messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many zeros does the function f(x) = 5(1|(1cos(2πx)) - 2| - 3) + 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) = (1(-4(-1cos(3π(2|x + 1| - 1) + 2) + 1) + 2) + 2)/(-3(-4(-1cos(3π(2|x + 1| - 1) + 2) + 1) + 2) - 2) 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) = -2sin(2π(-1|(-3x^2 - 2x + 4)|) - 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1077 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4((1(3sin(3πx + 2) + 2) - 3)/(-2(3sin(3πx + 2) + 2) - 3))^2 - 3((1(3sin(3πx + 2) + 2) - 3)/(-2(3sin(3πx + 2) + 2) - 3)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation -3(-1sin(3π(5x - 1) - 3) - 2)^2 - 5(-1sin(3π(5x - 1) - 3) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(-2sin(1π(3|(-3x - 1) + 2|)) - 2))/(-3(-2sin(1π(3|(-3x - 1) + 2|)) - 2) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 89 | MATH |
[
{
"content": "How many solutions does the equation -1cos(3π(5(3x + 5)^2 - 3(3x + 5) - 4) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1580 | MATH |
[
{
"content": "How many solutions does the equation 5((2(1(3cos(2πx - 2) + 2)^2 + 3(3cos(2πx - 2) + 2) + 1) - 1)/(-2(1(3cos(2πx - 2) + 2)^2 + 3(3cos(2πx - 2) + 2) + 1) + 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 -2sin(2π(-2|(5((1x - 2)/(3x - 2)) + 2) + 2| + 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(2|(-2sin(3π(-2x^2 + 2x - 4) - 2) + 3) - 3| - 1) + 2)/(1(2|(-2sin(3π(-2x^2 + 2x - 4) - 2) + 3) - 3| - 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1326 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(3cos(3π(4((2x - 2)/(3x + 1)) + 4) - 2) + 3)| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 116 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-1(2cos(1π(2|x| + 1) + 1) + 1) + 2)^2 + 5 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) = -2cos(2π(-3(3|(-5x + 1) + 2| + 3)^2 + 5(3|(-5x + 1) + 2| + 3) + 2) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1211 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2π(-1|(5x + 4) + 1| + 3) + 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(2π(-1|(5x - 3) - 1| + 1)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-3cos(2π(5(-1|x - 2| - 1)^2 + 1(-1|x - 2| - 1) + 1) + 3)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1647 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3π(-1((-1(-4x) + 3)/(2(-4x) - 3))^2 - 4((-1(-4x) + 3)/(2(-4x) - 3)) + 1) - 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-2(1sin(3π((3x + 1)/(-2x - 2)) + 3) + 3) + 3)^2 + 4(-2(1sin(3π((3x + 1)/(-2x - 2)) + 3) + 3) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "How many solutions does the equation -4(3(-1sin(1π((1x - 1)/(2x + 1)) + 1) + 2)^2 - 4(-1sin(1π((1x - 1)/(2x + 1)) + 1) + 2) - 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2sin(3π(5((2x)/(-2x - 3))^2 - 1((2x)/(-2x - 3)) - 3) - 3) - 2 have in the interval [-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) = -3sin(3π(1(-3|(1x + 4) + 1| - 2)^2 - 1(-3|(1x + 4) + 1| - 2) + 4)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1215 | MATH |
[
{
"content": "How many solutions does the equation (3(-1(-3cos(3π(2|x - 1|) + 2) + 2) + 2) + 3)/(-1(-1(-3cos(3π(2|x - 1|) + 2) + 2) + 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 zeros does the function f(x) = -1sin(2π((2(-5x^2 + 3x + 1))/(-1(-5x^2 + 3x + 1) - 1)) - 2) 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 -4(3(2sin(3πx + 1) + 1)^2 + 4(2sin(3πx + 1) + 1) - 1) - 4 = 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) = -3(-5(2cos(3πx - 1) - 2) - 2)^2 - 5(-5(2cos(3πx - 1) - 2) - 2) have in the interval [-10, 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) = 3cos(2π(3|((1x + 2)/(-3x + 2)) + 3| + 1) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(2sin(1π(-3x) + 1) + 2)^2 + 1(2sin(1π(-3x) + 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 zeros does the function f(x) = (2(-2sin(3π(-4(4x - 4)^2 + 3(4x - 4) + 2)) + 2) - 1)/(1(-2sin(3π(-4(4x - 4)^2 + 3(4x - 4) + 2)) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1082 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(-2cos(2π(-4((-1x + 3)/(3x + 3)) + 1) + 3) - 2)^2 - 4(-2cos(2π(-4((-1x + 3)/(3x + 3)) + 1) + 3) - 2) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107 | MATH |
[
{
