messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many zeros does the function f(x) = (1(2|(-1(2sin(1πx + 1) + 3) + 3)| + 1) - 3)/(-1(2|(-1(2sin(1πx + 1) + 3) + 3)| + 1) - 1) 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 -4(2cos(2π(1(-2|x + 1| - 3) + 5) - 1) - 1)^2 - 4(2cos(2π(1(-2|x + 1| - 3) + 5) - 1) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "How many solutions does the equation 4(-3sin(1π(2|(-3x + 3)| - 2) + 2) + 2)^2 + 5(-3sin(1π(2|(-3x + 3)| - 2) + 2) + 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(-3(2|x + 3| - 3) + 2) - 3) + 3 = 0 have in the range [-10, 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) = 3sin(2π(-2(3(3|x + 2| - 3)^2 + 3(3|x + 2| - 3) + 2) - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1579 | MATH |
[
{
"content": "How many solutions does the equation (2(2|(-3sin(3πx + 2)) - 2| + 1) - 2)/(-1(2|(-3sin(3πx + 2)) - 2| + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "How many solutions does the equation 3cos(2π(4((-1x + 3)/(-3x - 1))^2 - 5((-1x + 3)/(-3x - 1)) + 1) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 146 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(-5(3sin(2πx + 3) - 2) + 3) + 3| + 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) = 5(-3sin(2π((3x)/(3x + 3)) - 2)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(-2sin(3π((-3(-2x^2 - 5x + 2) - 1)/(3(-2x^2 - 5x + 2) + 2)) - 1) + 3) - 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(1|(-1sin(3π(-2x^2 + 1x - 2) + 3) + 2) - 1|) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1143 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(1π(3(2|((3x + 1)/(3x)) - 1| - 1)^2 + 4(2|((3x + 1)/(3x)) - 1| - 1) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-3(-1sin(2π(2|x - 3| - 1) + 2) - 2)^2 - 1(-1sin(2π(2|x - 3| - 1) + 2) - 2) + 4))/(1(-3(-1sin(2π(2|x - 3| - 1) + 2) - 2)^2 - 1(-1sin(2π(2|x - 3| - 1) + 2) - 2) + 4) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2π(-1|((-3x - 2)/(-3x - 3))|) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(2cos(1π(-1(-3|x + 3| + 3) - 1) - 2)) - 2)/(2(2cos(1π(-1(-3|x + 3| + 3) - 1) - 2)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation 2cos(1π(-3|((2x - 1)/(-1x - 1))| + 2) + 1) - 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 -3cos(1π((1(-2|(-3x^2 + 2x + 3) + 2| + 3) + 2)/(3(-2|(-3x^2 + 2x + 3) + 2| + 3) + 3)) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(3π((-2(-3|x + 1| + 2))/(-2(-3|x + 1| + 2) - 1)) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(3π(5(1(-2|x - 2| - 1)^2 - 4(-2|x - 2| - 1) + 4) - 5) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1504 | MATH |
[
{
"content": "How many solutions does the equation 1((-2(2cos(3πx) + 1) + 2)/(2(2cos(3πx) + 1) - 1))^2 - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation 1((-1(3cos(1π(-5x^2 + 4x - 3)) - 2))/(3(3cos(1π(-5x^2 + 4x - 3)) - 2) + 1)) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(-2(3cos(1πx - 3) + 2)^2 + 4(3cos(1πx - 3) + 2) + 4))/(-2(-2(3cos(1πx - 3) + 2)^2 + 4(3cos(1πx - 3) + 2) + 4) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation (2(5(1cos(1πx - 3) - 1) + 5) + 1)/(-2(5(1cos(1πx - 3) - 1) + 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 -3sin(3π(-1|((1(-4x + 5))/(1(-4x + 5) - 2)) + 1| - 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2((3(-4(-3cos(2πx + 1) + 2) - 1) + 2)/(-2(-4(-3cos(2πx + 1) + 2) - 1) + 3))^2 - 1((3(-4(-3cos(2πx + 1) + 2) - 1) + 2)/(-2(-4(-3cos(2πx + 1) + 2) - 1) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(1π(5(-2x^2 + 3x + 3) - 1) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1291 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(2π(-1(2|(-2x^2 + 2x - 1) - 2| + 1) + 3) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 676 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-3sin(2π((2(1|x + 1|) - 3)/(1(1|x + 1|))) + 3) + 3) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 89 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(5(1(-1cos(3πx + 1) - 3)^2 + 1(-1cos(3πx + 1) - 3) - 5) + 1)| + 2 have in the interval [-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) = 1cos(2π(1|(4(-4x - 5)^2 + 2(-4x - 5) - 1) + 1| - 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1589 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(-3(3cos(3πx - 1))^2 - 1(3cos(3πx - 1)) + 1) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(1π(-4((1(-1|x - 2| + 3) - 1)/(-2(-1|x - 2| + 3) - 2)) + 2) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 148 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(3π(5(-1|(2x + 4) - 2| - 1)^2 + 1(-1|(2x + 4) - 2| - 1)) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1320 | MATH |
[
{
"content": "How many solutions does the equation -3((1(3sin(3πx + 3) + 1) - 1)/(2(3sin(3πx + 3) + 1) - 1)) + 5 = 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(-2(2cos(3π((-2x + 3)/(-1x + 2)) - 1) - 1) + 1)^2 + 3(-2(2cos(3π((-2x + 3)/(-1x + 2)) - 1) - 1) + 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(3π(1((2(2|x + 1| - 3) + 1)/(-1(2|x + 1| - 3) + 2))^2 - 1((2(2|x + 1| - 3) + 1)/(-1(2|x + 1| - 3) + 2)) + 4) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3π(-3(1|((-1x + 3)/(-1x - 3)) + 3| + 3)^2 + 4(1|((-1x + 3)/(-1x - 3)) + 3| + 3) - 3) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 669 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(-3cos(3π((2x + 1)/(3x - 1)) - 3)) - 3| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "How many solutions does the equation -2((-1(3cos(1πx + 1) + 2) - 3)/(-2(3cos(1πx + 1) + 2) + 3))^2 + 4((-1(3cos(1πx + 1) + 2) - 3)/(-2(3cos(1πx + 1) + 2) + 3)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation 4(2sin(3π(-3|((-3x + 1)/(2x - 1)) + 1| - 3) + 1) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(4(3cos(2π(2x^2 + 3x + 3) - 1)) + 1) + 2)/(1(4(3cos(2π(2x^2 + 3x + 3) - 1)) + 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 342 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(3π(-1(-3|x + 1| - 3) + 1) - 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-3(-1|(3cos(3πx - 3) + 2) - 3| + 3))/(2(-1|(3cos(3πx - 3) + 2) - 3| + 3) - 3))^2 + 4((-3(-1|(3cos(3πx - 3) + 2) - 3| + 3))/(2(-1|(3cos(3πx - 3) + 2) - 3| + 3) - 3)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1cos(2π(2|(-1x^2 + 3x - 2) - 2| + 1) - 3) - 2) - 3)/(3(-1cos(2π(2|(-1x^2 + 3x - 2) - 2| + 1) - 3) - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(-2|(2sin(3π(-1x - 3) + 1)) + 2| + 3) + 3)/(-2(-2|(2sin(3π(-1x - 3) + 1)) + 2| + 3) + 1) 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) = 2(3sin(3π(-1x + 3) - 2) - 2)^2 - 4(3sin(3π(-1x + 3) - 2) - 2) - 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) = -3sin(1π(-2(-5((-2x - 3)/(-1x - 1))^2 + 5((-2x - 3)/(-1x - 1)) - 1) + 2) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(3cos(1π(-4((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) + 3) - 3)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 207 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(3cos(1π(-5x) - 1) - 1) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-1((-1(-2cos(1πx - 2) + 3) - 1)/(1(-2cos(1πx - 2) + 3) - 2)) + 3) + 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(3cos(2π(2x^2 - 1x) - 3) - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 789 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(4(-2sin(1π(-1|x - 2| + 1) - 1) - 1) + 5) + 1)/(-2(4(-2sin(1π(-1|x - 2| + 1) - 1) - 1) + 5) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(3sin(2π((3x + 3)/(-2x - 3)) - 3))^2 + 1(3sin(2π((3x + 3)/(-2x - 3)) - 3)) - 3 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) = -5(-2(3cos(1π(-1|x - 1| - 1)) + 2) + 2)^2 + 1(-2(3cos(1π(-1|x - 1| - 1)) + 2) + 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation -1sin(3π(-2|(-3x - 4) + 1| + 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "How many solutions does the equation 2(2cos(2π(4((-1x + 3)/(3x + 1))^2 + 5((-1x + 3)/(3x + 1)) - 1) - 3) + 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 152 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(3|(-2sin(3π(1x^2 - 5) + 2) + 1) - 1| - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 430 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2π(1|(-4(-1x^2 + 4x) - 4) + 1|) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1189 | MATH |
[
{
"content": "How many solutions does the equation -3cos(3π(5(3|((-1x)/(2x + 1)) + 3| + 2)^2 + 5(3|((-1x)/(2x + 1)) + 3| + 2) - 1) + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 449 | MATH |
[
{
"content": "How many solutions does the equation 4(-2|(3sin(1πx - 1) - 2) + 2| + 2) - 2 = 0 have in the range [-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) = -3cos(1π(-2((3x)/(-1x - 1))^2 + 5((3x)/(-1x - 1)) - 2) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 190 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1sin(1π((2(-1x + 2) - 1)/(1(-1x + 2) - 2)) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(1π((3(-1(-5x - 5)^2 - 3(-5x - 5) - 1) + 3)/(2(-1(-5x - 5)^2 - 3(-5x - 5) - 1))) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(1sin(1π((1x + 1)/(1x)) - 2) + 3) - 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "How many solutions does the equation 2cos(3π(-1(1(1|x + 2| + 3)^2 - 3(1|x + 2| + 3) - 4) + 1) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 365 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(3π((3(1x^2 + 5x - 4) - 1)/(-3(1x^2 + 5x - 4) - 2)) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(2π((-1(5x + 3) + 3)/(-3(5x + 3) + 2))) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "How many zeros does the function f(x) = (2(-2cos(1π(1x + 3) + 3) - 1) + 3)/(1(-2cos(1π(1x + 3) + 3) - 1) + 2) have in the interval [-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(-1sin(3π(-4x - 2) + 1) + 2) - 2)/(-1(-1sin(3π(-4x - 2) + 1) + 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(2π(2(-1|x| - 1) + 5) + 3) + 1 have 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 3(1cos(1π(2|x - 1| + 1) - 2) - 2)^2 + 1(1cos(1π(2|x - 1| + 1) - 2) - 2) - 4 = 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) = 1|(-3sin(3π(-3x^2 + 5x + 2)) + 3) + 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 753 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(2π(1(-5((1x + 2)/(-1x + 2)) + 1)^2 - 1(-5((1x + 2)/(-1x + 2)) + 1) - 4) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 404 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-3|(-3sin(2πx - 2) + 2)| + 2) + 2)/(2(-3|(-3sin(2πx - 2) + 2)| + 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-2(2cos(2πx - 1) - 2)^2 - 4(2cos(2πx - 1) - 2) + 2) - 3 have in the interval [-10, 10]?\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) = -3cos(2π((2(-2(-5x + 4)^2 - 5(-5x + 4) + 4) + 2)/(2(-2(-5x + 4)^2 - 5(-5x + 4) + 4) - 1)) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(2π(-2(-4x^2 + 1x + 3) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1663 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(2|(2x + 2)| + 1)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(1sin(2π(-3x^2 - 5x + 5) - 2) - 2) + 2)/(-2(1sin(2π(-3x^2 - 5x + 5) - 2) - 2) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1166 | MATH |
