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