messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1π(2(1|x| + 1) - 5) - 1) 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) = -2(2sin(1π((1(-5x) + 2)/(-2(-5x) - 2)) - 3) - 3)^2 + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2sin(1π(-2|(4(-1x + 1)^2 - 4(-1x + 1) + 2)|) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1376 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(1π(3(-3((1x - 2)/(-2x + 3))^2 - 1((1x - 2)/(-2x + 3))) + 2) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "How many solutions does the equation (3(-2cos(1π(-4(-2|x + 3| + 1)^2 + 1(-2|x + 3| + 1) + 4) + 3) - 3) + 3)/(-3(-2cos(1π(-4(-2|x + 3| + 1)^2 + 1(-2|x + 3| + 1) + 4) + 3) - 3) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 1023 | MATH |
[
{
"content": "How many solutions does the equation 2cos(2π((-2(4(-1|x + 1| + 3) - 5) - 1)/(-1(4(-1|x + 1| + 3) - 5) + 3)) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2cos(3π(2|((-1x - 1)/(1x)) - 3| - 3)) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(-2sin(2π(3(-2|x + 2| - 3) - 5) - 3) + 3)^2 - 1(-2sin(2π(3(-2|x + 2| - 3) - 5) - 3) + 3) - 4 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) = (2(-1sin(2π(3(-1|x - 2| + 3) + 1) - 3)))/(-2(-1sin(2π(3(-1|x - 2| + 3) + 1) - 3)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(3sin(3π(3(-2|x + 2| - 2)^2 - 2(-2|x + 2| - 2)) + 3) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1359 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(2π(-1(3|x - 2| - 2)^2 - 2(3|x - 2| - 2) + 4)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1063 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(5((-1(-2sin(3πx - 1) + 3) + 3)/(3(-2sin(3πx - 1) + 3) + 2))^2 - 4((-1(-2sin(3πx - 1) + 3) + 3)/(3(-2sin(3πx - 1) + 3) + 2)) + 1) - 2 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 1(-2cos(2π((-1(-5x^2 - 2x - 4) + 2)/(-1(-5x^2 - 2x - 4) - 2)) + 2) - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1((-2(5(2cos(1πx + 3) - 1) + 4) - 1)/(2(5(2cos(1πx + 3) - 1) + 4) - 1))^2 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(2|(3sin(3π(-1x - 2) - 3) + 2) - 1| + 1) + 3)/(-2(2|(3sin(3π(-1x - 2) - 3) + 2) - 1| + 1) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5((2(3sin(1πx + 3) - 3) + 3)/(2(3sin(1πx + 3) - 3) + 1)) - 5 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) = -2|(4(2sin(2π(3x + 3) - 1))^2 - 2(2sin(2π(3x + 3) - 1)) - 5) + 2| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 89 | MATH |
[
{
"content": "How many solutions does the equation 2((-2(-3|(2sin(1πx) + 1) - 3| + 3) + 3)/(-3(-3|(2sin(1πx) + 1) - 3| + 3) + 2)) + 2 = 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) = 3cos(2π(5(-1(1|x - 2| - 2)^2 - 4(1|x - 2| - 2) - 5)) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1264 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π(-3((2(-3x^2 - 1x + 5) + 3)/(-1(-3x^2 - 1x + 5) + 3)) - 5) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 221 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(2π(2((3x + 1)/(1x))^2 - 5((3x + 1)/(1x)) - 1) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3((-2(2|(1sin(1πx + 3) + 3) - 3|) + 3)/(3(2|(1sin(1πx + 3) + 3) - 3|) - 2))^2 - 5((-2(2|(1sin(1πx + 3) + 3) - 3|) + 3)/(3(2|(1sin(1πx + 3) + 3) - 3|) - 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(-2cos(3π(-1|x + 3| + 3) - 3) - 2) - 1)/(3(-2cos(3π(-1|x + 3| + 3) - 3) - 2) + 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) = 2sin(2π(-1|(1(-1x - 3)^2 - 1(-1x - 3) - 4) - 2| + 2) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 211 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3|(2cos(1πx + 1) - 2) + 3| + 3) + 1 equals zero.