messages listlengths 1 1 | ground_truth stringclasses 134 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "How many points of intersection exist between the functions f(x) = (-1(-3|x + 1| + 3) - 1)/(3(-3|x + 1| + 3)) and g(x) = 2x^2 - 2x - 4 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -1cos(3π(2x - 2)) - 3 and g(x) = -2x + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -2cos(2π(-4x^2 + 3x - 4) - 2) + 3 and g(x) = 1|x - 2| - 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 514 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π(-3x + 2) - 3) - 1 = (1x - 1)/(-2x + 1) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 179 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -1cos(3π(-2x^2 - 3x - 5) - 1) + 3 and g(x) = -4x + 5 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many solutions does the equation 2cos(1π(4x - 2) - 2) - 2 = (-3x - 2)/(2x) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -4(-2sin(2πx + 3) + 2)^2 + 5(-2sin(2πx + 3) + 2) and g(x) = -4x + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2(-5x^2 + 1x + 3)^2 - 1(-5x^2 + 1x + 3) - 3 and g(x) = -5x^2 - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = (-2(-1sin(1πx - 3) + 2) - 3)/(3(-1sin(1πx - 3) + 2) - 2) and g(x) = 1x + 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -1cos(1π(1x^2 + 1x + 3) - 3) and g(x) = (1x)/(3x + 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201 | MATH |
[
{
"content": "How many solutions does the equation -2sin(2π(-3|x - 3| - 1) - 3) - 1 = (-1x + 2)/(1x + 1) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -3sin(1π((3x - 1)/(1x - 2)) + 1) - 1 and g(x) = 1x + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 2cos(2π(4x^2 - 5) - 1) - 3 and g(x) = (-2x - 3)/(1x) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1164 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (-1(3|x + 1| - 2) + 3)/(2(3|x + 1| - 2) - 1) and g(x) = -1|x - 2| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -1|(-1sin(3πx - 2) - 3)| + 3 and g(x) = 2x^2 - 1x - 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 2sin(1π((-3x + 3)/(-2x + 3)) + 1) + 2 = 2|x| + 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 2cos(2π(5x^2 + 1x + 1) - 1) and g(x) = -3|x| + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -3sin(3π(-3|x - 2|) + 3) + 1 and g(x) = (-2x - 3)/(-1x - 2) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 173 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 2|(-3cos(3πx)) - 2| - 1 and g(x) = -5x + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 5(-2sin(3πx - 3) + 1) - 1 and g(x) = (1x + 3)/(3x + 1) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many solutions does the equation 3((-2x - 2)/(3x - 2))^2 - 5((-2x - 2)/(3x - 2)) - 1 = 3|x + 2| - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 2(1sin(3πx - 2) - 3) - 5 and g(x) = -3|x + 2| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -2cos(1π((1x + 1)/(-1x - 2)) + 2) - 1 and g(x) = -1|x + 1| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -1cos(3π(3x^2 + 3x - 4) + 2) + 2 and g(x) = -2|x - 2| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 85 | MATH |
[
{
"content": "How many solutions does the equation 3cos(1π(2|x + 2| - 1) - 1) - 3 = 1x have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -5(-1sin(2πx - 2)) - 5 and g(x) = -1x^2 + 5x - 4 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 3sin(3π((-3x)/(-3x - 3)) - 3) + 3 and g(x) = 1|x - 2| - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -3cos(2π(5x + 4) - 1) + 1 and g(x) = -1x^2 - 5x + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "How many solutions does the equation (1(-1|x - 2| + 1) + 2)/(3(-1|x - 2| + 1) - 2) = -4x^2 + 1x + 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 1sin(2π(2x^2 + 5x - 3) - 1) + 3 = (1x + 2)/(1x + 1) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 3sin(3π(1x^2 - 3x + 3)) - 1 and g(x) = 2x + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many solutions does the equation -2cos(1π(-5x + 5) - 2) - 3 = 4x + 