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