messages listlengths 1 1 | ground_truth stringclasses 22 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -4(-2sin(1πx - 2) + 2) + 5 and g(x) = 4x + 1 intersect 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) = (-1((-1x + 3)/(-1x + 2)) + 3)/(-3((-1x + 3)/(-1x + 2)) + 2) and g(x) = 1|x + 3| intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3|(1|x + 2| + 2) + 3| + 2 and g(x) = -1x^2 - 4x - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3(5x)^2 and g(x) = (2x - 1)/(2x + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -3((2x)/(-2x - 1)) - 2 and g(x) = 4x^2 + 1x + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -4(-2|x - 1|) - 5 and g(x) = (-2x + 2)/(-2x + 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) = (-1(4x^2 + 2x + 3) + 1)/(3(4x^2 + 2x + 3) - 2) and g(x) = 5x^2 + 3x - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -2|(-2|x + 1| + 3) - 1| + 3 and g(x) = 4x 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 x-coordinate where the graphs of f(x) = -2(3sin(2πx - 2) - 3)^2 + 4(3sin(2πx - 2) - 3) - 4 and g(x) = (2x)/(3x - 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) = -4(2sin(2πx + 3) + 3) - 2 and g(x) = (-2x + 1)/(-1x) 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) = 3(-2x^2 - 4x + 2)^2 - 4(-2x^2 - 4x + 2) - 5 and g(x) = -3|x - 3| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 1(2x - 2) - 5 and g(x) = -2|x| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -3(3x^2 + 5x + 2) - 2 and g(x) = -2x - 5 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1(-2|x - 2| + 2) - 1 and g(x) = (-2x + 2)/(2x - 1) intersect 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 leftmost x-coordinate where f(x) = -4((-3x)/(1x + 1)) - 4 and g(x) = (1x - 1)/(-2x - 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) = (3(-3x + 2) + 1)/(2(-3x + 2) - 1) and g(x) = 5x + 3 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) = -3|(-1x - 5) - 2| and g(x) = -5x^2 - 5x meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -5(1e^(1x) + 1)^2 - 4(1e^(1x) + 1) - 4 and g(x) = (1x - 3)/(3x - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (2(5x^2 + 3x + 1) + 3)/(1(5x^2 + 3x + 1)) and g(x) = (-3x - 1)/(-2x + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 5(3x + 3)^2 + 5(3x + 3) - 2 and g(x) = 1x^2 - 4x + 5 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": "user"
}
] | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1(1e^(1x) - 1) - 1 and g(x) = -2|x| + 2 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 x-coordinate where the graphs of f(x) = -3((1x)/(3x + 3)) + 5 and g(x) = -1|x - 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) = -2e^(-1(-4x + 1)) + 3 and g(x) = -3|x - 1| - 2 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 x-coordinate where the graphs of f(x) = 3(2x^2 + 5x + 3) + 4 and g(x) = (3x)/(1x + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (1((-2x + 2)/(3x)) + 3)/(-2((-2x + 2)/(3x)) + 3) and g(x) = (3x + 3)/(1x) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(-1x^2 - 2x - 1) - 1)/(1(-1x^2 - 2x - 1) - 3) and g(x) = (-2x - 2)/(-1x + 2) 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 x-coordinate where the graphs of f(x) = 5(1x^2 + 5) + 1 and g(x) = (3x)/(-2x + 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(-1|x - 3|) + 1 and g(x) = 3|x + 3| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1sin(2π(-2|x - 1| - 2) - 2) + 1 and g(x) = -3x - 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) = 4(1x^2 - 2x - 4) + 5 and g(x) = -3|x - 2| + 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) = 2|(5x + 2) + 2| and g(x) = 3x + 5 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": "user"
}
] | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (-1((3x + 2)/(1x)) + 3)/(-2((3x + 2)/(1x)) + 3) and g(x) = -1|x| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(-5x^2 + 2x))/(-2(-5x^2 + 2x) - 1) and g(x) = 1x + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1sin(1π(1x + 2) + 2) and g(x) = 2x^2 - 5x - 4 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(-1x^2 + 5x + 4) + 3 and g(x) = 1x^2 + 3x 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": "user"