"content": "How many solutions does the equation 3|(-2cos(1π(1x^2 - 1x + 4) + 3) - 3) + 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 402 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(-3cos(3π(3(-1|x + 1| - 3)^2 + 2) + 1)) - 2)/(2(-3cos(3π(3(-1|x + 1| - 3)^2 + 2) + 1)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1276 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(1(1|x - 1| + 2) - 1) + 3) - 3 = 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(1|(-2sin(2π(4x + 3) + 2) + 1) + 3| - 3)^2 + 5(1|(-2sin(2π(4x + 3) + 2) + 1) + 3| - 3) - 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 zeros does the function f(x) = 3|((1(-3sin(1π(5x - 1) + 2) - 1) + 3)/(-2(-3sin(1π(5x - 1) + 2) - 1) - 1)) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-1cos(1π(-2|x - 2| - 3) + 3) - 1)^2 + 5(-1cos(1π(-2|x - 2| - 3) + 3) - 1) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(5(-3cos(1π(-1x^2 - 1x + 2) + 1) - 2) + 4) + 2)/(-3(5(-3cos(1π(-1x^2 - 1x + 2) + 1) - 2) + 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 194 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(2π(3((-2(5x - 5) - 3)/(2(5x - 5)))^2 + 2((-2(5x - 5) - 3)/(2(5x - 5))) + 5) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1π(-2|(5((2x + 1)/(1x - 3))^2) - 3| + 2) + 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 354 | MATH |
[
{
"content": "How many solutions does the equation (2(2cos(1π(-3x - 2) + 1) + 2))/(-1(2cos(1π(-3x - 2) + 1) + 2) + 3) = 0 have in the range [-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) = 3cos(2π(1(1|x - 2| + 2) + 5) + 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 zeros does the function f(x) = -1cos(3π(3(5x^2 + 2x + 4) - 3) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1164 | MATH |
[
{
"content": "How many solutions does the equation 1sin(1π(5((-2(2|x + 1| - 2) - 3)/(-3(2|x + 1| - 2) + 1)) - 4) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1sin(1π(2(5(3|x - 1| - 3)^2 + 3(3|x - 1| - 3) + 1) + 2) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1584 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(-3(2cos(1πx + 1))^2 + 3(2cos(1πx + 1)) + 2) + 2| + 1 where -10 ≤ x ≤ 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) = 1cos(2π((3(-3(-2|x - 1| + 1) - 3) - 3)/(2(-3(-2|x - 1| + 1) - 3) + 3)) - 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3π(-5(-3(-1|x + 3| + 2)^2 - 1(-1|x + 3| + 2) + 3) - 1) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1544 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1cos(3π((2(3x) - 3)/(-1(3x) - 2)) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5(-1sin(1π(3|(5x^2 + 1x + 1) + 1| - 3) - 1)) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1033 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1cos(1π(-4(3|x - 3| + 2)^2 + 2(3|x - 3| + 2) - 5) + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1137 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4((3(3cos(2π(3x^2 - 5x - 4) + 2) + 2) + 1)/(3(3cos(2π(3x^2 - 5x - 4) + 2) + 2) + 3)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1168 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3cos(3π(1|((3x - 3)/(2x - 3)) - 1| - 3) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(3sin(3π(-1x) - 1) + 1) - 1| - 3 have in the interval [-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) = -3(-2sin(1π(-3|(-3x^2 - 5x + 4)|) - 2) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1423 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-3cos(3π(2x^2 + 4x - 2) + 1) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 750 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(5(-2cos(2π((1x)/(3x + 2)) - 3) - 1)^2 - 3(-2cos(2π((1x)/(3x + 2)) - 3) - 1) + 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(-1cos(3π(5(3|x + 2|) - 5) - 2)) + 2)/(2(-1cos(3π(5(3|x + 2|) - 5) - 2)) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 900 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(-3cos(1π(-2x^2 + 5x + 4) + 2) + 2) - 2)/(2(-3cos(1π(-2x^2 + 5x + 4) + 2) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 393 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1sin(2π(3((2x + 2)/(3x + 2))^2 - 4((2x + 2)/(3x + 2)) + 2) + 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "How many solutions does the equation -1|(3(2cos(3πx + 3) + 3) - 4) + 1| + 1 = 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) = -2|(4(2sin(2πx + 1) + 1)^2 - 3(2sin(2πx + 1) + 1)) - 3| + 3 where -10 ≤ x ≤ 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) = (-2(3(1|(2sin(3πx - 1) - 1) + 2|)^2 + 2(1|(2sin(3πx - 1) - 1) + 2|) - 1) - 1)/(1(3(1|(2sin(3πx - 1) - 1) + 2|)^2 + 2(1|(2sin(3πx - 1) - 1) + 2|) - 1)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 120 | MATH |
[
{
"content": "How many solutions does the equation -3cos(1π((3(-1x^2 - 2x - 1) + 2)/(-3(-1x^2 - 2x - 1) - 1)) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "How many solutions does the equation 1((-1(-3cos(1πx + 1) + 2) + 3)/(1(-3cos(1πx + 1) + 2) - 2)) - 1 = 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) = (1(2(3sin(3π(5x^2 + 4x + 5) + 1) + 1) + 2) - 2)/(-1(2(3sin(3π(5x^2 + 4x + 5) + 1) + 1) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 987 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(1π(4(1|x - 1| - 3)^2 - 2(1|x - 1| - 3) + 4) + 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 452 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-2sin(2π(-1|((2x + 3)/(-1x - 1)) + 2| + 2) - 2) + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "How many solutions does the equation -3cos(3π(3(3(2|x - 3|) - 3)^2 - 5(3(2|x - 3|) - 3) + 3) + 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1213 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2π(4(-4((1x + 3)/(2x + 2)) - 5)^2 + 5(-4((1x + 3)/(2x + 2)) - 5) + 4) + 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 364 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2π(-2|((-1x + 2)/(3x + 2)) + 3| + 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(1π(5(1|x + 1| - 1)^2 + 1(1|x + 1| - 1) + 2) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 820 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(2π(2|((2x + 1)/(-1x + 3)) + 2| - 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3cos(1π(-2|(-1(3x^2 + 2x + 2) - 4) - 1| + 2) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1167 | MATH |
