messages listlengths 1 1 | ground_truth stringclasses 23 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 4((3(-3|(-3x - 5) + 3| - 3) - 2)/(-2(-3|(-3x - 5) + 3| - 3) - 1))^2 - 2((3(-3|(-3x - 5) + 3| - 3) - 2)/(-2(-3|(-3x - 5) + 3| - 3) - 1)) - 2 and g(x) = 1(1|((2x + 1)/(-1x - 1)) - 1| - 2)^2 - 2(1|... | -1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2cos(2π((-1(1|x + 1| + 3) + 1)/(-2(1|x + 1| + 3) - 3)) - 3) - 2 and g(x) = 2(-2|x - 3| + 2) + 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -1cos(2π(3((3(2|x - 1| + 1) - 3)/(-3(2|x - 1| + 1) - 2))^2 - 4((3(2|x - 1| + 1) - 3)/(-3(2|x - 1| + 1) - 2)) + 1) + 3) - 1 and g(x) = -1sin(3π(2(1x - 1)^2 + 1(1x - 1) - 5) - 3) - 3 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the a... | 6 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2|(-1((3(2x + 1) - 2)/(2(2x + 1) + 3))^2 - 1) - 2| + 2 and g(x) = 1(-1|(1x^2 + 4x - 1) + 1| + 1) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 1e^(-2(-3((1x)/(-1x - 3))^2 - 1((1x)/(-1x - 3)))) - 2 and g(x) = (2(2e^(-1x) - 3) - 2)/(3(2e^(-1x) - 3) + 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) = 2|(-4(-2(2e^(2x) - 2)^2 - 2(2e^(2x) - 2) + 1) + 5) + 3| + 1 and g(x) = 2e^(1(5(-1x - 5)^2 - 2(-1x - 5) - 3)) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Yo... | -5 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 5(-2(2sin(2πx - 1) - 2)^2 - 3(2sin(2πx - 1) - 2) - 3) + 4 and g(x) = (-2(-3|x + 2| + 3) + 3)/(2(-3|x + 2| + 3) + 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) = 5(4(1|((1x - 2)/(3x - 2)) - 2| + 2) - 5)^2 - 4(4(1|((1x - 2)/(3x - 2)) - 2| + 2) - 5) and g(x) = 1(2|(4x^2 + 4) - 2| - 1) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer... | -7 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3|(2(-4x^2 + 5x - 1) + 2) - 3| - 2 and g(x) = (3(-1sin(2πx + 3) - 3) - 1)/(2(-1sin(2πx + 3) - 3) - 1) 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) = 3|(1(2cos(2πx + 1) - 1)^2 + 5(2cos(2πx + 1) - 1) - 3)| and g(x) = -2|(5x^2 + 2) - 3| + 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}",
... | -1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-1(-3(-2x - 3)^2 + 2(-2x - 3) + 1) + 3)/(1(-3(-2x - 3)^2 + 2(-2x - 3) + 1) + 2) and g(x) = 2|(3e^(-1x)) - 3| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 3|(2(-5(-3e^(-1x)) - 3)^2 - 5(-5(-3e^(-1x)) - 3) - 3)| - 2 and g(x) = 2|(-3e^(2((2x)/(-2x + 3))) + 1) + 2| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1cos(2π((2(4(-3|x - 2| - 1) + 3) + 2)/(-2(4(-3|x - 2| - 1) + 3) + 1)) + 2) - 3 and g(x) = -1|(-5(4x + 1)^2 + 3(4x + 1) - 1)| + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2|((-1(-3sin(1πx + 1) - 2) - 2)/(-2(-3sin(1πx + 1) - 2) - 2)) - 1| - 2 and g(x) = -3((-2x - 2)/(-3x - 2))^2 + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | -1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 2|(3e^(1(5(-3x^2 + 2x + 4) + 3))) - 1| - 3 and g(x) = -1e^(-1((-2(3x - 2) + 2)/(-2(3x - 2) + 1))) + 1 