}
] | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 1|(-1sin(3πx + 1) + 3) - 1| - 1 and g(x) = -2x - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -1(3|x + 3| + 1) + 2 and g(x) = 1|x + 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}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 4(4x^2 + 4x - 5) - 4 and g(x) = (2x - 2)/(-1x + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1sin(2π((-2x - 3)/(2x + 2)) - 1) - 3 and g(x) = -1x^2 - 1x + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1((-3x + 1)/(-3x))^2 - 5((-3x + 1)/(-3x)) - 4 and g(x) = 5x^2 + 4x + 4 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 smallest x-value where the functions f(x) = (2(-1x^2 - 3x) - 1)/(2(-1x^2 - 3x)) and g(x) = (-2x - 1)/(-1x - 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 1(-2e^(-1x) + 1)^2 + 5(-2e^(-1x) + 1) + 2 and g(x) = -2x^2 - 1x + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (1(-3|x + 3| + 2) + 3)/(-2(-3|x + 3| + 2) + 3) and g(x) = -1x^2 + 3x - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | -3 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (-1(2x^2 + 3x - 3) + 1)/(1(2x^2 + 3x - 3) + 2) and g(x) = -4x - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4(3|x - 3|)^2 + 3(3|x - 3|) + 2 and g(x) = -3x + 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) = -3|(1x + 5) - 3| - 1 and g(x) = (-1x + 2)/(2x + 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) = -1e^(-1(-2x^2 + 5x + 5)) + 2 and g(x) = (-2x + 3)/(2x + 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(1e^(-1x) - 2) - 3)/(1(1e^(-1x) - 2) + 3) and g(x) = 4x^2 + 5x - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 1((2x - 1)/(1x - 2)) + 2 and g(x) = -2|x| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1((-3x + 3)/(2x))^2 - 5((-3x + 3)/(2x)) + 4 and g(x) = 1|x - 2| intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-2(1sin(3πx - 1) + 3) - 1)/(3(1sin(3πx - 1) + 3)) and g(x) = (2x + 3)/(-1x + 3) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1e^(-1(2x^2 - 5x + 4)) + 2 and g(x) = 5x + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-3(-4x - 3) - 3)/(-1(-4x - 3)) and g(x) = -4x^2 - 2x + 3 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1(1x^2 + 4x - 3) + 5 and g(x) = 3|x| + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(-2e^(1x)) + 3)/(-1(-2e^(1x)) - 3) and g(x) = 3x + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 3|(-2|x + 3| + 3)| - 3 and g(x) = 2|x - 2| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -4(-3x^2 + 4x - 2) + 3 and g(x) = (1x - 2)/(3x + 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 largest x-value where the functions f(x) = 2(5x^2 - 4x + 2)^2 - 4(5x^2 - 4x + 2) - 4 and g(x) = 4x^2 - 3x - 4 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) = (-1(-1x^2 + 4x - 1) - 3)/(1(-1x^2 + 4x - 1) + 1) and g(x) = -3x^2 + 5x + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2(-4x^2 - 1x + 4)^2 + 1(-4x^2 - 1x + 4) + 3 and g(x) = 4x^2 + 5x - 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) = (3(1x^2 - 5x - 3) - 2)/(1(1x^2 - 5x - 3) + 2) and g(x) = -4x - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-3(1|x - 2| - 1) - 2)/(-2(1|x - 2| - 1) - 3) and g(x) = -1|x + 2| + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -3((-3x - 3)/(2x - 1)) + 1 and g(x) = 3x^2 + 3x + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (3(-2|x + 1| - 2) + 1)/(1(-2|x + 1| - 2) - 3) and g(x) = -4x - 2 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(1x - 1) - 1)/(-2(1x - 1) - 1) and g(x) = -3|x - 1| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2(5x - 3)^2 - 4(5x - 3) - 3 and g(x) = -2|x + 2| + 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 value closest to the x-coordinate where f(x) = (-3(3|x + 1| + 1) - 1)/(1(3|x + 1| + 1) - 3) and g(x) = 2x + 2 intersect in the range -10 ≤ x ≤ 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) = -2cos(1π(1x + 3)) - 3 and g(x) = (2x - 3)/(1x + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(-1e^(1x) - 1) + 1 and g(x) = 2|x - 1| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -1(3x^2 + 5x + 1)^2 - 1(3x^2 + 5x + 1) + 5 and g(x) = -1|x + 3| + 1 meet 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) = -1|((-2x + 1)/(2x - 3)) - 1| and g(x) = -3x^2 + 5x + 5 in the interval [-10, 10], rounded to the nearest integer.