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) = 4(2sin(3π(-3(3|x - 3| - 1)^2 - 5(3|x - 3| - 1) + 2) - 1) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1116 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(2sin(3π(-2|(-2x^2 - 1x - 3) + 3| + 2) - 3)) + 2)/(2(2sin(3π(-2|(-2x^2 - 1x - 3) + 3| + 2) - 3)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1022 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(3cos(2π((-2(-5x^2 - 2x + 2) - 3)/(-2(-5x^2 - 2x + 2) + 1)) + 2) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-3(-3|(-1sin(1πx - 2) + 2) - 1| + 1)^2 + 2) - 2)/(1(-3(-3|(-1sin(1πx - 2) + 2) - 1| + 1)^2 + 2) + 3) 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) = 3sin(3π((1(-5x + 1) - 3)/(-2(-5x + 1) + 3)) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "How many solutions does the equation 2|((3(2sin(1πx + 2) - 1) + 2)/(2(2sin(1πx + 2) - 1) - 1)) + 1| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1π(5((-3(3|x| - 3) - 3)/(-1(3|x| - 3)))^2 - 1((-3(3|x| - 3) - 3)/(-1(3|x| - 3)))) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 298 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(1cos(2π(5x + 2) + 2) - 2) - 1)/(3(1cos(2π(5x + 2) + 2) - 2) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "How many solutions does the equation -3|(-1cos(1π((-1(3x^2 - 4x - 1) + 2)/(2(3x^2 - 4x - 1) - 1)) + 2) - 2) + 2| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|((-1(1sin(1π(-1x - 2) + 2) - 1) + 3)/(-2(1sin(1π(-1x - 2) + 2) - 1) - 1)) - 3| + 1 where -10 ≤ x ≤ 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|((1(2x - 5) + 1)/(3(2x - 5) - 1)) + 3| + 2) - 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(3(2sin(1π(2|x + 3| + 3) - 3))^2 - 3))/(-1(3(2sin(1π(2|x + 3| + 3) - 3))^2 - 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many solutions does the equation (-3(2cos(1π(1(-2x - 4)^2 + 4(-2x - 4)) - 3) + 1) + 2)/(1(2cos(1π(1(-2x - 4)^2 + 4(-2x - 4)) - 3) + 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 513 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(-2|(2cos(2π(5x + 4) - 1) - 3) + 1|))/(3(-2|(2cos(2π(5x + 4) - 1) - 3) + 1|) - 1) have in the interval [-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|(2cos(1π(1x - 4) - 1) + 3) - 1| - 1 have in the interval [-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(-1(-4(-1cos(3πx + 3))^2 + 5(-1cos(3πx + 3)) + 3) + 1) + 1)/(1(-1(-4(-1cos(3πx + 3))^2 + 5(-1cos(3πx + 3)) + 3) + 1) - 2) have in the interval [-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(-2sin(1π(2|x - 1| + 1) - 2) + 2))/(2(-2sin(1π(2|x - 1| + 1) - 2) + 2) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation -3cos(3π(-1|((-2(-1x^2 - 4x) + 2)/(1(-1x^2 - 4x) + 2)) + 1| + 2) + 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(1sin(3π(3x^2 - 2x + 3) + 3)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1375 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(4(-1sin(1πx + 2)))^2 + 2(4(-1sin(1πx + 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) = (-3(-5(2sin(2π(-1|x - 3| + 2) - 3) + 2)^2 - 1(2sin(2π(-1|x - 3| + 2) - 3) + 2) + 3) + 3)/(2(-5(2sin(2π(-1|x - 3| + 2) - 3) + 2)^2 - 1(2sin(2π(-1|x - 3| + 2) - 3) + 2) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Yo... | 40 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(1π(-3(5(-2|x - 3|)^2 + 3) + 5)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1421 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(-2cos(2π(3(-2|x - 2| - 3) - 3) - 3) + 1)^2 - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "How many solutions does the equation -1sin(1π(-1|((-1(-5x^2 + 3x + 4))/(-3(-5x^2 + 3x + 4) + 4)) - 1| - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(3π(4((3(3x - 4) - 3)/(-2(3x - 4) - 1))^2 - 5((3(3x - 4) - 3)/(-2(3x - 4) - 1)) - 2) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 173 | MATH |
[
{
"content": "How many solutions does the equation -2|(5(2sin(3π((-2x - 1)/(2x - 3)) + 1) - 2)) - 1| + 3 = 0 have in the range [-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) = 3cos(1π((-3(2|x + 2| - 3) + 3)/(2(2|x + 2| - 3) + 3)) - 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(3sin(2π(5(3|x| + 2) - 1) - 2) + 1) + 1)/(-3(3sin(2π(5(3|x| + 2) - 1) - 2) + 1) + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "How many solutions does the equation -1cos(3π(-2|(3((3x + 1)/(2x - 3))) - 3| - 2) + 2) + 1 = 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) = 1|((3(-3(3sin(2πx) - 1)^2 + 1(3sin(2πx) - 1)) + 3)/(-2(-3(3sin(2πx) - 1)^2 + 1(3sin(2πx) - 1)) + 