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... | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -2|(2sin(1π((1x + 3)/(2x + 1)) - 2) + 2) + 2| + 3 and g(x) = (3(3x - 1))/(3(3x - 1) - 2) intersect 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) = (2(-3(3|(-1sin(2πx + 2) + 1) - 3| - 1)^2 - 2(3|(-1sin(2πx + 2) + 1) - 3| - 1) + 1) - 1)/(-2(-3(3|(-1sin(2πx + 2) + 1) - 3| - 1)^2 - 2(3|(-1sin(2πx + 2) + 1) - 3| - 1) + 1) - 1) and g(x) = (-1(2(2|x + 1| - 1)^2 + 1(2|x ... | -2 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3|(5(-2e^(-1((-1x + 1)/(-2x - 3))) - 2)^2 + 2(-2e^(-1((-1x + 1)/(-2x - 3))) - 2)) - 3| + 2 and g(x) = 5((3(-1x^2 - 2x + 4) - 2)/(2(-1x^2 - 2x + 4) + 2)) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex fo... | -3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (2(4(1(-1sin(1πx + 3) - 1) - 5)^2 + 1(1(-1sin(1πx + 3) - 1) - 5) - 3) - 1)/(-1(4(1(-1sin(1πx + 3) - 1) - 5)^2 + 1(1(-1sin(1πx + 3) - 1) - 5) - 3) + 2) and g(x) = 1((-2(3|x + 3| - 1) - 3)/(-2(3|x + 3| - 1))) + 2 meet in the ... | -3 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3|(2sin(1π((1x)/(2x + 3)) + 2) + 3) + 3| - 1 and g(x) = -1(-2e^(2x) - 1)^2 + 4(-2e^(2x) - 1) + 2 meet 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 largest x-value where the functions f(x) = -1cos(1π(5((2x - 1)/(-2x - 3)) - 3) + 3) - 1 and g(x) = -3e^(-1(1x^2 - 4x + 2)) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -5(-2|(-2((3x + 3)/(1x - 2)) + 1) - 1| - 3)^2 - 4(-2|(-2((3x + 3)/(1x - 2)) + 1) - 1| - 3) - 1 and g(x) = -2|(-2((2x - 1)/(1x)) + 3) + 2| intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: ... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2cos(2π(-1((-3x - 1)/(2x - 1)) + 1) + 2) - 1 and g(x) = -1|(-1x - 5)| - 2 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 rightmost x-coordinate where f(x) = (-1(-1(-1x - 3)^2 - 2(-1x - 3) + 1) + 2)/(1(-1(-1x - 3)^2 - 2(-1x - 3) + 1) + 3) and g(x) = (1(-2x^2 + 4x - 4) + 1)/(3(-2x^2 + 4x - 4) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\bo... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-2(2(-2|(-3x - 3) + 3| + 3)^2 - 2(-2|(-3x - 3) + 3| + 3) + 4) + 3)/(-2(2(-2|(-3x - 3) + 3| + 3)^2 - 2(-2|(-3x - 3) + 3| + 3) + 4) - 1) and g(x) = -2|(-3((-3x - 3)/(3x + 2)) - 3) - 3| + 3 intersect in the interval [-10, ... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-1(-3|(-4(2x^2 + 3x + 1) + 2) - 3| + 3) - 3)/(1(-3|(-4(2x^2 + 3x + 1) + 2) - 3| + 3) - 2) and g(x) = -2(-1((1x - 1)/(1x - 2))^2 - 2) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxe... | -1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -1(3((3(3|x + 3| - 1) + 1)/(2(3|x + 3| - 1) + 2)) + 4)^2 - 5(3((3(3|x + 3| - 1) + 1)/(2(3|x + 3| - 1) + 2)) + 4) + 4 and g(x) = 4(-1e^(2(2x^2 + 2x + 2))) + 3 in the interval [-10, 10], rounded to the near... | 0 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 2((1(-3(-2|x - 1| - 2)^2 + 4) - 3)/(-1(-3(-2|x - 1| - 2)^2 + 4))) + 3 and g(x) = 3e^(-2((-2(-1x^2 + 5x - 4) + 1)/(-3(-1x^2 + 5x - 4) + 