[
{
"content": "How many solutions does the equation (2(4(-3sin(3π(-3x^2 + 4x - 2) - 2) + 3) - 4) - 3)/(1(4(-3sin(3π(-3x^2 + 4x - 2) - 2) + 3) - 4) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 807 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-1(-3sin(1π(4x^2 + 5x + 1) + 1) + 3) + 3)/(-1(-3sin(1π(4x^2 + 5x + 1) + 1) + 3) + 2)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 266 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-3sin(1π((-3(1|x - 1|))/(-2(1|x - 1|) + 3)) - 1) + 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(2(3(2|x + 2|)^2 - 3(2|x + 2|) + 1) + 3) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1090 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(2sin(1π(-2|(-4x^2 + 2) - 1| - 3)) - 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 675 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1π((-2(3|x - 2| - 1))/(2(3|x - 2| - 1) - 1)) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "How many solutions does the equation 3(3(-1cos(2π((-2x + 2)/(-1x + 2)) - 1) - 1)^2 + 1(-1cos(2π((-2x + 2)/(-1x + 2)) - 1) - 1) + 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 69 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3π(-1(1(-2|x - 2| + 2) + 1)^2 - 4(1(-2|x - 2| + 2) + 1) - 5) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 667 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(-4((1(-3cos(2πx - 2) + 3) - 3)/(3(-3cos(2πx - 2) + 3) + 1)) - 1) - 1| + 1 have in the interval [-10, 10]?\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) = 2|((1(4(2sin(2πx - 3)) + 4) - 1)/(2(4(2sin(2πx - 3)) + 4) - 1)) + 1| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(2π((-1(4x - 1) + 1)/(-3(4x - 1) - 1)) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many solutions does the equation (-3(-2sin(1π(-5x + 2) - 1) - 2))/(1(-2sin(1π(-5x + 2) - 1) - 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4((3(-1(-2cos(3πx + 3) - 2) - 3) - 1)/(-2(-1(-2cos(3πx + 3) - 2) - 3) + 3))^2 + 2((3(-1(-2cos(3πx + 3) - 2) - 3) - 1)/(-2(-1(-2cos(3πx + 3) - 2) - 3) + 3)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 60 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (2(-2sin(3π(-4x - 5) + 3) + 1) - 2)/(-3(-2sin(3π(-4x - 5) + 3) + 1) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(1π(1((-3(3|x + 1| - 3) + 2)/(-1(3|x + 1| - 3) + 2)) + 3) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "How many solutions does the equation 3(3cos(2π(2(-1|x + 3| + 1)^2 - 4(-1|x + 3| + 1) - 5) + 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 825 | MATH |
[
{
"content": "How many solutions does the equation -1cos(1π(2|(-4x + 2) + 1| + 2) - 3) + 1 = 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) = -2cos(1π(4(4(-3|x - 2| - 1) + 1)^2 + 4(4(-3|x - 2| - 1) + 1) - 5) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1395 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(1cos(3π(-4((-3x + 2)/(1x))^2 - 1((-3x + 2)/(1x)) + 2) - 1)) + 1| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 215 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(3cos(1π(4((2x - 1)/(-1x + 2))) - 2) + 2)^2 - 3(3cos(1π(4((2x - 1)/(-1x + 2))) - 2) + 2) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 165 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(-3(3cos(1πx + 1) + 2)^2 - 5(3cos(1πx + 1) + 2) + 1) + 2)/(-2(-3(3cos(1πx + 1) + 2)^2 - 5(3cos(1πx + 1) + 2) + 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
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