messages listlengths 1 1 | ground_truth stringclasses 23 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1|((-1(3x^2 + 5x - 3) + 2)/(1(3x^2 + 5x - 3))) + 2| - 1 and g(x) = 3e^(1(2x - 4)) - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-1(-2|(-2(-3x - 3)^2 + 2(-3x - 3))| + 3))/(-1(-2|(-2(-3x - 3)^2 + 2(-3x - 3))| + 3) - 3) and g(x) = -2e^(1(-2(4x + 3)^2 + 4(4x + 3) + 4)) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your ... | -1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 2(4((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3)) - 5) + 2 and g(x) = (-2(2x^2 + 4x - 2) + 2)/(-2(2x^2 + 4x - 2)) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 1 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2((-1(-4(1|x + 1| + 2)^2 - 5(1|x + 1| + 2)))/(-3(-4(1|x + 1| + 2)^2 - 5(1|x + 1| + 2)) + 2)) - 3 and g(x) = (-1(-3|(3e^(1x)) - 3| + 3) + 1)/(-2(-3|(3e^(1x)) - 3| + 3) - 2) in the interval [-10, 10], rounde... | -1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1|((-1(4(1x^2 + 1x - 3) - 5) - 2)/(2(4(1x^2 + 1x - 3) - 5) + 3)) - 1| - 3 and g(x) = -1(-1|(-2e^(1x) + 1) + 3| + 2)^2 + 4(-1|(-2e^(1x) + 1) + 3| + 2) - 3 in the interval [-10, 10], rounded to the nearest ... | 1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -2(1|((3(-3x + 2) - 2)/(-2(-3x + 2) - 2)) + 1| - 2)^2 - 1(1|((3(-3x + 2) - 2)/(-2(-3x + 2) - 2)) + 1| - 2) - 4 and g(x) = (2(1|(-5x^2 + 4x - 1) + 2| - 2) - 2)/(2(1|(-5x^2 + 4x - 1) + 2| - 2) - 1) meet in the interval [-10, 10] and roun... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 4(-5((3(2e^(1x) - 3) - 3)/(-1(2e^(1x) - 3) - 2)) - 5)^2 + 3(-5((3(2e^(1x) - 3) - 3)/(-1(2e^(1x) - 3) - 2)) - 5) + 1 and g(x) = (-2(-3(-3x - 2)^2 + 3(-3x - 2) + 2) + 2)/(-2(-3(-3x - 2)^2 + 3(-3x - 2) + 2) - 1) intersect in... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-3(-2|(5x - 5) - 3| + 3) + 2)/(-3(-2|(5x - 5) - 3| + 3) - 2) and g(x) = -1sin(1π(-1x - 5) + 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 leftmost x-coordinate where f(x) = (-1(-3(-3|x + 2|)^2 - 5(-3|x + 2|) - 3) - 2)/(2(-3(-3|x + 2|)^2 - 5(-3|x + 2|) - 3) + 3) and g(x) = 1(-2e^(-1x))^2 + 3(-2e^(-1x)) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{You... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 4(-1((3(-1|x + 3| + 2) - 2)/(-3(-1|x + 3| + 2) - 2)) - 4)^2 - 3(-1((3(-1|x + 3| + 2) - 2)/(-3(-1|x + 3| + 2) - 2)) - 4) - 3 and g(x) = -5((1(1|x - 2| - 2) - 1)/(-2(1|x - 2| - 2)))^2 + 5((1(1|x - 2| - 2) - 1)/(-2(1|x - 2| ... | -6 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -1|(1cos(1π(-1(3x^2 - 5x + 5) + 4) - 2) + 3) - 2| - 3 and g(x) = 5(1|((1x + 2)/(-2x + 3)) - 1| - 3) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed... | 3 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 2(-2((3(3|x + 2|) - 2)/(3(3|x + 2|) + 2))^2 + 3((3(3|x + 2|) - 2)/(3(3|x + 2|) + 2)) - 2) + 5 and g(x) = (-1(-3(-3e^(2x))^2) - 2)/(1(-3(-3e^(2x))^2) + 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) = (2(-1(1|x - 2| + 3)^2 + 5(1|x - 2| + 3) - 2) - 2)/(-2(-1(1|x - 2| + 3)^2 + 5(1|x - 2| + 3) - 2) - 2) and g(x) = -3e^(1(4x + 1)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 3|(1((-3(-1x - 3) - 1)/(3(-1x - 3) - 2))^2 - 1((-3(-1x - 3) - 1)/(3(-1x - 3) - 2)) + 5) - 1| - 3 and g(x) = (-3(5(-2x^2 + 4x + 1) - 3) - 2)/(3(5(-2x^2 + 4x + 1) - 3) - 1) intersect in the ... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (1(2(-4(-2|x + 2| - 2) - 3)^2 - 3(-4(-2|x + 2| - 2) - 3) + 3) - 3)/(-3(2(-4(-2|x + 2| - 2) - 3)^2 - 3(-4(-2|x + 2| - 2) - 3) + 3)) and g(x) = -2(2((3x + 1)/(1x))^2 - 2((3x + 1)/(1x)) - 3) - 4 intersect in the interval [-... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 3(-2|(1cos(2π((1x - 1)/(-3x - 1)) - 1) - 3) - 3|) - 3 and g(x) = (3(-1(2x^2 + 5x - 3)) + 3)/(2(-1(2x^2 + 5x - 3)) - 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 5(-4((3(-1|x + 1| + 2) + 1)/(3(-1|x + 1| + 2) - 2)) + 4)^2 - 4 and g(x) = 5((1(-1cos(1πx) + 3) + 1)/(-3(-1cos(1πx) + 3) + 1)) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 6 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 2|((-2(-5(-5x - 1)^2 + 5(-5x - 1) + 4) - 1)/(-1(-5(-5x - 1)^2 + 5(-5x - 1) + 4))) - 3| - 1 and g(x) = -3|(-2e^(1(-4x)) - 1) + 1| + 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 rightmost x-coordinate where f(x) = -2cos(2π(-1(-1(3|x - 2| - 2)^2 - 1(3|x - 2| - 2) - 2) + 4) + 2) + 3 and g(x) = -1(2e^(-2(5x - 2)) - 1)^2 - 4(2e^(-2(5x - 2)) - 1) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Yo... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -1(5(1|(2e^(2x) - 1) - 2|) + 3)^2 - 1(5(1|(2e^(2x) - 1) - 2|) + 3) - 3 and g(x) = (-2(-3|(-5x - 1) - 3| + 3) + 2)/(-1(-3|(-5x - 1) - 3| + 3) - 3) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -3cos(1π((-1(-1(-1|x + 3| + 1) + 3) - 3)/(3(-1(-1|x + 3| + 1) + 3) - 2)) - 2) + 1 and g(x) = 2(-1|((1x - 2)/(-2x - 3))| + 3) + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in... | -3 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 2|(-3(2((-1x + 1)/(3x - 2))^2 + 5((-1x + 1)/(3x - 2)) - 1) - 3) + 2| and g(x) = (2(-1|(-3sin(3πx + 3) + 3) - 1| + 1) + 1)/(-1(-1|(-3sin(3πx + 3) + 3) - 1| + 1) + 2) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex f... | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -5(2cos(2π((2(-2|x - 3|) - 1)/(3(-2|x - 3|) + 2)) + 3) + 2)^2 - 1(2cos(2π((2(-2|x - 3|) - 1)/(3(-2|x - 3|) + 2)) + 3) + 2) - 2 and g(x) = (-2(3(-1e^(1x)) + 3) - 3)/(-2(3(-1e^(1x)) + 3) - 2) intersect in the interval [-10, 10]?\n\nPresent the ... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 1|((-3(2cos(3πx - 2) - 3) + 3)/(-3(2cos(3πx - 2) - 3) - 3)) + 2| + 1 and g(x) = (2(2e^(-1x) - 3) - 3)/(-3(2e^(-1x) - 3) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2|(-3(3((-2x + 2)/(3x - 2))^2 + 5((-2x + 2)/(3x - 2)) - 4) - 4)| + 1 and g(x) = (-1(1e^(-2(-3|x + 2| + 3)) - 2) - 1)/(-3(1e^(-2(-3|x + 2| + 3)) - 2) + 1) 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) = (1(1(-1x^2 + 1) + 5) - 3)/(-1(1(-1x^2 + 1) + 5) - 1) and g(x) = (1(-2cos(3πx - 3) - 2) + 3)/(1(-2cos(3πx - 3) - 2) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 2(1(1|(-3e^(1x) + 2)|)^2 + 5(1|(-3e^(1x) + 2)|) - 4) + 2 and g(x) = 1|(-4(3x^2 - 1x + 3) + 1) - 3| + 3 