[
{
"content": "How many solutions does the equation 1|(1sin(2π(4((3x - 2)/(-3x - 3)) - 3) - 2) - 3) + 1| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "How many solutions does the equation 1(-2sin(3π(-4x - 5) - 2))^2 + 2(-2sin(3π(-4x - 5) - 2)) - 5 = 0 have in the range [-10, 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) = -1cos(1π(3(-2|x - 2| - 3)^2 + 4(-2|x - 2| - 3) - 4) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1129 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(3sin(2π(2((-3x + 2)/(-2x + 3))^2 - 3) - 3)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 123 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(4(-3sin(2πx) + 1)^2 - 1(-3sin(2πx) + 1) - 2) - 5 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) = -2cos(3π(1|(-5((2x - 1)/(1x + 3)) - 2) + 3| - 3) + 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 209 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(2π(4(3(3|x - 2| - 2) + 2)^2 - 1(3(3|x - 2| - 2) + 2) + 2) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1210 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(5(-2cos(2π((2x + 1)/(-1x + 2)) + 2) - 2)^2 + 5(-2cos(2π((2x + 1)/(-1x + 2)) + 2) - 2) - 2) - 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3sin(1π(5(-2|x - 3| + 3) + 5) + 1) + 1) - 1)/(-1(3sin(1π(5(-2|x - 3| + 3) + 5) + 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) = 1(1cos(2π((-2x + 2)/(1x + 3)) + 2) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(3π(-4(-2x^2 + 5x) + 1) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1064 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(-3sin(2π(2|(4x^2 + 4x + 3) - 2| + 1) + 2) - 2) - 2)/(1(-3sin(2π(2|(4x^2 + 4x + 3) - 2| + 1) + 2) - 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 986 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|((2(2sin(3π(-1x + 1) - 2) - 2) + 3)/(3(2sin(3π(-1x + 1) - 2) - 2))) + 3| + 3 have in the interval [-10, 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) = -3sin(3π(2|(1((1x + 3)/(1x)) - 4) - 3| + 1) + 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 134 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(2cos(2π(2x + 4) - 3) + 2) + 3| - 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) = 1|(2((2(-1cos(1πx + 3) + 1))/(3(-1cos(1πx + 3) + 1) - 2))^2 + 2((2(-1cos(1πx + 3) + 1))/(3(-1cos(1πx + 3) + 1) - 2)) - 4) + 2| - 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(-1sin(1π(-1(-1|x + 2| - 3)^2 - 4(-1|x + 2| - 3) + 4)) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 123 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(-2cos(1π(3x + 1) + 2) + 2) - 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) = 3|(1sin(1π(3x^2 - 1x - 5) + 2) + 2) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(2π(1(4(1|x - 1| + 3)^2 + 1(1|x - 1| + 3)) + 5) + 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1047 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-3cos(3π(5((-2x - 3)/(3x - 1)) - 3) - 1) + 2) - 3| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "How many solutions does the equation -2|((-2(5(-1cos(2πx + 3))^2 + 5(-1cos(2πx + 3)) - 5) + 1)/(-1(5(-1cos(2πx + 3))^2 + 5(-1cos(2πx + 3)) - 5) - 3)) - 2| + 3 = 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(3π(-1((-2x + 1)/(-2x))^2 - 5((-2x + 1)/(-2x)) - 2) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 103 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(-3sin(3π((-1(2|x - 3| - 3) + 3)/(-1(2|x - 3| - 3))) + 1) + 2)^2 + 4(-3sin(3π((-1(2|x - 3| - 3) + 3)/(-1(2|x - 3| - 3))) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 166 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1cos(1π((3(-1x^2 + 4x) + 3)/(-3(-1x^2 + 4x) + 2)) - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "How many solutions does the equation (1(-4(-2sin(2π(-1x^2 + 4x) + 3) + 3) + 4))/(2(-4(-2sin(2π(-1x^2 + 4x) + 3) + 3) + 4) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 205 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|(4(1sin(2πx + 3)) + 2) - 2| + 2 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(2π(-3|x| + 2) + 3)))/(-1(1cos(2π(-3|x| + 2) + 3)) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
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