messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(1π(-1|((-1x + 1)/(-3x - 2)) + 1| + 2)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1sin(2π(-1((-2(-3x + 4) - 1)/(-3(-3x + 4) + 4))^2 - 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2π(-1(-2|x - 3| - 3) - 4) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(-3sin(1π(2(2x^2 + 5x + 4)) - 3)) + 3)/(2(-3sin(1π(2(2x^2 + 5x + 4)) - 3)) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 399 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2π(5(4(-1|x|) - 1)^2 - 1(4(-1|x|) - 1) + 5) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1217 | MATH |
[
{
"content": "How many solutions does the equation 3cos(2π(3|((-2x - 3)/(-3x - 3)) - 2| - 3) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "How many zeros does the function f(x) = (2(4(3sin(3π(-5x^2 - 3x - 5) + 3)) + 3) + 3)/(2(4(3sin(3π(-5x^2 - 3x - 5) + 3)) + 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 349 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(-2sin(3π(-2(-1|x - 2| + 2) - 3) - 1) + 1)^2 + 5(-2sin(3π(-2(-1|x - 2| + 2) - 3) - 1) + 1) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(3|(-2sin(2πx + 1) - 3) + 1| - 1))/(3(3|(-2sin(2πx + 1) - 3) + 1| - 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation (-2(1(2cos(1πx - 2))^2 + 5(2cos(1πx - 2)) - 2) - 3)/(2(1(2cos(1πx - 2))^2 + 5(2cos(1πx - 2)) - 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1((2(3(1cos(2πx - 3) + 1)^2 + 3(1cos(2πx - 3) + 1) - 3) - 2)/(-3(3(1cos(2πx - 3) + 1)^2 + 3(1cos(2πx - 3) + 1) - 3) + 2)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-3cos(3π(-2|x + 2| + 1) - 2) - 3)^2 + 4(-3cos(3π(-2|x + 2| + 1) - 2) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2π(-1(-3(3|x|) + 2)^2 - 5(-3(3|x|) + 2) + 4)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1234 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(3π(2(-1|(-2x) + 2| - 1)^2 - 5(-1|(-2x) + 2| - 1) - 5) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1094 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(4(-3cos(1πx + 1) - 3)^2 + 4(-3cos(1πx + 1) - 3) + 1) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(1|(-2sin(3π((1x - 1)/(3x + 1))) + 1) - 2| - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "How many solutions does the equation 2cos(2π(5((1x)/(2x - 1)) + 5)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1π(3|((1x - 3)/(1x))| - 2) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(3sin(2π(-1|x + 2| + 3) + 1) + 3)^2 - 1(3sin(2π(-1|x + 2| + 3) + 1) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(-2cos(3π(-1(-2|x - 1| + 2)^2 + 5(-2|x - 1| + 2) + 1) + 1) + 1) + 3)/(-1(-2cos(3π(-1(-2|x - 1| + 2)^2 + 5(-2|x - 1| + 2) + 1) + 1) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 1628 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(2π((1(-1|x + 2| + 2) - 1)/(-2(-1|x + 2| + 2) - 2)) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(1sin(3π(1x^2 + 3x + 1) + 3) - 3) + 1| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 287 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-5(1sin(3π(-1|x - 3| - 2) - 3) - 1)^2 + 2(1sin(3π(-1|x - 3| - 2) - 3) - 1) + 2) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(1|(-1cos(2π(1x - 2) - 2) - 1) - 1| - 1)^2 + 2(1|(-1cos(2π(1x - 2) - 2) - 1) - 1| - 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-1(2|(2sin(3πx) + 3) + 1| - 1) + 5) - 3)/(-2(-1(2|(2sin(3πx) + 3) + 1| - 1) + 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-5(3sin(1π(-2|x - 1| + 3) + 1) - 3)^2 - 2(3sin(1π(-2|x - 1| + 3) + 1) - 3) + 1) - 1)/(-1(-5(3sin(1π(-2|x - 1| + 3) + 1) - 3)^2 - 2(3sin(1π(-2|x - 1| + 3) + 1) - 3) + 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|((-3(-1cos(2πx + 3) - 1) - 1)/(1(-1cos(2πx + 3) - 1))) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3π((-1(4x - 1) - 3)/(1(4x - 1) + 2)) - 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "How many solutions does the equation -4((-2(3|(-2cos(1πx - 1) + 2) - 3| - 2) + 3)/(3(3|(-2cos(1πx - 1) + 2) - 3| - 2) + 3))^2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(2π(-2|((1x - 1)/(1x - 2)) - 1|) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-2cos(1π(2x + 2) - 2) - 1)^2 + 5(-2cos(1π(2x + 2) - 2) - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π(-4(3|((-1x + 2)/(1x))| - 2)^2 - 5(3|((-1x + 2)/(1x))| - 2) + 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 428 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(2π(-3|(-3x + 5)| - 2) + 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 178 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(4(3cos(3π(-1x^2 + 1x + 4) - 1) + 1) + 2))/(-1(4(3cos(3π(-1x^2 + 1x + 4) - 1) + 1) + 2) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 267 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(1π(2|(-1(-3x^2 + 2) - 2) - 1| - 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 511 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2sin(1π(-1((-1x)/(2x + 1)) - 2) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1sin(2π((-3(1(-2x + 2)^2 + 2(-2x + 2) + 1) + 1)/(-2(1(-2x + 2)^2 + 2(-2x + 2) + 1))) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-1sin(1π(3|x - 3| + 1) - 2) + 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-3sin(1π(2|(-4x - 4) + 1|)))^2 + 5(-3sin(1π(2|(-4x - 4) + 1|))) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 319 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π((-2(1x^2 + 5x - 2) - 2)/(-1(1x^2 + 5x - 2) + 2)) + 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "How many solutions does the equation -1(-3cos(2π(-3|x|) - 3)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3π(-3|(-1x^2 - 4x + 3) - 2|) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 767 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1π(1(-1((1x - 2)/(-3x + 2))^2 + 3((1x - 2)/(-3x + 2)) + 3) + 3) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(-4(3cos(3π(3|x| + 2) + 3) + 3)^2 + 4) - 2)/(1(-4(3cos(3π(3|x| + 2) + 3) + 3)^2 + 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(2π(-1(3x - 3)^2 - 3(3x - 3)) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1709 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(1π(5((1x)/(-1x + 2))) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "How many solutions does the equation 4(2sin(1π(3x - 4) + 2) + 1)^2 + 1(2sin(1π(3x - 4) + 2) + 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation -3(-2((3(-3sin(1πx - 2) - 3) + 1)/(-3(-3sin(1πx - 2) - 3) - 3)) + 2)^2 + 1(-2((3(-3sin(1πx - 2) - 3) + 1)/(-3(-3sin(1πx - 2) - 3) - 3)) + 2) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2π(1|(-2((-2x + 2)/(2x + 1)) + 5) + 2| - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-5(1cos(2π(1|x - 1| - 3) + 2) + 1) + 4) - 2)/(-3(-5(1cos(2π(1|x - 1| - 3) + 2) + 1) + 4) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-5(3|(-1cos(3πx + 1) - 2) + 1|)^2 + 4(3|(-1cos(3πx + 1) - 2) + 1|) - 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation 2(3sin(3π(-4x^2 + 2x + 1) + 3) + 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 940 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5((1(-1cos(1πx)) - 3)/(3(-1cos(1πx)) + 1))^2 + 4((1(-1cos(1πx)) - 3)/(3(-1cos(1πx)) + 1)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation (-1(3(2cos(2π(-2|x + 2| - 2) + 2) - 1) + 2))/(2(3(2cos(2π(-2|x + 2| - 2) + 2) - 1) + 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1(2sin(1πx + 3) - 1) + 3) + 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(2(-4((-2x + 3)/(-2x - 2))^2 + 4((-2x + 3)/(-2x - 2)) + 2) - 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 327 | MATH |
[
{
"content": "How many solutions does the equation -3|(-4(-3cos(1π(1x - 3)) - 1)^2 + 5) - 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(-1cos(2π((-1x)/(2x + 2)) - 2) + 3) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "How many solutions does the equation (-3(1(3cos(3πx + 3) - 2) + 2) - 2)/(2(1(3cos(3πx + 3) - 2) + 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(2π(3(-5(1|x + 3| + 2) + 2)^2 + 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1571 | MATH |
[
{
"content": "How many solutions does the equation 3sin(1π(-2|(-4x + 3) + 1| - 3) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-3|((3(-3cos(2πx - 3) - 2))/(3(-3cos(2πx - 3) - 2) + 3)) + 2| - 3)^2 - 2(-3|((3(-3cos(2πx - 3) - 2))/(3(-3cos(2πx - 3) - 2) + 3)) + 2| - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 30 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-2(-2sin(1π((2x + 3)/(2x - 1)) + 1) - 1)^2 + 2(-2sin(1π((2x + 3)/(2x - 1)) + 1) - 1)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(4(-1|(-2cos(1πx + 3) + 1) + 1| + 1) + 3)^2 + 3(4(-1|(-2cos(1πx + 3) + 1) + 1| + 1) + 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(3sin(1π(-2|x + 2| + 2) + 2)) + 1)/(-1(3sin(1π(-2|x + 2| + 2) + 2)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(1π((1(2|(2x) - 1| - 1) + 3)/(-3(2|(2x) - 1| - 1) + 1)) + 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(3(3|x + 1|)^2 - 2(3|x + 1|) + 4)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1099 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3π(1(-2|((-1x - 2)/(-1x + 2)) - 1| - 1)^2 + 5) + 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 290 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(2π(-1|(-1(1x^2 - 3) + 4) + 1|) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 191 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(3sin(3π(-4x^2 + 2x - 1) - 3) + 3) - 2)/(-2(3sin(3π(-4x^2 + 2x - 1) - 3) + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 429 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3π(-2|(-5(-1x + 5)^2 + 4(-1x + 5) + 3) - 2| - 1)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1161 | MATH |