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 1cos(2π((-1x - 2)/(2x))) - 1 and g(x) = 5x - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -2|(2sin(3πx - 3) + 2) + 1| - 1 and g(x) = 2x^2 - 4x - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 2sin(1π(-3|x| - 1) - 2) + 1 and g(x) = (-3x)/(-3x + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = (3(-3sin(2πx + 2) - 1) + 3)/(-2(-3sin(2πx + 2) - 1) - 3) and g(x) = -3|x + 3| - 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (1(2cos(3πx + 1) - 2) + 3)/(2(2cos(3πx + 1) - 2) - 1) and g(x) = -1x - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 1(1cos(3πx - 2) - 2)^2 + 1 and g(x) = 3x^2 + 4 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -1cos(3π(-5x - 5) - 3) + 1 and g(x) = (3x - 3)/(3x) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 269 | MATH |
[
{
"content": "How many solutions does the equation -1cos(2π(-3x^2 + 5x - 1) - 2) - 2 = 4x^2 - 3x - 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 2cos(3π(3|x + 3| + 1) - 1) - 1 and g(x) = (-1x + 1)/(-1x - 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (2(2sin(2πx)) + 1)/(-3(2sin(2πx)) + 4) and g(x) = -5x where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 3sin(2π(2x^2 - 5x + 5) + 2) - 2 and g(x) = -5x^2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 1|(2sin(3πx + 1)) + 1| - 3 and g(x) = 1x - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "How many solutions does the equation -1cos(3π(-3|x + 3| + 2)) + 3 = -1x - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "How many solutions does the equation -3cos(3π(-5x + 1) + 3) = -5x + 5 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -3sin(3π(-1x - 5) + 1) + 2 and g(x) = -3x^2 + 4x + 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -3sin(3π(1x^2 + 4x - 3) - 2) + 2 and g(x) = 1x^2 + 1x - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 3sin(2π(2x^2 - 3x + 4) + 2) - 3 and g(x) = 1x + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 317 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 2sin(2π(3|x - 1| + 1) - 3) and g(x) = 1x^2 + 5x + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "How many solutions does the equation (-3(2sin(3πx - 2) - 1) + 2)/(2(2sin(3πx - 2) - 1) + 1) = 1x + 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 2cos(3π(-1x^2 - 3x + 4) + 1) - 3 and g(x) = 1x - 4 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many solutions does the equation 1sin(3π(-2x + 1)) = 1x + 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 2cos(3π(-1|x + 2| - 1)) - 1 and g(x) = 1|x + 2| in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -3sin(1π((-2x + 3)/(3x + 2))) + 1 and g(x) = -5x - 4 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2sin(1π(2x^2 + 2x - 3) - 1) - 1 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"
}
] | 165 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2(4x^2 + 4x - 2)^2 + 5(4x^2 + 4x - 2) + 4 and g(x) = -1x intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -3(-2sin(2πx - 3) + 3) - 4 and g(x) = 2x + 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -2cos(3π(-3|x| - 3) - 3) + 3 and g(x) = (2x + 1)/(2x) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 5(-3sin(3πx + 2) + 3)^2 - 2(-3sin(3πx + 2) + 3) - 2 and g(x) = (3x - 1)/(-3x - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 2cos(2π((2x + 3)/(1x)) - 1) - 1 and g(x) = (-2x - 2)/(-1x) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 3cos(2π(-1x + 2) - 3) - 3 and g(x) = (2x - 2)/(-2x - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 2cos(2π(-1x + 5) + 1) + 2 and g(x) = 2|x + 2| + 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -2(-3cos(1πx - 1) - 2)^2 - 3(-3cos(1πx - 1) - 2) - 4 = -3|x + 2| - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 1(-3sin(3πx + 3) + 2) - 1 and g(x) = -2|x| + 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (2(-2x^2 - 5x - 1) + 3)/(-3(-2x^2 - 5x - 1) - 3) and g(x) = 2|x - 2| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -2sin(2π(-4x^2 - 1x - 2) - 3) - 1 and