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