[
{
"content": "How many solutions does the equation 1|(2(2sin(3πx - 2) + 2)^2 - 2(2sin(3πx - 2) + 2) + 5) - 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(1(1cos(2π(5x + 5) - 1) + 3)^2 - 1(1cos(2π(5x + 5) - 1) + 3) - 5))/(-3(1(1cos(2π(5x + 5) - 1) + 3)^2 - 1(1cos(2π(5x + 5) - 1) + 3) - 5) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 200 | MATH |
[
{
"content": "How many solutions does the equation 3sin(2π(-1(-2|((-2x + 2)/(3x - 1)) - 2| + 3) + 4) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-2(-1sin(2πx + 3) + 2)^2 + 3(-1sin(2πx + 3) + 2) - 4) + 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(-3(2sin(2π(-1|x - 2| + 3)) + 1) + 2)^2 - 3(-3(2sin(2π(-1|x - 2| + 3)) + 1) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-5(-3cos(3πx - 2)) + 4)^2 + 3(-5(-3cos(3πx - 2)) + 4) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "How many solutions does the equation 2sin(1π(-4(1((-2x + 3)/(3x - 1)) - 1)^2 + 1(1((-2x + 3)/(3x - 1)) - 1) + 2)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "How many solutions does the equation (1(5(3cos(3πx + 3) - 3)^2 - 2(3cos(3πx + 3) - 3)) - 2)/(1(5(3cos(3πx + 3) - 3)^2 - 2(3cos(3πx + 3) - 3)) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation -1((3(-2sin(1πx + 3) + 1) - 2)/(-3(-2sin(1πx + 3) + 1) - 2))^2 + 3((3(-2sin(1πx + 3) + 1) - 2)/(-3(-2sin(1πx + 3) + 1) - 2)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation (-1(-3|(-2sin(1π(-3x^2 - 2x) + 2) - 2) + 2|) - 1)/(-1(-3|(-2sin(1π(-3x^2 - 2x) + 2) - 2) + 2|) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 528 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1π(1((2x + 3)/(-1x - 1))^2 + 4((2x + 3)/(-1x - 1)) - 4) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1π(-5(-2|((3x + 1)/(-1x - 3)) - 1| + 1) + 4) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 302 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(-5(-2cos(3πx - 3) + 1)^2 + 3(-2cos(3πx - 3) + 1) + 5) - 1)/(-1(-5(-2cos(3πx - 3) + 1)^2 + 3(-2cos(3πx - 3) + 1) + 5)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(2|(3(-2cos(3πx + 3) + 1)^2 + 4(-2cos(3πx + 3) + 1) + 1) - 2| + 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(3π(-1((2x - 2)/(-1x - 1)) - 2) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 114 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-2cos(3π((-1x - 1)/(1x - 2)) + 1) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 105 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(3(2sin(1π(-5x + 4) + 1))^2 - 3(2sin(1π(-5x + 4) + 1)) + 1) + 3)/(-1(3(2sin(1π(-5x + 4) + 1))^2 - 3(2sin(1π(-5x + 4) + 1)) + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3cos(3π(-1(3(-2|x - 3| + 2) - 4)^2 - 2(3(-2|x - 3| + 2) - 4)) - 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1290 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(2cos(2π(-1|x - 1| + 1) + 2) + 2)^2 - 3(2cos(2π(-1|x - 1| + 1) + 2) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(-3sin(3π(2x^2 - 5x + 2) + 2) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 881 | MATH |
[
{
"content": "How many solutions does the equation -2(-1|(-3sin(1πx - 2)) + 1| + 3)^2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation 3(-3(1cos(1π((3x)/(3x + 2)) - 2) - 2)^2 - 4(1cos(1π((3x)/(3x + 2)) - 2) - 2)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-2|(1sin(3πx + 2) + 1)|) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(3π(2|(4((3x - 2)/(3x + 1)) + 4) - 1| + 1) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(2sin(1π(1((-3x)/(1x + 2)) + 4) - 1) + 2) + 1| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1π((2(4x^2 - 1x - 1) + 1)/(-2(4x^2 - 1x - 1) + 3)) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation -2|((-1(1cos(1π(-3x^2 - 3x - 2) + 3) + 3) + 2)/(-1(1cos(1π(-3x^2 - 3x - 2) + 3) + 3) - 2)) + 1| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 278 | MATH |
[
{
"content": "How many solutions does the equation -1sin(1π(-1|(-1x^2 + 2x) - 1| + 2) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 102 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(1π((-2(-1|x - 1| - 1) - 2)/(1(-1|x - 1| - 1) + 3)) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 135 | MATH |
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