g(x) = -1x^2 - 2x - 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -3|(-1cos(3πx + 1) - 2) - 3| + 3 and g(x) = 4x - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 2|(1|x + 1| - 1) - 3| - 2 and g(x) = (1x)/(-2x - 2) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -2cos(2π(-1x + 4)) - 1 and g(x) = 1x - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = (1(-3sin(2πx + 3) + 2) - 3)/(-3(-3sin(2πx + 3) + 2) + 2) and g(x) = -1|x + 2| + 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π(1x + 1) - 3) + 1 = (-2x - 3)/(1x + 3) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many solutions does the equation -3(-2cos(3πx + 1))^2 = -4x - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 3(2cos(3πx - 2) + 1)^2 - 5(2cos(3πx - 2) + 1) + 5 and g(x) = -5x^2 - 3x + 4 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many solutions does the equation -2sin(3π(-1x^2 + 1) - 1) - 2 = -2x^2 - 5x - 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = -3sin(1π(-5x - 4) - 3) - 1 and g(x) = -1x^2 - 1x - 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 2cos(2π(-1x^2 - 3x - 3) + 1) + 2 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"
}
] | 5 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π(-2|x + 3|)) + 2 = -1x + 5 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2|(-2cos(1πx) + 3) - 2| + 3 and g(x) = 1x + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = (-1(-4x^2 + 4x + 1) + 1)/(-2(-4x^2 + 4x + 1) - 1) and g(x) = -1x^2 - 4x - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = -1cos(3π(5x^2 - 3x - 1) + 2) + 1 and g(x) = 3x - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 1cos(2π(-3x^2 + 1x - 4) + 2) - 1 and g(x) = 2x + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "How many solutions does the equation (-1(-2sin(2πx - 3) - 2))/(3(-2sin(2πx - 3) - 2) + 3) = -2x^2 + 2x - 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (2(-3cos(1πx - 1) + 1) - 2)/(2(-3cos(1πx - 1) + 1)) and g(x) = 4x - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 1cos(1π((-2x - 1)/(3x + 2)) + 3) and g(x) = (1x)/(-2x + 1) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = (1(3cos(1πx + 1) - 2) - 3)/(-2(3cos(1πx + 1) - 2) - 2) and g(x) = 3|x + 3| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation 1cos(3π(-4x^2 + 2x + 2) - 1) - 2 = (-2x - 3)/(3x - 2) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "How many solutions does the equation -1(-1sin(2πx + 3) - 3) + 1 = 1x - 4 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = (3(2sin(2πx - 2) + 1) + 1)/(-2(2sin(2πx - 2) + 1) - 2) and g(x) = -2x^2 - 3x + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many points of intersection exist between the functions f(x) = 3(-2cos(2πx) - 2) + 2 and g(x) = -4x + 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -1|(-3cos(2πx + 2) - 3) + 3| + 2 and g(x) = 2x - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many solutions does the equation -3sin(3π(4x^2 - 3x) - 2) + 1 = -5x^2 - 3x + 4 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "How many solutions does the equation 3sin(2π((-1x)/(-1x + 2)) - 2) + 1 = 2|x + 1| - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation -3|(1sin(1πx + 2) + 1) + 1| + 1 = 1x - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 1sin(3π(-4x^2 + 1x - 5) + 3) + 2 and g(x) = 4x - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = -2sin(2π(3x + 3) + 1) + 2 and g(x) = -3|x - 3| + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of intersection points between the functions f(x) = 3sin(1π((1x - 2)/(2x - 1)) + 3) - 1 and g(x) = -3x - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 2cos(3π(5x - 5) + 2) - 2 and g(x) = (2x - 3)/(3x - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many solutions does the equation 1(-1cos(3πx - 1) + 1)^2 - 1(-1cos(3πx - 1) + 1) + 2 = 1x + 4 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the number of times the graphs of f(x) = 3cos(3π((3x)/(-1x - 3)) + 2) - 2 and g(x) = 5x^2 + 4x - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.