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