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4((-2(1(-1|x - 1|)^2 - 5(-1|x - 1|) + 5) + 1)/(-2(1(-1|x - 1|)^2 - 5(-1|x - 1|) + 5) + 1)) and g(x) = -3(2e^(2(-4x^2 - 1x + 5)) - 3) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxe... | 1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (-1(-3|(-1e^(2x) + 3) - 3| - 3) - 3)/(-2(-3|(-1e^(2x) + 3) - 3| - 3)) and g(x) = (-1(1x^2 + 1x + 2) + 3)/(-1(1x^2 + 1x + 2) + 2) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in... | -1 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 3e^(1((2(1(-1x + 5)^2 - 2(-1x + 5) + 4) - 2)/(3(1(-1x + 5)^2 - 2(-1x + 5) + 4) + 3))) - 1 and g(x) = -4(-1|((-2x - 3)/(1x + 3))| + 1) - 5 in the interval [-10, 10], rounded to the nearest integer.\n\nPrese... | -5 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (3(2|(-1(-1x^2 + 3x) - 2) - 1| + 3) + 1)/(-3(2|(-1(-1x^2 + 3x) - 2) - 1| + 3) + 2) and g(x) = -1(5(-3e^(-1x) + 3)^2 + 2(-3e^(-1x) + 3) - 1) + 1 intersect 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(1|x|) + 3) + 3)/(3(-5(1|x|) + 3)) and g(x) = -4(1sin(3πx + 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 sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1(2cos(3π(-4(-2|x - 2| + 3)^2 + 1(-2|x - 2| + 3) - 4) + 3) - 2) - 2 and g(x) = -3(1((-2x + 2)/(-2x + 3)) + 5)^2 + 4(1((-2x + 2)/(-2x + 3)) + 5) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex f... | 3 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 5(-2|((-1x - 2)/(-2x)) - 1| + 1) + 1 and g(x) = -1|(-2x^2 - 5x + 4) - 1| - 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 rightmost x-coordinate where f(x) = 2(-2|((2(1cos(3πx - 1) - 3) + 3)/(3(1cos(3πx - 1) - 3) + 1)) - 3| - 2) + 4 and g(x) = -1|((1(-5x - 2) + 2)/(2(-5x - 2) - 3)) - 1| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Yo... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1|(1e^(-1(5x - 1)) - 2)| - 2 and g(x) = -1cos(3π(3x^2 - 4x + 1) + 1) - 2 intersect 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 smallest x-value where the functions f(x) = -1((-1(-2(2|x + 1| + 1)^2 + 1(2|x + 1| + 1) + 5) - 2)/(3(-2(2|x + 1| + 1)^2 + 1(2|x + 1| + 1) + 5) - 1)) + 1 and g(x) = 3|(1(1e^(-1x) + 1) + 1)| - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1(1(-3|x| + 3) + 1) + 1)/(-1(1(-3|x| + 3) + 1) + 3) and g(x) = 4(1|x - 1| - 3)^2 + 2(1|x - 1| - 3) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 4(-3(-3|((-1x - 1)/(3x + 3)) - 2| + 2) - 1)^2 - 3(-3(-3|((-1x - 1)/(3x + 3)) - 2| + 2) - 1) + 2 and g(x) = 3(4((2x - 2)/(-1x - 1)) + 1)^2 - 2 intersect 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|(5x^2 + 2x) + 2| - 1))/(2(-2|(5x^2 + 2x) + 2| - 1) - 1) and g(x) = (-1(-2|x| + 3) - 3)/(-1(-2|x| + 3) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3|((2(-1x))/(3(-1x) + 2)) - 3| + 3 and g(x) = -3sin(1π(1x - 1) - 3) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -4((3(-1e^(1x) - 2) - 2)/(3(-1e^(1x) - 2) + 3)) + 5 and g(x) = (-1(2x) - 3)/(-2(2x) - 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (2(-2e^(-1(2|x - 3|)) + 1) - 1)/(-1(-2e^(-1(2|x - 3|)) + 1) - 3) and g(x) = 1|(5x - 2) - 1| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1sin(2π(2|(-5((1x - 2)/(-3x))^2 - 1((1x - 2)/(-3x)) + 3) - 2| + 1) + 1) and g(x) = 4(1((-3x - 1)/(3x - 2)) - 4)^2 - 5 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in La... | 0 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -4(3((-2(-2|x| + 1) + 3)/(-1(-2|x| + 1) - 3)) + 2)^2 - 3(3((-2(-2|x| + 1) + 3)/(-1(-2|x| + 1) - 3)) + 2) - 2 and g(x) = (-2(3(5x - 3)^2 + 5(5x - 3) - 4) - 3)/(-1(3(5x - 3)^2 + 5(5x - 3) - 4) + 2) intersect in the inter... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3|(-3((-2x - 1)/(3x + 1))^2 - 3((-2x - 1)/(3x + 1)) + 3) + 3| - 2 and g(x) = -1|(3x - 1)| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 4(-1|((3(-1x^2 + 2x - 1) + 3)/(1(-1x^2 + 2x - 1))) - 1| + 3) - 1 and g(x) = -2cos(3π((-2(-3|x + 1| + 3) - 2)/(1(-3|x + 1| + 3) + 1)) + 2) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\... | 2 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -2|(3((-1x - 2)/(-2x + 1))^2 + 4((-1x - 2)/(-2x + 1)) + 1) - 1| - 1 and g(x) = 3cos(2π(1|x| + 1) - 3) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | -2 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1((-3(-3|(5x + 4) - 2| - 2) + 1)/(-1(-3|(5x + 4) - 2| - 2) - 1))^2 - 5((-3(-3|(5x + 4) - 2| - 2) + 1)/(-1(-3|(5x + 4) - 2| - 2) - 1)) - 5 and g(x) = (2(-2sin(3π(4x - 2) - 1) - 2) + 2)/(-3(-2sin(3π(4x - 2) - 1) - 2) + 2) me... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 3((1(3|(3x - 1) - 3| + 1) + 3)/(-2(3|(3x - 1) - 3| + 1) + 3))^2 + 1 and g(x) = 5(-1|(1x) - 3|)^2 + 2(-1|(1x) - 3|) - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex for... | 5 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (1(3|(-5(4x^2 + 2x + 5) - 5) - 1| - 2) + 1)/(2(3|(-5(4x^2 + 2x + 5) - 5) - 1| - 2) + 1) and g(x) = (-2(-1(-3|x - 1| - 1) - 4))/(2(-1(-3|x - 1| - 1) - 4) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex fo... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -3sin(2π(-5(1((1x - 1)/(1x + 2)))^2 + 3(1((1x - 1)/(1x + 2))) - 2) + 2) - 2 and g(x) = 2(-5((-1x + 1)/(-1x))^2 - 1((-1x + 1)/(-1x)) - 1) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\b... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4(1((2(1e^(2x) - 3) - 2)/(-1(1e^(2x) - 3) + 2)) - 5)^2 - 5(1((2(1e^(2x) - 3) - 2)/(-1(1e^(2x) - 3) + 2)) - 5) + 2 and g(x) = -1sin(1π((-1(4x + 4))/(-1(4x + 4) - 2)) + 1) + 1 intersect in the interval [-10, 10]?\n\nPrese... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2(3|((-2x + 1)/(-2x + 1)) - 1| + 3)^2 + 5(3|((-2x + 1)/(-2x + 1)) - 1| + 3) + 5 and g(x) = -2((-2x + 3)/(-2x - 1)) + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -3((-1(-5(-1e^(1x) + 3) + 3) - 1)/(-1(-5(-1e^(1x) + 3) + 3)))^2 + 5((-1(-5(-1e^(1x) + 3) + 3) - 1)/(-1(-5(-1e^(1x) + 3) + 3))) and g(x) = -2|(5((1x + 1)/(1x + 2))^2 - 4((1x + 1)/(1x + 2)))| + 1 meet in the interval [-10, 10... | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 4(-2e^(1((-1x)/(-2x + 3))) + 1)^2 - 4(-2e^(1((-1x)/(-2x + 3))) + 1) - 3 and g(x) = -1cos(1π(1|x| + 1) + 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) = -2|((3(-2(3x + 5)^2 + 3) - 