\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|(1x - 3) + 1| + 3 and g(x) = (-2x - 2)/(-2x - 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -2e^(2((2x - 1)/(3x + 1))) and g(x) = -2|x + 2| + 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 4(2cos(3πx - 2))^2 - 1(2cos(3πx - 2)) + 2 and g(x) = (1x - 2)/(-1x + 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -2((1x + 3)/(2x - 1))^2 + 4((1x + 3)/(2x - 1)) - 3 and g(x) = (-3x + 2)/(1x + 1) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3|(2sin(3πx) - 3) - 3| and g(x) = (2x + 1)/(1x - 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) = 1|(-2e^(-2x) - 1) + 1| + 3 and g(x) = 3|x - 3| + 2 meet 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) = -2sin(1π((2x + 3)/(-2x - 1)) + 3) - 2 and g(x) = (-1x - 1)/(1x) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 1(1x + 2) and g(x) = 2x^2 + 2x 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((-1x + 1)/(-1x - 1)) - 3)/(-1((-1x + 1)/(-1x - 1)) + 2) and g(x) = -1x + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 6 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-3(1x + 4) + 1)/(-2(1x + 4) + 3) and g(x) = 1x^2 + 2x - 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -3|(1e^(-1x) - 3) - 2| - 2 and g(x) = 3x + 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 2(-2x^2 + 4x - 1) - 2 and g(x) = (-2x + 3)/(-3x) 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 x-coordinate where the graphs of f(x) = -2e^(-2(3|x + 1| + 1)) - 2 and g(x) = (-2x + 3)/(-2x - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 1|(3x - 3) + 3| - 3 and g(x) = (2x + 1)/(2x + 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 value closest to the x-coordinate where f(x) = (-2((2x + 2)/(1x)) + 3)/(3((2x + 2)/(1x)) + 1) and g(x) = -3x^2 + 1x + 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 x-coordinate where the graphs of f(x) = -1e^(-1(-1x^2 - 3x - 3)) - 1 and g(x) = (3x - 3)/(-1x - 2) 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 x-coordinate where the graphs of f(x) = -5(3e^(2x) - 3)^2 - 4(3e^(2x) - 3) - 5 and g(x) = 5x - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 2(1|x - 2| - 1)^2 - 2(1|x - 2| - 1) + 5 and g(x) = (-1x)/(-3x + 2) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 1(1cos(2πx - 3) - 3) + 3 and g(x) = -2x - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1|(1cos(3πx + 2)) - 1| - 3 and g(x) = (-1x - 1)/(2x - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2(-2|x - 1| + 1)^2 + 3 and g(x) = -3|x| + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3|((1x + 1)/(-1x + 2)) - 1| + 1 and g(x) = 4x - 1 intersect in the interval [-10, 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 third x-coordinate (rounded to the nearest integer) where f(x) = (2((2x - 3)/(1x + 3)) + 3)/(2((2x - 3)/(1x + 3)) + 2) and g(x) = 1|x| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 2 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-2(-3x + 3) + 1)/(-1(-3x + 3) + 2) and g(x) = 3x^2 + 1x 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) = (2((-1x)/(2x - 1)))/(-2((-1x)/(2x - 1)) - 2) and g(x) = (1x + 2)/(-1x - 2) intersect in the range -10 ≤ x ≤ 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 first x-coordinate (rounded to the nearest integer) where f(x) = -2sin(2π(2|x| + 2) - 1) - 1 and g(x) = -4x + 5 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(2cos(1πx + 3) + 1) - 1 and g(x) = -4x meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-1((-3x + 2)/(-1x + 3)) + 1)/(2((-3x + 2)/(-1x + 3)) + 3) and g(x) = (-2x + 1)/(3x + 2) meet in the interval [-10, 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((-2x - 2)/(-2x))^2 - 5((-2x - 2)/(-2x)) - 1 and g(x) = -2x^2 + 2x - 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 2 | MATH |
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