1))) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format... | 5 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2(4(-1|((3x - 3)/(-2x + 3)) - 3| - 2) + 3)^2 - 1(4(-1|((3x - 3)/(-2x + 3)) - 3| - 2) + 3) + 5 and g(x) = -4(3|(1x + 4) + 2| + 3)^2 + 2(3|(1x + 4) + 2| + 3) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer i... | -2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2(1|((1x + 2)/(-3x - 3)) - 3| + 3) + 2 and g(x) = -1|(2x^2 + 2x + 1) - 3| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -3|((-3(1(-2e^(-2x)) + 5) + 1)/(3(1(-2e^(-2x)) + 5))) - 1| and g(x) = 5((-2(-1e^(-1x) - 1) + 3)/(-1(-1e^(-1x) - 1) - 3)) + 2 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 leftmost x-coordinate where f(x) = 1|(-4(4((1x - 2)/(1x + 3))^2 - 5) + 5)| + 1 and g(x) = 1sin(3π(1(-1|x + 1| - 2) + 5) + 2) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3e^(-1((1(2(-2x^2 + 5x + 2) + 1) - 3)/(3(2(-2x^2 + 5x + 2) + 1) + 2))) + 1 and g(x) = -2(1|((3x + 2)/(-2x + 3)) + 1| - 1)^2 - 2(1|((3x + 2)/(-2x + 3)) + 1| - 1) + 3 meet in the interval [-10, 1... | 2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1(-1((3(2|x| - 1) - 1)/(1(2|x| - 1))) + 2)^2 + 2(-1((3(2|x| - 1) - 1)/(1(2|x| - 1))) + 2) - 1 and g(x) = -3e^(2((2(5x + 2))/(3(5x + 2) + 2))) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -1|(5(1((2x + 3)/(1x))^2 + 3((2x + 3)/(1x)) - 2) + 5) - 1| + 2 and g(x) = -4(1(1|x + 1| - 1)^2 + 3(1|x + 1| - 1) - 4) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 5(1|((-2(3x + 5) - 2)/(1(3x + 5) + 3)) - 3|)^2 - 1(1|((-2(3x + 5) - 2)/(1(3x + 5) + 3)) - 3|) + 5 and g(x) = 5(2|(-3x - 5) - 3| + 2)^2 + 5(2|(-3x - 5) - 3| + 2) - 2 intersect in the interval [-10, 10]?\n\nPresent the ans... | -3 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3(1|((-1x - 1)/(-3x - 2)) + 1| + 2) - 3 and g(x) = 4((2x - 3)/(-3x + 1)) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1(5(1sin(2π((2x - 3)/(-2x + 3)) - 3) + 3)^2 + 4(1sin(2π((2x - 3)/(-2x + 3)) - 3) + 3) - 2) - 1 and g(x) = 5(2|((-3x + 3)/(-3x - 3)) + 2| + 2)^2 - 5(2|((-3x + 3)/(-3x - 3)) + 2| + 2) meet in the ... | 0 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 4(-5(2|((-2x - 3)/(-2x + 1)) - 2| + 1) - 2)^2 - 5(-5(2|((-2x - 3)/(-2x + 1)) - 2| + 1) - 2) - 5 and g(x) = 3(-1|(-2x + 5) - 3| - 2)^2 - 3(-1|(-2x + 5) - 3| - 2) + 5 in the interval [-10, 10], rounded to th... | -9 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 4((-3(3(1|x| + 2) - 3) + 2)/(-2(3(1|x| + 2) - 3) - 2))^2 + 4((-3(3(1|x| + 2) - 3) + 2)/(-2(3(1|x| + 2) - 3) - 2)) and g(x) = 2|(-5(4x + 1)^2 + 1(4x + 1) + 4) - 2| + 3 meet in the interval [-10, ... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -2|((-1(2x^2 - 5x + 2) - 1)/(-1(2x^2 - 5x + 2) - 2)) - 1| - 1 and g(x) = -1|((2x - 1)/(1x)) - 2| - 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 closest to the largest x-value where the functions f(x) = 2((-1(1(3cos(3πx + 3) + 3)^2 - 2(3cos(3πx + 3) + 3) + 3) - 2)/(-2(1(3cos(3πx + 3) + 3)^2 - 2(3cos(3πx + 3) + 3) + 3) + 3)) + 2 and g(x) = (-3(-5(-1x + 1)^2 - 1(-1x + 1) + 5) - 1)/(3(-5(-1x + 1)^2 - 1(-1x + 1) + 5) - 2) meet... | 2 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1|(-5((2(-3x^2 + 3x) + 3)/(3(-3x^2 + 3x) - 1)) + 5) + 1| - 3 and g(x) = 5((2(2x + 1))/(3(2x + 1) + 2))^2 + 1((2(2x + 1))/(3(2x + 1) + 2)) + 5 in the interval [-10, 10], rounded to the nearest integer.\n\n... | 1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1|(-4(5x^2 + 1x - 3) + 2) - 3| + 2 and g(x) = (-2(-1|x - 3| - 2) + 2)/(1(-1|x - 3| - 2) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 3 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2e^(1(3|(-1(2x^2 + 4x - 1) + 5) + 2| + 2)) + 3 and g(x) = -2|((-1(3x) - 2)/(1(3x) - 3))| + 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (2(-3(1e^(-1x) - 1)^2 - 3(1e^(-1x) - 1) + 4) + 1)/(1(-3(1e^(-1x) - 1)^2 - 3(1e^(-1x) - 1) + 4) - 2) and g(x) = 2e^(2(-1x^2 + 4x - 4)) - 1 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) = 3|(-3((1x - 1)/(1x)) - 2) + 3| and g(x) = -5(1|x - 2|)^2 - 4(1|x - 2|) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -3e^(1(3(3|((-1x + 1)/(-1x)) + 3|)^2 + 5(3|((-1x + 1)/(-1x)) + 3|) - 1)) + 3 and g(x) = 1(-2(2|x - 3| - 3)^2 - 3(2|x - 3| - 3) + 2) - 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the an... | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-3(3(3e^(2x) - 2)^2 - 1(3e^(2x) - 2) - 4) + 3)/(2(3(3e^(2x) - 2)^2 - 1(3e^(2x) - 2) - 4) + 2) and g(x) = 2|(-4x^2 + 2x)| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in ... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 2(-1cos(1π((1(3x^2 - 1x + 1) + 1)/(1(3x^2 - 1x + 1) + 2)) - 3) - 1) - 5 and g(x) = -2|(3e^(-2((-3x + 2)/(-2x + 3))) - 1)| + 3 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1|(-2(3sin(1π(-2x + 2) + 1) + 3)^2 - 2(3sin(1π(-2x + 2) + 1) + 3) - 5) + 2| + 2 and g(x) = 1(-3|(-4x)| - 1)^2 - 2(-3|(-4x)| - 1) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1((-1(-3|(3x - 1) - 2| + 1) - 2)/(-1(-3|(3x - 1) - 2| + 1) + 2))^2 + 3((-1(-3|(3x - 1) - 2| + 1) - 2)/(-1(-3|(3x - 1) - 2| + 1) + 2)) - 3 and g(x) = -5((-3(1sin(2πx + 1) + 1) - 1)/(-1(1sin(2πx + 1) + 1))) + 4 meet in the ... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 1|(3e^(-1(-5x + 3)) - 1) - 2| - 2 and g(x) = (3(-3x^2 + 2x) + 1)/(-1(-3x^2 + 2x)) meet 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) = (1(-1sin(3π(4(1|x - 1| + 1) + 1)) + 3) + 2)/(2(-1sin(3π(4(1|x - 1| + 1) + 1)) + 3) + 1) and g(x) = 3((-2(-1|x + 3| + 1) - 2)/(-1(-1|x + 3| + 1) - 3)) intersect in the interval [-10, 10]?\... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 2(2sin(1π((-2(-1|x - 2| - 2))/(2(-1|x - 2| - 2) + 2)) + 2) + 3) - 1 and g(x) = -1(4(-2|x + 1| - 1)^2 + 5(-2|x + 1| - 1) - 4) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1|(2(-2x^2 + 5x + 1) + 3) - 3| + 1 and g(x) = (3(3|x + 2| - 3) + 2)/(1(3|x + 2| - 3) + 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 4(5((2x + 2)/(-3x - 2))^2 + 3((2x + 2)/(-3x - 2)) - 3) + 2 and g(x) = 2|((-2x + 3)/(2x)) - 1| meet 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) = -1|(-1((-1(-5x^2 + 5x - 2) - 1)/(1(-5x^2 + 5x - 2))) + 3) + 2| - 1 and g(x) = -1(3|(-2e^(1x)) + 1| - 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 second x-coordinate (rounded to the nearest integer) where f(x) = -5(1((-3(1sin(3πx + 3) + 1) - 2)/(2(1sin(3πx + 3) + 1) - 3)) - 3)^2 + 5(1((-3(1sin(3πx + 3) + 1) - 2)/(2(1sin(3πx + 3) + 1) - 3)) - 3) - 3 and g(x) = (2(-3(-3x^2 + 2x + 4) - 2) + 2)/(1(-3... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -5(3|(1x + 1) + 3|)^2 + 3(3|(1x + 1) + 3|) + 1 and g(x) = -3sin(2π((1x - 1)/(-1x)) - 2) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-2(4(2|x - 3|) - 4) - 2)/(-3(4(2|x - 3|) - 4)) and g(x) = (-2(-5x - 4) + 2)/(2(-5x - 4) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2|(-2((-2x + 1)/(2x + 3)) - 2) - 3| - 3 and g(x) = 2cos(2π(3x + 1)) - 2 intersect 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) = 4(-5(-1|((-1x + 2)/(-3x + 1)) + 2| + 3)^2 + 5(-1|((-1x + 2)/(-3x + 1)) + 2| + 3) - 5) and g(x) = -3(3|((-2x + 1)/(2x + 2))|) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaT... | -4 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 5(-2cos(1π(-2|x + 3| + 2) + 3) + 3) - 4 and g(x) = (1(2e^(-1x) - 1) + 3)/(-2(2e^(-1x) - 1) + 3) 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 x-coordinate where the graphs of f(x) = 1|(4(1((-1x - 2)/(-1x - 2)))^2 + 3(1((-1x - 2)/(-1x - 2))) + 4) - 1| and g(x) = (2(-1(-1e^(1x) - 1) - 3) + 3)/(-1(-1(-1e^(1x) - 1) - 3) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\bo... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (3(1|(-5x^2 + 4x - 2) + 1| - 3) - 1)/(2(1|(-5x^2 + 4x - 2) + 1| - 3)) and g(x) = 1sin(1π(-1x - 2) - 2) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -4(-1cos(3π(3|(5x + 1) + 1|) + 3) + 2)^2 + 2(-1cos(3π(3|(5x + 1) + 1|) + 3) + 2) - 2 and g(x) = (1(-3|(4x) + 1| - 1) + 1)/(-1(-3|(4x) + 1| - 1) - 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\b... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2(-1((-1x)/(-2x + 3)) + 4)^2 - 5 and g(x) = -1sin(1π((-3x + 2)/(3x - 2)) - 1) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(1sin(1π(3|x + 3| - 2) + 2) - 3) - 2)/(3(1sin(1π(3|x + 3| - 2) + 2) - 3) - 2) and g(x) = -1|(3x - 2) + 1| intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1(-3|(-2((1x + 1)/(-2x + 3))^2 + 3((1x + 1)/(-2x + 3)) + 3) - 3| + 3) + 5 and g(x) = -1(-1(-1e^(-1x) - 2)^2 - 1(-1e^(-1x) - 2) - 1) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 1e^(-1((1(2x^2 - 2x - 1))/(3(2x^2 - 2x - 1) - 2))) - 3 and g(x) = -2(3e^(-2x) - 2) + 5 meet 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 leftmost x-coordinate where f(x) = -4(2|((-2(4x^2 - 4x + 4) + 1)/(2(4x^2 - 4x + 4) + 1)) + 3| - 2) + 2 and g(x) = -4(5(-1e^(-2x) + 2) + 5)^2 + 4(5(-1e^(-2x) + 2) + 5) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 5(-2|((2x + 3)/(1x + 2)) - 2| - 3)^2 - 1(-2|((2x + 3)/(1x + 2)) - 2| - 3) + 3 and g(x) = (2(3x^2 + 3x - 3) - 3)/(-3(3x^2 + 3x - 3) - 2) intersect in the interval [-10, 10]?