\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) = 3|((2(2sin(2πx + 1)))/(2(2sin(2πx + 1)) - 1)) - 3| - 3 equals zero.\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(4(3cos(1π(3|x - 1| + 2) + 3) + 1)^2 + 4(3cos(1π(3|x - 1| + 2) + 3) + 1) - 5) - 3)/(3(4(3cos(1π(3|x - 1| + 2) + 3) + 1)^2 + 4(3cos(1π(3|x - 1| + 2) + 3) + 1) - 5) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 120 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(1π(-2(3|(1x^2 - 5x - 3) - 3| - 1) + 3) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1043 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((2(-1sin(1π(5x + 2) + 2) + 1) - 3)/(-2(-1sin(1π(5x + 2) + 2) + 1))) + 1| - 2 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) = 2(2((3(-3sin(3πx + 3) - 1) + 1)/(-2(-3sin(3πx + 3) - 1) - 3)) - 1)^2 + 2(2((3(-3sin(3πx + 3) - 1) + 1)/(-2(-3sin(3πx + 3) - 1) - 3)) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 120 | MATH |
[
{
"content": "How many solutions does the equation -2cos(1π(-2|(2(-4x - 4)^2 + 4(-4x - 4) + 5) + 1| + 2) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1179 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(-1cos(3π(-1x^2 - 4x - 3) - 3))| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 542 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2sin(2π(-1|(4(-5x^2 - 5x - 5) - 5) - 3| - 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1613 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2π(1(-3|x + 2| + 3) - 3) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(3π(-3|(3x^2 + 2) - 1| + 3) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1286 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(2(-4(1cos(2πx + 2) - 1)^2 + 3) - 1) + 2)/(-1(2(-4(1cos(2πx + 2) - 1)^2 + 3) - 1) - 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 -4(-2sin(1π(-4(-3|x| + 1)^2 + 5(-3|x| + 1)) - 1) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1304 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(1cos(3π(-1x) + 2) - 2)| + 2 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 3|((-3(4(3sin(2πx - 2) - 1)) + 1)/(2(4(3sin(2πx - 2) - 1)) + 3))| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-1cos(2π(1|(-3x^2 - 4x - 2) - 2| + 1) - 3) - 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1086 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π((-2(-1|x + 2| + 2) + 3)/(1(-1|x + 2| + 2) + 2)) + 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 231 | MATH |
[
{
"content": "How many solutions does the equation 2cos(1π(-1|(1x - 1) + 1| + 3)) - 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 solutions does the equation -1((-1(2cos(3π(3|x + 3| + 1) - 2) - 1) + 1)/(-2(2cos(3π(3|x + 3| + 1) - 2) - 1) + 1)) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many solutions does the equation -2(-3cos(1π((-2x - 3)/(2x - 1))) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "How many solutions does the equation 4((2(1sin(3π(2x^2 + 4x + 5) - 3) + 1) - 2)/(-2(1sin(3π(2x^2 + 4x + 5) - 3) + 1) + 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 482 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3π(1|(3(-2x^2 - 5x + 2) + 5) - 2| + 3)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1145 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(3π(-3(3|x|) + 2) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 267 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π((-1(4(3x^2 + 4x - 2) - 3) - 1)/(-3(4(3x^2 + 4x - 2) - 3) + 1)) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(3|((-2(-5x^2 - 1x + 4) + 3)/(-2(-5x^2 - 1x + 4) + 1)) - 2| - 3) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "How many solutions does the equation -2sin(3π(1(2|(3x^2 - 5x - 4) + 3| - 2) - 1) + 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1159 