3)/(-2(-2(3x + 5)^2 + 3) + 1)) + 1| - 1 and g(x) = (-3(1(2|x| - 3) - 4))/(-2(1(2|x| - 3) - 4) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in... | 3 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3(2|(4((2x - 1)/(-3x - 1)) + 2)| - 2)^2 + 1(2|(4((2x - 1)/(-3x - 1)) + 2)| - 2) + 5 and g(x) = 1(-1((-2x)/(-1x + 3))^2 - 1) - 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Y... | -1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -4((-3(3x^2 - 4x - 5) - 2)/(-2(3x^2 - 4x - 5) - 3)) + 4 and g(x) = 2|(3sin(1πx + 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1|(-4((1x - 3)/(-1x - 1))^2 + 1((1x - 3)/(-1x - 1)) + 4)| + 3 and g(x) = (-3(2x - 1) + 2)/(1(2x - 1) - 2) meet 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) = -4(3|((3x + 1)/(-2x + 3)) - 3| + 3)^2 - 3(3|((3x + 1)/(-2x + 3)) - 3| + 3) - 1 and g(x) = 2((1x + 3)/(2x + 1)) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 5(-2((-3x - 3)/(1x))^2 + 4((-3x - 3)/(1x)) + 2) - 3 and g(x) = -3((2x - 3)/(1x))^2 + 2((2x - 3)/(1x)) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -2 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-2(2|(1(5x^2 + 1) - 2) - 3|) + 3)/(-3(2|(1(5x^2 + 1) - 2) - 3|)) and g(x) = -2sin(1π((3(2|x + 2| + 1) - 1)/(-2(2|x + 2| + 1) - 2)) + 3) + 1 intersect in the interval [-10, 10]?\n\nPresent... | -3 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 1(-2e^(-2((-3x - 1)/(-3x))) - 1)^2 + 5(-2e^(-2((-3x - 1)/(-3x))) - 1) - 3 and g(x) = 3(-2e^(2x) + 2)^2 - 1(-2e^(2x) + 2) - 3 intersect in the range -10 ≤ x ≤ 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) = (-1(-3|(2(5x - 3)^2 + 4(5x - 3) + 4) - 3|) + 1)/(-1(-3|(2(5x - 3)^2 + 4(5x - 3) + 4) - 3|) - 3) and g(x) = (2(-2|(3x - 4) + 1| - 2) + 1)/(1(-2|(3x - 4) + 1| - 2) + 1) intersect in the int... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(-2e^(-2(-4(-1x^2 - 4x - 4))) - 3) + 3| + 2 and g(x) = -1(-3((2x - 1)/(-1x - 3)) - 2)^2 + 1(-3((2x - 1)/(-1x - 3)) - 2) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your... | 5 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 3(-1cos(3π((3x + 3)/(-1x))) - 3) + 1 and g(x) = (-1(-2e^(1x) + 3) - 2)/(-3(-2e^(1x) + 3) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-3(-1cos(2π(3x^2 - 4x - 5) - 1) + 1))/(1(-1cos(2π(3x^2 - 4x - 5) - 1) + 1)) and g(x) = 3((-3x - 3)/(2x + 1)) - 3 intersect in the range -10 ≤ x ≤ 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|(-4((3x + 1)/(-1x - 1)) + 4) + 1| + 1)^2 + 4(1|(-4((3x + 1)/(-1x - 1)) + 4) + 1| + 1) + 5 and g(x) = (1(1(1|x - 3| + 3) - 1) - 1)/(1(1(1|x - 3| + 3) - 1)) intersect in the interval [-10, 10]?\n\nPresent the answer i... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 3|(1(2sin(2π(1x^2 + 3x + 3) + 1) + 3) + 4) + 3| - 1 and g(x) = -4(-1|(-2e^(-2x)) - 3| + 3) - 5 intersect in the range -10 ≤ x ≤ 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) = -3(-4(1|(3e^(-1x) + 1) + 3| - 3)^2 + 3) + 5 and g(x) = 3(1|(5x^2 + 3x - 2) - 3| - 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 second x-coordinate (rounded to the nearest integer) where f(x) = (2(1(-1|(-2x^2 - 5x - 3)| - 1) + 3))/(-3(1(-1|(-2x^2 - 5x - 3)| - 1) + 3) + 1) and g(x) = 1cos(3π(3|(-3x^2 + 4x + 4) - 2| - 3) + 2) + 3 intersect in the interval [-10, 10]?