\n\nPresent the ... | -2 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -5(-3|((-1(4x^2 - 2x) + 3)/(-3(4x^2 - 2x)))| + 3) + 2 and g(x) = (-1(1(-2x - 4)^2 - 4(-2x - 4) + 3) - 1)/(1(1(-2x - 4)^2 - 4(-2x - 4) + 3) + 2) in the interval [-10, 10], rounded to the nearest integer.\n... | 1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 5((1(-3(-2|x - 3| + 1)^2 + 5(-2|x - 3| + 1) + 4))/(-2(-3(-2|x - 3| + 1)^2 + 5(-2|x - 3| + 1) + 4))) - 4 and g(x) = (-2(-3(3x + 4)^2 - 1(3x + 4) + 3) - 3)/(3(-3(3x + 4)^2 - 1(3x + 4) + 3) - 2) meet in the interval [-10, 10]... | -2 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(2|(2cos(1π(1x - 4) + 1) + 2) + 1| + 2) - 3)/(1(2|(2cos(1π(1x - 4) + 1) + 2) + 1| + 2) + 1) and g(x) = (1(-1|(-2e^(1x) + 3) + 1| + 1) + 2)/(-2(-1|(-2e^(1x) + 3) + 1| + 1) - 2) intersect in the interval [-10, 10].\n\... | 1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 4(-2|(-3((3x - 2)/(3x - 2))^2 - 5((3x - 2)/(3x - 2)) - 2) - 1| + 2) and g(x) = -1(-1((2x)/(-3x - 2)) - 2)^2 - 1(-1((2x)/(-3x - 2)) - 2) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2((1(3|(4x^2 + 5x - 4) + 2| + 2) + 3)/(1(3|(4x^2 + 5x - 4) + 2| + 2) - 3)) and g(x) = (-1(-2|(5x + 2) - 3| + 2) - 1)/(2(-2|(5x + 2) - 3| + 2) + 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex forma... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3((-1(2|(3x^2 + 1x - 2) + 1| - 3) + 3)/(3(2|(3x^2 + 1x - 2) + 1| - 3) - 1)) + 2 and g(x) = 3(1|(-2x^2 - 3x - 4) - 3| + 3) - 5 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|(-4((1(-1x + 3) + 2)/(-1(-1x + 3)))^2 + 1((1(-1x + 3) + 2)/(-1(-1x + 3))) - 1) - 3| + 2 and g(x) = -1sin(3π(3|((2x - 2)/(1x + 1))| - 1)) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed... | 4 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 3e^(-1((3(-3(-2|x - 3| - 1)^2 - 1) - 2)/(3(-3(-2|x - 3| - 1)^2 - 1) + 1))) - 1 and g(x) = 1(1|(-3e^(1x) + 2) - 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 largest x-value where the functions f(x) = (1(3(-3|(1x - 3) + 1| - 1)^2 + 3(-3|(1x - 3) + 1| - 1) + 1) - 1)/(-2(3(-3|(1x - 3) + 1| - 1)^2 + 3(-3|(1x - 3) + 1| - 1) + 1) + 1) and g(x) = 1sin(1π((2(-2x^2 + 2x - 1) - 1)/(1(-2x^2 + 2x - 1) - 2))) - 1 meet in the interva... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 5(-4(2|(3sin(1πx - 1) + 3) + 3| - 2) + 3)^2 - 1(-4(2|(3sin(1πx - 1) + 3) + 3| - 2) + 3) and g(x) = 1e^(-1((3(2x^2 - 5x - 4) - 3)/(1(2x^2 - 5x - 4) + 1))) + 2 intersect in the interval [-1... | 3 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1e^(-2(-5((-3x - 2)/(1x + 2))^2 - 5((-3x - 2)/(1x + 2)) - 1)) and g(x) = 2e^(-2(1|x + 1|)) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 3|(-5((2(1x^2 - 3x - 4) - 2)/(-3(1x^2 - 3x - 4) + 2)) + 3) + 3| and g(x) = -2sin(3π(1|(5x - 4) + 1| + 3) + 2) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 5(1sin(2π((-3(-1|x - 3| - 3))/(2(-1|x - 3| - 3) - 3)) - 