 5)^2 - 5(-2((3x + 3)/(1x)) + 5) - 1 intersect in the interva... | 1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1(4(-2|(-2cos(3πx + 1) - 1)| - 2)^2 - 2(-2|(-2cos(3πx + 1) - 1)| - 2) + 5) and g(x) = -1|(-5((-1x + 2)/(2x + 1)) + 5) + 3| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex for... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3|(4((-3(5x^2 + 4x - 2) - 1)/(2(5x^2 + 4x - 2)))) + 2| - 2 and g(x) = -1|(-3cos(1π(1x^2 + 4) - 1) + 2) + 1| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -2 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(2(1sin(1πx + 2) + 3) - 2) - 3)/(2(2(1sin(1πx + 2) + 3) - 2) + 2) and g(x) = (1(3e^(-1x)) - 3)/(1(3e^(-1x)) + 3) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1(-3e^(1(1(-3x^2 + 3x - 2) + 4)) + 2) + 2)/(-3(-3e^(1(1(-3x^2 + 3x - 2) + 4)) + 2) - 2) and g(x) = -5(2|(-1e^(-1x) + 2) - 2| - 3)^2 - 2(2|(-1e^(-1x) + 2) - 2| - 3) - 5 intersect in the interval [-10, 10]?\n\nPresent the ... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -1((1(-3e^(1(-1x^2 + 4x + 2)) + 2))/(-1(-3e^(1(-1x^2 + 4x + 2)) + 2) - 3)) + 1 and g(x) = -1|(1e^(2(-2x^2 + 4x - 1)) - 2) + 2| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 5 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (3(2(5x^2 - 3x + 2)) - 3)/(3(2(5x^2 - 3x + 2))) and g(x) = -2|(-1e^(-1x)) + 2| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -1cos(3π(-1((1x)/(1x - 3)) - 2) - 3) + 2 and g(x) = -5((3x)/(-3x + 1)) - 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -14 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 5((-3(1x^2 + 3x))/(-3(1x^2 + 3x) + 1)) + 4 and g(x) = -1(-1cos(2πx + 1) + 1)^2 + 5(-1cos(2πx + 1) + 1) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | -3 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (2(-2|(1cos(3π(3x + 4)) - 3)| - 2) - 3)/(-1(-2|(1cos(3π(3x + 4)) - 3)| - 2) + 3) and g(x) = -2e^(-2((3(3x) - 3)/(-3(3x) - 3))) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 4(-1|(2sin(1π(-1x^2 + 1x + 5) - 3)) - 2|) + 3 and g(x) = 2|(-2(1x^2 - 2x - 4) + 2) - 2| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-2(-3|(-5x^2 + 5x - 2)| + 1) - 3)/(1(-3|(-5x^2 + 5x - 2)| + 1) - 3) and g(x) = -1|((-1x + 1)/(-2x - 2)) + 3| + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Y... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -4(2|((-3(-1cos(2πx + 1) - 2) + 1)/(3(-1cos(2πx + 1) - 2))) + 3| + 3) + 4 and g(x) = -3|(1((2x + 2)/(3x + 2))^2 - 4((2x + 2)/(3x + 2)) + 1)| + 2 intersect in the interval [-10, 10]?\n\nPre... | -1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -3|((1(-1(-3e^(-1x) - 3) + 4) + 3)/(2(-1(-3e^(-1x) - 3) + 4) + 2))| + 2 and g(x) = -2((-1(4x + 1) + 1)/(-2(4x + 1)))^2 + 5((-1(4x + 1) + 1)/(-2(4x + 1))) - 2 in the interval [-10, 10], rounded to the near... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1(-1e^(2((1(2|x + 3| - 3) - 2)/(3(2|x + 3| - 3) - 2))) - 2)^2 + 4(-1e^(2((1(2|x + 3| - 3) - 2)/(3(2|x + 3| - 3) - 2))) - 2) + 5 and g(x) = -2(3e^(-2((-2x + 1)/(-3x - 2))) + 3) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-1(1(-2|(-2x - 5) + 1| - 2)^2 + 3(-2|(-2x - 5) + 1| - 2) - 3) - 3)/(2(1(-2|(-2x - 5) + 1| - 2)^2 + 3(-2|(-2x - 5) + 1| - 2) - 3)) and g(x) = 2|((-1(-2cos(1πx - 2) - 3) - 2)/(3(-2cos(1πx - 2) - 3))) - 2| + 3 intersect in ... | -2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 1|(-4(-3(1cos(1πx)) - 3)^2 + 3(-3(1cos(1πx)) - 3) - 4) - 3| + 2 and g(x) = 1|(-2e^(-1(-5x - 4)) - 1) + 2| - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (2(3|(5(1x + 1)^2 - 3(1x + 1) + 4) + 2| + 1) - 3)/(1(3|(5(1x + 1)^2 - 3(1x + 1) + 4) + 2| + 1) + 2) and g(x) = -1((-1(4x - 1))/(1(4x - 1) - 3))^2 + 4((-1(4x - 1))/(1(4x - 1) - 3)) meet in the interval [-10, 10] and round to the nearest... | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 2(3(-1|((-2x + 1)/(2x))| - 2) + 3)^2 + 2(3(-1|((-2x + 1)/(2x))| - 2) + 3) + 5 and g(x) = 2|(3((-3x)/(-1x - 3))^2 + 2((-3x)/(-1x - 3)) - 1) + 2| intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your a... | -2 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -4((2(-2|(1x^2 + 4x - 4)| + 1) - 3)/(-2(-2|(1x^2 + 4x - 4)| + 1) - 2)) - 1 and g(x) = 5((-1(-2|x + 2| + 1) - 3)/(3(-2|x + 2| + 1) + 2))^2 - 4((-1(-2|x + 2| + 1) - 3)/(3(-2|x + 2| + 1) + 2... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(2sin(1π(2x + 1) + 3) + 3) + 1)/(-3(2sin(1π(2x + 1) + 3) + 3) - 1) and g(x) = -1(2|x - 1| - 2)^2 - 5(2|x - 1| - 2) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 2 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(4((1x + 3)/(-1x + 3))^2 - 4((1x + 3)/(-1x + 3)) - 2) - 3| - 2 and g(x) = -2((-3x + 3)/(2x - 1))^2 - 1((-3x + 3)/(2x - 1)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 2 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1(-1|((-3(-2x^2 - 3x + 5) + 2)/(2(-2x^2 - 3x + 5) - 3)) + 3| - 2) - 2 and g(x) = -4(-2(-2e^(-1x) + 3) + 3)^2 + 2(-2(-2e^(-1x) + 3) + 3) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Yo... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 2(-2|(-2sin(2π((3x + 3)/(-3x)))) + 2| + 2)^2 + 2(-2|(-2sin(2π((3x + 3)/(-3x)))) + 2| + 2) + 3 and g(x) = (-2(2|(-3x + 5) - 1| - 2) + 2)/(-3(2|(-3x + 5) - 1| - 2) + 4) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format:... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -4((-1(3|x + 2|))/(-1(3|x + 2|) - 3)) + 3 and g(x) = 5(3|x + 1| + 1)^2 - 5(3|x + 1| + 1) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1(2|(1(-3e^(2x) - 3)^2 - 3(-3e^(2x) - 3)) + 1| + 2) - 1 and g(x) = (-2(1(2x - 3)^2 + 3(2x - 3)) - 2)/(-2(1(2x - 3)^2 + 3(2x - 3)) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Yo... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (3(-1|(3x^2 + 5x + 2) + 2| - 3) - 3)/(-1(-1|(3x^2 + 5x + 2) + 2| - 3) - 1) and g(x) = -1(3|x - 2| - 3)^2 - 2(3|x - 2| - 3) + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in L... | 4 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -2((-2(5(3e^(1x) - 2) + 3) - 1)/(1(5(3e^(1x) - 2) + 3) + 2))^2 - 4((-2(5(3e^(1x) - 2) + 3) - 1)/(1(5(3e^(1x) - 2) + 3) + 2)) + 1 and g(x) = -4(5(-3sin(1πx - 2) + 3) + 3)^2 - 1(5(-3sin(1πx - 2) + 3) + 3) - 3 meet in the inte... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 1|(2e^(-2((-2x + 3)/(1x + 2))) - 3)| + 3 and g(x) = 2e^(-1(2x^2 - 4x - 1)) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3e^(-1(-1(-5((1x + 3)/(1x))^2 - 1((1x + 3)/(1x)) + 4) + 4)) and g(x) = 4(-3e^(-2(3|x + 3| + 2)) + 1) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -5 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 3|((-1(3x - 1) - 1)/(1(3x - 1))) + 1| - 1 and g(x) = (-2(1cos(2πx + 1) + 2) - 1)/(-1(1cos(2πx + 1) + 2)) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(-3|(1x - 1) + 2| + 1) + 2)/(-2(-3|(1x - 1) + 2| + 1) + 1) and g(x) = -2|((3x)/(1x))| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (3(-1(-1x^2 + 2x - 1) - 4) - 1)/(2(-1(-1x^2 + 2x - 1) - 4) - 1) and g(x) = (-2(3e^(-1x) + 2) + 1)/(2(3e^(-1x) + 2) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex... | 3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 1(-4((-1(2|x + 2|) + 1)/(1(2|x + 2|))) + 4)^2 - 3(-4((-1(2|x + 2|) + 1)/(1(2|x + 2|))) + 4) + 4 and g(x) = 1|((2(-4x - 4) + 3)/(1(-4x - 4) - 2)) - 1| - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format... | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (-2(3|(3sin(3π(3x + 5) + 1) - 2) + 2| + 3))/(-3(3|(3sin(3π(3x + 5) + 1) - 2) + 2| + 3) - 3) and g(x) = 3(-2e^(2((3x)/(2x - 1))))^2 + 1(-2e^(2((3x)/(2x - 1)))) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\b... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 2(-2e^(-1(5(3|x + 3| - 2)^2 + 2(3|x + 3| - 2) + 4)) - 2) - 3 and g(x) = -1|(-1(5x + 4)^2 - 2(5x + 4) - 5) + 2| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2(-1|(-4((2x - 1)/(-2x - 3))^2 + 1((2x - 1)/(-2x - 3)) - 1) - 2| - 3) + 1 and g(x) = -2(3((3x + 2)/(-3x + 4)) + 2)^2 - 2(3((3x + 2)/(-3x + 4)) + 2) - 4 meet in the interval [-10, 10]?\n\nPresent... | 2 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -1|((-1(-1(-1x^2 + 1x + 5) - 2))/(-3(-1(-1x^2 + 1x + 5) - 2) - 3)) - 3| + 3 and g(x) = 5(-1|(-1x^2 - 2x - 5) - 1| - 1) + 4 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | -2 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -3|(-1cos(2π((-3x - 2)/(1x)) + 2) - 1) - 3| + 2 and g(x) = (1(-1x + 2) + 2)/(3(-1x + 2) - 2) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -2(2e^(1(-4(-1|x| + 1)^2 - 4(-1|x| + 1) - 3)) - 1) and g(x) = 1|(-1(5x - 2)^2 + 1(5x - 2) + 1) + 1| - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(-1((-1(2x + 3) + 3)/(-2(2x + 3) - 2))^2 + 4((-1(2x + 3) + 3)/(-2(2x + 3) - 2)) + 4) - 1| + 3 and g(x) = 1|(-2e^(-1(-5x + 2)) + 2) + 2| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: ... | -1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1(-3((-3(-2|x| - 1) + 1)/(-3(-2|x| - 1) + 1))^2 - 2((-3(-2|x| - 1) + 1)/(-3(-2|x| - 1) + 1)) + 3) - 4 and g(x) = (3(-5(3|x + 1| - 3) + 5) - 2)/(-2(-5(3|x + 1| - 3) + 5)) meet in the interval [-1... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1|(2((-3(4x^2 + 3x) - 1)/(2(4x^2 + 3x))) - 1) + 1| - 3 and g(x) = 3|(-4(-3cos(1πx - 1))^2 - 2(-3cos(1πx - 1)) - 3) + 1| - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1((3(-1|x + 3| + 2) - 3)/(3(-1|x + 3| + 2) - 2)) + 1 and g(x) = (-1(3e^(-2x)) + 2)/(1(3e^(-2x)) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1|((-3(3x - 4) + 3)/(3(3x - 4) - 1)) + 3| - 1 and g(x) = 2|(3sin(3πx + 3) + 2) + 3| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1(1(3|((-2x - 1)/(2x - 1)) - 3| + 2)^2 - 5(3|((-2x - 1)/(2x - 1)) - 3| + 2)) - 2 and g(x) = 5(-1|(3e^(-1x) - 3) - 3| - 2) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 0 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (2(5(3(-3|x + 3|)^2 - 5(-3|x + 3|) - 1) + 1) - 3)/(3(5(3(-3|x + 3|)^2 - 5(-3|x + 3|) - 1) + 1) + 3) and g(x) = (-1(-1sin(1π(-4x - 3) - 3) - 1) + 2)/(1(-1sin(1π(-4x - 3) - 3) - 1) + 1) intersect in the interval [-10, 10... | -6 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2|((-3(-2(4x - 2)^2 - 1(4x - 2) + 3))/(3(-2(4x - 2)^2 - 1(4x - 2) + 3) - 1)) + 1| - 2 and g(x) = -1|(-4(3x - 1)^2 + 4) + 1| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex fo... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -3(2e^(-1(4((-3x)/(-1x + 2)) + 4)) + 1)^2 + 3(2e^(-1(4((-3x)/(-1x + 2)) + 4)) + 1) + 4 and g(x) = 3e^(1(3|((3x + 2)/(3x - 2)) - 2| - 3)) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -7 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2cos(2π(2|((-3(2x - 3) + 1)/(3(2x - 3) - 1)) - 1| + 2) + 3) - 2 and g(x) = -2e^(2((2(5x^2 + 4x) + 2)/(1(5x^2 + 4x) + 2))) + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex forma... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -4(2((-3(3|x - 2| - 1) - 2)/(3(3|x - 2| - 1) - 2)))^2 + 5(2((-3(3|x - 2| - 1) - 2)/(3(3|x - 2| - 1) - 2))) + 5 and g(x) = -3|(2e^(-2(-2x - 4)) + 2) - 1| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Y... | -2 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -1((1(-2|(3x + 1) - 1| - 2) + 1)/(1(-2|(3x + 1) - 1| - 2) + 2))^2 + 3 and g(x) = 3(3((-2x + 2)/(2x + 2)))^2 + 1(3((-2x + 2)/(2x + 2))) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your ... | 4 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (2(1|(1(-5x + 4)^2 - 1(-5x + 4) + 2) - 3| - 3) + 3)/(-3(1|(1(-5x + 4)^2 - 1(-5x + 4) + 2) - 3| - 3)) and g(x) = -2e^(-1((-3(3|x - 1| + 2) - 2)/(2(3|x - 1| + 2) - 1))) + 2 meet in the interval [-10, 10].\n\nPresent the answ... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -2(-3sin(2π((-2(-1|x + 3| - 2) - 1)/(-3(-1|x + 3| - 2))) - 1))^2 + 5(-3sin(2π((-2(-1|x + 3| - 2) - 1)/(-3(-1|x + 3| - 2))) - 1)) + 4 and g(x) = -3(-1|(-1x^2 - 2x + 2) - 2| + 2) meet in the interval [-10, 10] and round to the nearest in... | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -4((-3(1(-2|x - 1| - 3)^2 + 3) + 2)/(-1(1(-2|x - 1| - 3)^2 + 3) - 2)) - 5 and g(x) = -5(-1((1x + 3)/(-1x + 2)) - 1)^2 - 4(-1((1x + 3)/(-1x + 2)) - 1) + 5 intersect in the interval [-10, 1... | 5 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2|(-1(-1e^(-2x) - 3)^2 - 2)| - 1 and g(x) = (-2(1|x + 3|))/(-1(1|x + 3|) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 3((2(-5(3|x - 2| + 1) + 5) - 1)/(-1(-5(3|x - 2| + 1) + 5) + 2))^2 + 2((2(-5(3|x - 2| + 1) + 5) - 1)/(-1(-5(3|x - 2| + 1) + 5) + 2)) + 2 and g(x) = (2(-3(1|x + 1| + 1) - 5) + 1)/(1(-3(1|x + 1| + 1) - 5) + 2) meet in the inte... | 2 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(-4(-2((2x + 2)/(-3x + 2))^2 + 5((2x + 2)/(-3x + 2)) - 5) + 3) - 3| and g(x) = (1(-1(2x^2 - 3x - 2) + 2) + 2)/(2(-1(2x^2 - 3x - 2) + 2) + 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format:... | 2 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -1(-1|(-1((-1x + 2)/(-2x - 1))^2 + 2) - 2| + 1) - 4 and g(x) = (-2(2(-3x - 5)^2 - 4(-3x - 5)) + 1)/(1(2(-3x - 5)^2 - 4(-3x - 5)) + 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent ... | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (-1(-1|(4(-4x + 1)^2 - 5(-4x + 1) - 4) + 2| - 3) + 1)/(-2(-1|(4(-4x + 1)^2 - 5(-4x + 1) - 4) + 2| - 3) + 3) and g(x) = -3e^(2(1(1x^2 + 4x - 3) - 1)) + 2 intersect in the interval [-10, 10... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2e^(-1(-2((1(-1|x - 1|) - 1)/(3(-1|x - 1|) + 3))^2 + 2((1(-1|x - 1|) - 1)/(3(-1|x - 1|) + 3)))) + 2 and g(x) = (-3(2|(-2x) - 3| - 2))/(3(2|(-2x) - 3| - 2) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer i... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (3(3|(-5(-2x^2 - 1x - 4) - 1) - 3| + 3) - 3)/(-2(3|(-5(-2x^2 - 1x - 4) - 1) - 3| + 3)) and g(x) = -4((1(5x - 4))/(1(5x - 4) + 1))^2 + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Y... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1(1((-2(2|x + 2| - 2) - 3)/(-1(2|x + 2| - 2) + 2))^2 - 5((-2(2|x + 2| - 2) - 3)/(-1(2|x + 2| - 2) + 2)) - 5) + 3 and g(x) = -2(2e^(-1(-5x^2 - 5x + 2)) - 3) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer ... | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -3|(5((2(3x + 2) + 2)/(1(3x + 2) + 3))^2 + 1((2(3x + 2) + 2)/(1(3x + 2) + 3)) + 5) - 1| + 2 and g(x) = (-2(-2|(-3x - 4) - 2| + 3) + 1)/(-2(-2|(-3x - 4) - 2| + 3) - 3) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 2|(2(-2((1x - 2)/(3x + 3)) - 5)^2 + 4(-2((1x - 2)/(3x + 3)) - 5) - 2) - 2| + 2 and g(x) = 5(1(-1|x - 2| + 1) + 4)^2 + 3(1(-1|x - 2| + 1) + 4) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex form... | -4 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -4((-1(3(-1|x|)^2 + 2(-1|x|) + 3) + 3)/(-3(3(-1|x|)^2 + 2(-1|x|) + 3) + 4)) + 2 and g(x) = 2((-3(4x^2 - 5x) - 1)/(-1(4x^2 - 5x) + 2)) + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the ... | 1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (2(1(2e^(2x) - 3)^2 - 3(2e^(2x) - 3) + 5) - 2)/(1(1(2e^(2x) - 3)^2 - 3(2e^(2x) - 3) + 5)) and g(x) = (-3(5x^2 - 2x - 2) - 1)/(-1(5x^2 - 2x - 2) - 1) in the interval [-10, 10], rounded to the nearest integ... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1(-3|(-3(1x^2 + 4x - 4) - 2) - 1| + 3) - 2)/(2(-3|(-3(1x^2 + 4x - 4) - 2) - 1| + 3) - 1) and g(x) = 3|(-3cos(3π(4x - 1) + 2) + 1)| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Y... | -5 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (3(-3e^(1(-3(3|x - 2| - 2) - 1)) - 2) + 3)/(-1(-3e^(1(-3(3|x - 2| - 2) - 1)) - 2) + 2) and g(x) = 3(-2((-2x - 3)/(3x - 2)) - 3)^2 - 4(-2((-2x - 3)/(3x - 2)) - 3) - 4 meet in the interval [-10, 10].\n\nPresent the answer in ... | 3 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1((1(1|(-1x + 1) + 3| + 2) + 3)/(2(1|(-1x + 1) + 3| + 2) - 1))^2 + 4((1(1|(-1x + 1) + 3| + 2) + 3)/(2(1|(-1x + 1) + 3| + 2) - 1)) - 5 and g(x) = (2(3(-1|x - 1| + 1) + 2) - 1)/(1(3(-1|x - 1| + 1) + 2) - 3) meet in the interval [-10, 10]... | 5 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 3|((2(4(-2x^2 - 2x + 2) - 1) + 3)/(-1(4(-2x^2 - 2x + 2) - 1) - 1)) - 2| and g(x) = 2cos(3π(2|((-3x - 3)/(-3x + 4)) - 3| - 3) - 3) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{You... | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(1(1e^(-1x) - 3)) + 3)/(-2(1(1e^(-1x) - 3)) - 3) and g(x) = -2((3x - 1)/(1x + 2))^2 + 4((3x - 1)/(1x + 2)) - 2 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-1(-1cos(2π(2|x - 1| + 3) - 2) + 2))/(1(-1cos(2π(2|x - 1| + 3) - 2) + 2) + 2) and g(x) = -2|((1x + 3)/(1x)) + 3| + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\box... | -1 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -5(-1e^(2(-3|x - 2| - 3)) + 1)^2 - 1(-1e^(2(-3|x - 2| - 3)) + 1) + 2 and g(x) = -4((2x + 1)/(-3x + 2))^2 - 2((2x + 1)/(-3x + 2)) + 4 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent th... | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (3(3(2|x + 3| - 1) - 5))/(2(3(2|x + 3| - 1) - 5) - 3) and g(x) = (2(-3|x - 2| - 2) + 1)/(1(-3|x - 2| - 2) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 3|(1((2(-3x^2 + 2x - 4) + 2)/(3(-3x^2 + 2x - 4) + 2)) + 3) + 1| + 1 and g(x) = 3(4(-2|x + 1|)^2 + 3(-2|x + 1|) - 5) + 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(1|(2cos(3πx + 1) + 3) - 1| + 2) - 1)/(-1(1|(2cos(3πx + 1) + 3) - 1| + 2) - 3) and g(x) = 5(4x^2 + 1x) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (2(3(-3e^(-2(1|x + 1| + 1)) - 1)^2 + 3(-3e^(-2(1|x + 1| + 1)) - 1) + 5) + 3)/(1(3(-3e^(-2(1|x + 1| + 1)) - 1)^2 + 3(-3e^(-2(1|x + 1| + 1)) - 1) + 5)) and g(x) = 1|(-1((-1x - 2)/(-2x)) + 5) - 2| + 1 intersect in the... | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1(3(-1e^(-2((1x)/(-2x - 2))) - 2)^2 + 1(-1e^(-2((1x)/(-2x - 2))) - 2) - 2) + 1 and g(x) = -5(-2|(-1x) + 3| - 3)^2 - 1(-2|(-1x) + 3| - 3) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (-2(-3e^(-2(2x^2 + 4x - 5))) - 1)/(-2(-3e^(-2(2x^2 + 4x - 5))) - 1) and g(x) = (1(2x + 3) - 3)/(3(2x + 3) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
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