\n\nPresent the... | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3(2((3(1|x - 1| - 2) - 3)/(-3(1|x - 1| - 2) + 4)) + 1)^2 - 3(2((3(1|x - 1| - 2) - 3)/(-3(1|x - 1| - 2) + 4)) + 1) - 3 and g(x) = -2|(-4(-2e^(2x) + 2) + 4) + 2| + 1 meet in the interval [-10, 10... | 2 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -3|(-1(1((-2x + 2)/(3x + 1)))^2 - 4(1((-2x + 2)/(3x + 1))) + 4) + 2| - 1 and g(x) = 1sin(2π((3(-1|x - 1| + 2) + 1)/(-1(-1|x - 1| + 2) + 3)) + 3) - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\b... | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -2|(1e^(1(1(2x^2 - 1x) + 3)) - 2) + 2| + 3 and g(x) = (1(-1(2e^(2x) - 3)^2) - 1)/(3(-1(2e^(2x) - 3)^2) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\bo... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -2(-2sin(1π((-3(-5x^2 - 2x - 2) + 1)/(3(-5x^2 - 2x - 2) + 1)) - 3) + 1) + 4 and g(x) = 1(-2(-1e^(2x))^2 - 4(-1e^(2x)) + 5) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 4((-1(-2|(-3x^2 - 1x - 2) + 1| + 3) - 3)/(1(-2|(-3x^2 - 1x - 2) + 1| + 3) - 2)) - 2 and g(x) = (-2(-2e^(-1(-2x + 5)) + 2) - 3)/(-1(-2e^(-1(-2x + 5)) + 2) - 3) meet in the interval [-10, 10] and round to the nearest integer, what do you... | 3 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2|((2(2(-3x + 1)^2 + 3(-3x + 1) - 1) + 3)/(-1(2(-3x + 1)^2 + 3(-3x + 1) - 1) - 3)) - 3| + 3 and g(x) = -4((2(-3x + 2) - 2)/(-2(-3x + 2) - 3))^2 - 1((2(-3x + 2) - 2)/(-2(-3x + 2) - 3)) - 2 intersect in the interval [-10,... | 5 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-1(-1(-2|(4x^2 - 3) + 1|) - 5) - 3)/(-3(-1(-2|(4x^2 - 3) + 1|) - 5) - 1) and g(x) = 2sin(2π((-3(2x + 1) + 3)/(2(2x + 1) - 3)) - 2) + 3 intersect 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) = (2(1|(2x - 1) + 3|) - 1)/(-3(1|(2x - 1) + 3|) + 4) and g(x) = (2(3|x| - 1) + 3)/(1(3|x| - 1) + 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2|(4((-1x)/(1x + 3))) + 1| - 1 and g(x) = (-2(-2|x - 2| - 2) - 3)/(-1(-2|x - 2| - 2) - 1) intersect 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) = -3e^(-1(-1|((2x - 3)/(-2x + 3)) + 1| + 3)) - 1 and g(x) = -2(-2x^2 - 4x + 4) - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 3cos(1π(-3(1(-1|x + 2| + 2)^2 - 2(-1|x + 2| + 2) + 5) - 3) - 3) - 1 and g(x) = 5((2(-1e^(-1x) + 2) + 2)/(1(-1e^(-1x) + 2))) - 2 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -3(1e^(-2((-2x + 3)/(-1x - 2))) + 3)^2 - 5(1e^(-2((-2x + 3)/(-1x - 2))) + 3) + 4 and g(x) = (-1(-2x - 1) + 2)/(1(-2x - 1) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -2 | MATH |
[
{
