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