1) - 1) + 2 and g(x) = -2(2e^(1((-2x)/(-2x - 2)))) - 2 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 rightmost x-coordinate where f(x) = 5(3((1(-3|x| - 3) + 3)/(-2(-3|x| - 3) - 2)) - 1)^2 + 1(3((1(-3|x| - 3) + 3)/(-2(-3|x| - 3) - 2)) - 1) + 3 and g(x) = 1|((3(4x - 5) + 2)/(3(4x - 5) - 2)) - 1| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -5((3(3|(-2x - 5)| + 3) + 2)/(3(3|(-2x - 5)| + 3) - 2))^2 + 2((3(3|(-2x - 5)| + 3) + 2)/(3(3|(-2x - 5)| + 3) - 2)) - 1 and g(x) = 5(1sin(2π(-2|x - 3| - 2)) - 2) - 3 intersect in the interv... | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3|(3(1e^(-1(4x)) + 3)^2 - 1(1e^(-1(4x)) + 3) + 1) + 1| - 2 and g(x) = (-3(4(2sin(3πx - 3) + 1) + 4) + 3)/(-2(4(2sin(3πx - 3) + 1) + 4) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\bo... | 5 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1(-3((-3x + 1)/(-1x))^2 - 1((-3x + 1)/(-1x))) - 4 and g(x) = 2cos(3π((3x + 1)/(3x + 3)) - 2) meet 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) = -1cos(2π(1((-2(-4x^2 + 1x - 1) - 1)/(1(-4x^2 + 1x - 1))) - 2) - 2) - 2 and g(x) = -3((3(-3|x - 1| + 1) + 3)/(1(-3|x - 1| + 1) + 3)) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 2(-1((-2(-1cos(1πx + 3) - 3) + 3)/(2(-1cos(1πx + 3) - 3) - 3))^2 - 3((-2(-1cos(1πx + 3) - 3) + 3)/(2(-1cos(1πx + 3) - 3) - 3)) - 2) + 5 and g(x) = 2|((-2(4x + 1) + 1)/(-2(4x + 1) - 2)) - 3| - 1 intersect in the int... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (3(2|(-2x^2 + 5x) + 1|) - 1)/(1(2|(-2x^2 + 5x) + 1|)) and g(x) = 1|((2x - 3)/(-2x + 1))| + 2 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) = -1((-1(1x) + 3)/(-2(1x) + 1))^2 - 2((-1(1x) + 3)/(-2(1x) + 1)) + 4 and g(x) = 2((1x - 2)/(1x))^2 + 4((1x - 2)/(1x)) + 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex fo... | 4 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (-2(2cos(1π(2x - 1) + 1)) + 1)/(-2(2cos(1π(2x - 1) + 1)) + 1) and g(x) = (1(2x^2 - 4x + 1))/(-2(2x^2 - 4x + 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... | 2 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 4((3(5x^2 - 3x - 1) - 2)/(1(5x^2 - 3x - 1) + 3)) - 3 and g(x) = -3|((2x - 1)/(1x + 3)) - 1| - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2|(4((-3x - 2)/(3x + 2))^2 - 5((-3x - 2)/(3x + 2))) - 2| + 1 and g(x) = 1(2|x + 2| - 1)^2 - 4(2|x + 2| - 1) 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) = (-2(4(-1|(-2e^(-2x)) + 3|)^2 - 3(-1|(-2e^(-2x)) + 3|) - 5) - 3)/(-1(4(-1|(-2e^(-2x)) + 3|)^2 - 3(-1|(-2e^(-2x)) + 3|) - 5) - 2) and g(x) = (-1(2sin(3π(3x + 5) - 3) + 3) + 3)/(1(2sin(3π(3x + 5) - 3) + 3) - 3) meet in the in... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (2(-5(1x - 3)^2 + 1(1x - 3) + 2) - 1)/(1(-5(1x - 3)^2 + 1(1x - 3) + 2) - 3) and g(x) = (1(3e^(1x) - 3) - 3)/(3(3e^(1x) - 3) + 1) meet 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) = -1cos(2π(4((-3x - 3)/(-2x - 1)) + 3) + 3) and g(x) = -3|(-2e^(-1x) + 3) - 3| + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 7