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(2π(-2|(-1x - 1) + 3| + 3) - 2) - 1 where -10 ≤ x ≤ 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) = (-3(-1|(-3sin(2π(5x^2 - 4x + 4) - 2) - 1) + 2| + 1) + 2)/(-2(-1|(-3sin(2π(5x^2 - 4x + 4) - 2) - 1) + 2| + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 487 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(-4(-2cos(2πx + 1) - 2) - 3)^2 + 5(-4(-2cos(2πx + 1) - 2) - 3) - 5 where -10 ≤ x ≤ 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(2|(-3(2sin(2πx + 1) - 2)^2 + 4(2sin(2πx + 1) - 2) - 4) + 2| - 1) - 3)/(3(2|(-3(2sin(2πx + 1) - 2)^2 + 4(2sin(2πx + 1) - 2) - 4) + 2| - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(-4((3(-3cos(1πx - 1) - 3) + 2)/(-1(-3cos(1πx - 1) - 3) - 1)) + 1) - 2| + 2 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) = -2|((3(-1sin(2πx + 2)) - 1)/(3(-1sin(2πx + 2)))) + 1| + 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) = 1(1cos(1π(3x^2 - 2) - 2) + 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2sin(1π(-1(-3|x| + 2)^2 + 3(-3|x| + 2) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1412 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3cos(1π(-3(-2|x - 2| - 2)^2 + 2(-2|x - 2| - 2) + 5) + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1694 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(-3|(-5(-1sin(2πx + 2))^2 - 3(-1sin(2πx + 2)) - 2) + 3| + 2) have in the interval [-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) = 3sin(1π((2(-1x - 4) + 3)/(2(-1x - 4) - 3)) - 3) - 3 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 -2cos(1π(-5(-2|x + 3|) + 4)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(3π(-3|((1(-5x + 5))/(-3(-5x + 5) + 2)) + 3| - 1) - 2) + 1 have in the interval [-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) = -2|(1cos(2π((-3x)/(3x - 2)) - 3) - 1) + 1| + 2 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 3(1cos(2π(-5x + 1) - 3) + 1)^2 - 4 = 0 have in the range [-10, 10]?\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((-3(1(3cos(1πx - 2) + 3) - 3) - 3)/(3(1(3cos(1πx - 2) + 3) - 3) - 2))^2 + 2((-3(1(3cos(1πx - 2) + 3) - 3) - 3)/(3(1(3cos(1πx - 2) + 3) - 3) - 2)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 40 | MATH |
[
{
"content": "How many solutions does the equation -4(1sin(3π(-4x^2 - 1x - 2) + 2)) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 942 | MATH |
[
{
"content": "How many solutions does the equation 2sin(1π(2(3|x + 2| - 2) - 3)) - 1 = 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 3cos(1π(5((3x - 2)/(2x - 1)) + 3) + 2) = 0 have in the range [-10, 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) = 3|(-3(3cos(2πx) - 3)^2 - 5(3cos(2πx) - 3) + 2) + 2| - 2 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(-2sin(1π(4(-2|x + 3| + 3) + 2) - 2) + 3) - 3)/(2(-2sin(1π(4(-2|x + 3| + 3) + 2) - 2) + 3) - 1) have in the interval [-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) = 5(-3(-1sin(3πx + 3) + 1) + 2)^2 - 2(-3(-1sin(3πx + 3) + 1) + 2) - 2 have in the interval [-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) = -2cos(2π(-4(-2|(-3x - 5) + 1| + 1)^2 - 5(-2|(-3x - 5) + 1| + 1) - 3) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1418 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π(5(1x^2 + 5x - 2) - 4) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1065 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(3(-2cos(1π(-3|x + 1| - 1) + 3)) + 3))/(2(3(-2cos(1π(-3|x + 1| - 1) + 3)) + 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(1π((-1(1|x + 3| - 1) - 3)/(1(1|x + 3| - 1))) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 127 