"content": "When ordered from left to right, what is the third x-coordinate (rounded to the nearest integer) where f(x) = 2(1|(1e^(-1x))| - 1) - 5 and g(x) = 2|(2sin(3πx + 2) + 3) - 3| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -1(2((2(-3|x| - 3) + 3)/(1(-3|x| - 3))) + 3)^2 - 3(2((2(-3|x| - 3) + 3)/(1(-3|x| - 3))) + 3) + 1 and g(x) = -1|((2(2e^(1x) - 2))/(2(2e^(1x) - 2) + 2)) + 2| + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex ... | -1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -3|((-1(1sin(2πx) + 1) - 2)/(1(1sin(2πx) + 1) + 1)) + 1| + 2 and g(x) = 1(-3x^2 + 5) - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -3e^(2(1|(1(-2x^2 - 5x) - 5)| + 2)) + 2 and g(x) = -1((-1(-1|x + 1| + 3))/(1(-1|x + 1| + 3) - 2))^2 + 1((-1(-1|x + 1| + 3))/(1(-1|x + 1| + 3) - 2)) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: ... | -2 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (2(-2(-2|(-1x + 2)|)^2 - 1(-2|(-1x + 2)|) + 1) - 2)/(1(-2(-2|(-1x + 2)|)^2 - 1(-2|(-1x + 2)|) + 1) + 1) and g(x) = (1(1(3x - 1)^2 - 2) + 3)/(2(1(3x - 1)^2 - 2)) intersect in the interval [... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -2((-3(3|(3x) - 3| - 1) - 2)/(3(3|(3x) - 3| - 1) + 3))^2 + 5((-3(3|(3x) - 3| - 1) - 2)/(3(3|(3x) - 3| - 1) + 3)) + 2 and g(x) = 3((1(3x^2 - 5x + 2) - 1)/(2(3x^2 - 5x + 2) - 1)) + 3 meet in the interval [-10, 10].\n\nPresent... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1sin(1π(-1|(3x^2 - 1x - 3)|) + 1) + 2 and g(x) = -1(-3e^(-1x) + 1)^2 - 4(-3e^(-1x) + 1) - 2 intersect 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) = -2cos(3π(1|((-3x - 2)/(3x - 2)) + 2| + 1) + 3) - 2 and g(x) = -3e^(-2(-1x^2 - 3x - 2)) + 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) = -2e^(-2(2|((1(-2x - 1) + 3)/(-3(-2x - 1) + 1)) - 3| + 2)) and g(x) = 1|(-2e^(1((-1x - 2)/(2x + 2))) - 1) + 3| - 3 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-2(-2|(1(1x^2 - 2x + 5)) - 1|) + 2)/(2(-2|(1(1x^2 - 2x + 5)) - 1|) + 2) and g(x) = -2|(5(-2e^(2x) + 1)^2 - 3(-2e^(2x) + 1) - 4) - 2| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your ... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -1|((1(1cos(1π(2x^2 + 1) + 1) - 1) - 3)/(-1(1cos(1π(2x^2 + 1) + 1) - 1) - 3)) + 1| - 3 and g(x) = -3|(-4((-1x)/(-2x - 1)) + 1) - 3| - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the an... | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -3sin(1π((2(5x^2 - 4x + 2) - 3)/(2(5x^2 - 4x + 2) - 1)) - 1) + 1 and g(x) = 1|((-1x + 2)/(2x - 1)) + 3| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\b... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 2|(-5(-2((1x - 2)/(-2x + 3)) - 4)^2 + 5(-2((1x - 2)/(-2x + 3)) - 4)) - 1| and g(x) = (1(2sin(1π(1x + 3) - 3) + 3) + 1)/(3(2sin(1π(1x + 3) - 3) + 3) - 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 1(-1(-1e^(2((2x + 3)/(3x - 2))) - 2)^2 - 2(-1e^(2((2x + 3)/(3x - 2))) - 2)) - 4 and g(x) = -4(1(-2|x - 2| + 3) + 4)^2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 7 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (-2(-3(3|x + 1| - 3) - 2) + 2)/(-1(-3(3|x + 1| - 3) - 2) - 2) and g(x) = 1cos(3π((1x)/(-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{... | -2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1(-1(3|((3x - 3)/(2x - 3))| + 3)^2 - 4(3|((3x - 3)/(2x - 3))| + 3) - 4) - 4 and g(x) = (3(3e^(-1(1x + 3)) - 2) - 3)/(2(3e^(-1(1x + 3)) - 2) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | -2 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.