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-1sin(1π(-3x + 3) + 2) - 1)^2 - 2(-1sin(1π(-3x + 3) + 2) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation 3cos(2π(5((-3(5x + 1) + 1)/(3(5x + 1) + 1))^2 - 3((-3(5x + 1) + 1)/(3(5x + 1) + 1)) + 5) + 3) - 1 = 0 have in the range [-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) = (-2(-2|(5(2sin(3πx - 1) - 1) + 2) + 2| + 1) - 2)/(-1(-2|(5(2sin(3πx - 1) - 1) + 2) + 2| + 1) + 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) = 2cos(3π(5((-1x - 2)/(-3x + 1)) + 1)) - 2 where -10 ≤ x ≤ 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) = 1(-1sin(2π(4(1|x - 2| + 1) + 1) + 3) + 1)^2 + 2(-1sin(2π(4(1|x - 2| + 1) + 1) + 3) + 1) - 5 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) = -1sin(1π((-2(3|x + 2| - 3) + 1)/(-2(3|x + 2| - 3) - 1)) + 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(2π(1|(3((-2x - 1)/(3x + 3)) + 1) + 1| + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(1(2cos(1π(1x + 5) - 3))^2 - 1(2cos(1π(1x + 5) - 3)) - 5) + 3)/(3(1(2cos(1π(1x + 5) - 3))^2 - 1(2cos(1π(1x + 5) - 3)) - 5) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(1π(2(-3|x| + 1)^2 - 3(-3|x| + 1) - 5)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1126 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(1π(4((1(1|x - 2|) - 1)/(-2(1|x - 2|) - 1)) - 3) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(2cos(3π((1(2x^2 - 3x - 4) + 1)/(-3(2x^2 - 3x - 4))) - 3) - 1) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "How many solutions does the equation (-1(2cos(1π(5(1x - 3)^2 + 3(1x - 3) + 1) - 2)) - 1)/(2(2cos(1π(5(1x - 3)^2 + 3(1x - 3) + 1) - 2)) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 813 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1π(4(-1|(5x + 1) + 1| - 1)^2 - 4(-1|(5x + 1) + 1| - 1) + 3) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1556 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(1cos(1π((3(-3x^2 - 2x + 3) + 2)/(2(-3x^2 - 2x + 3) + 3)) - 1) - 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "How many solutions does the equation -3|(-2sin(3π(5((2x + 2)/(-1x + 3)) - 1) - 3) - 2)| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 337 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(3|(-4(3sin(1πx) + 2) - 1) - 3| - 2) - 3)/(-3(3|(-4(3sin(1πx) + 2) - 1) - 3| - 2) - 1) have 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 -3sin(3π(-2|(1x^2 - 5x - 1)| - 1) - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 537 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(1π((1(-2|(-1x - 5) + 1| + 1))/(2(-2|(-1x - 5) + 1| + 1) - 1)) - 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1π(-1(3|((-1x + 1)/(3x)) - 1| - 3)^2 + 1(3|((-1x + 1)/(3x)) - 1| - 3) - 3) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3((-2(-3sin(2π(3|x + 3|) + 3) - 1) + 3)/(3(-3sin(2π(3|x + 3|) + 3) - 1) + 1))^2 + 5((-2(-3sin(2π(3|x + 3|) + 3) - 1) + 3)/(3(-3sin(2π(3|x + 3|) + 3) - 1) + 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 170 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-1cos(2π(-1|(-3x^2 + 2x + 2) + 3| + 2) + 1)) - 1)/(-2(-1cos(2π(-1|(-3x^2 + 2x + 2) + 3| + 2) + 1)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 523 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|(3cos(3π(5x^2 - 5x - 2)) + 1) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 479 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(1π(3|(1(-1x + 4)^2 + 4(-1x + 4) + 5) + 2| - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3sin(1π((3x + 1)/(1x - 3)) - 2) + 3)^2 - 2(3sin(1π((3x + 1)/(1x - 3)) - 2) + 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 114 | MATH |
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