3))| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(3π(3(-1|(-2x^2 - 2x - 1) - 3| - 3) + 1) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1615 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(2sin(3π(5x^2 + 2x - 5)) - 3) - 1)/(-3(2sin(3π(5x^2 + 2x - 5)) - 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1100 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(3|(-3cos(2π((3x + 1)/(2x - 1)) - 3) - 2) + 2| - 2)^2 - 5(3|(-3cos(2π((3x + 1)/(2x - 1)) - 3) - 2) + 2| - 2) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 82 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(3sin(3π((2x - 2)/(-2x + 3)) - 3) + 2) - 1| where -10 ≤ x ≤ 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) = -3sin(2π(-1|(-1x^2 + 5x + 2)| - 2) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 424 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-1cos(3π(3(1|x - 1| - 2) - 3) + 1))^2 + 4(-1cos(3π(3(1|x - 1| - 2) - 3) + 1)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many solutions does the equation 1cos(3π(2|((-2(-1x - 5) + 3)/(-1(-1x - 5) + 3)) - 2|) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 88 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(1π((-2(1x + 3) - 1)/(-1(1x + 3) - 3)) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3cos(2π(-5(1x + 2)^2 + 4(1x + 2) - 5) + 1) + 2))/(-2(3cos(2π(-5(1x + 2)^2 + 4(1x + 2) - 5) + 1) + 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 770 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-3cos(3π(1x^2 + 5x - 5) + 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 636 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(-1sin(3π(-3((2x - 1)/(-1x - 3)) + 2) - 3)) + 1| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 284 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(1(3cos(2πx - 2) + 1)^2 - 1(3cos(2πx - 2) + 1) + 2) + 2)/(-2(1(3cos(2πx - 2) + 1)^2 - 1(3cos(2πx - 2) + 1) + 2) + 3) 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 3cos(1π(2(-5x + 1)^2 + 3(-5x + 1) + 4) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1579 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(3(1x + 2)^2 + 2(1x + 2) + 1) - 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 789 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(2sin(2π(1((2x + 3)/(-3x + 2)) - 2) + 1) - 2)^2 + 2(2sin(2π(1((2x + 3)/(-3x + 2)) - 2) + 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(2(5(-2sin(3πx + 1) - 1)^2 + 2(-2sin(3πx + 1) - 1) - 2) + 2) + 1| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(-3sin(1π(-2|x + 3| - 1) + 2) + 2) + 4 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|(-3sin(2π((1(1x^2 + 4x + 1) + 3)/(1(1x^2 + 4x + 1) - 3)) + 1) + 3) - 1| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(3cos(3π(-3x) - 2) - 1))/(-1(3cos(3π(-3x) - 2) - 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(-3cos(3π(-3|x - 1| + 2) + 3))^2 - 1(-3cos(3π(-3|x - 1| + 2) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(3π((-1(-4(-2x^2 + 4x + 4)))/(-2(-4(-2x^2 + 4x + 4)) - 3)) + 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "How many zeros does the function f(x) = (2(-3sin(1π(-2|x + 1| + 1)) + 3))/(-1(-3sin(1π(-2|x + 1| + 1)) + 3) - 1) have in the interval [-10, 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) = -2|(3cos(1π((2x + 1)/(-1x + 2)) - 3) - 2) - 1| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(2(3|x + 2| + 1) - 3) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 359 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(-3(-1cos(1π(-1x) - 2) - 2)^2 - 3(-1cos(1π(-1x) - 2) - 2) + 3) - 2| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "How many zeros does the function f(x) = (2(1(-1sin(2πx - 1) + 3)^2 - 2(-1sin(2πx - 1) + 3) - 3) + 1)/(-1(1(-1sin(2πx - 1) + 3)^2 - 2(-1sin(2πx - 1) + 3) - 3) - 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) = (-1(1(-1sin(2π(2|x - 2| - 1) + 2) - 1) - 2) - 3)/(-2(1(-1sin(2π(2|x - 2| - 1) + 2) - 1) - 2) + 1) where -10 ≤ x ≤ 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(2(-3sin(2π((-1x - 2)/(2x + 3)) + 1) - 1) - 5)^2 + 2(2(-3sin(2π((-1x - 2)/(2x + 3)) + 1) - 1) - 5) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-2sin(3π(1|x - 2| - 3) + 1) + 1) - 1 where -10 ≤ x ≤ 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(-3sin(2π((-1x + 2)/(-3x - 2)) - 1) - 1)^2 - 1(-3sin(2π((-1x + 2)/(-3x - 2)) - 1) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|((3(1(-3sin(2πx + 2) - 2)^2 - 5(-3sin(2πx + 2) - 2) - 4) + 2)/(-3(1(-3sin(2πx + 2) - 2)^2 - 5(-3sin(2πx + 2) - 2) - 4) + 2)) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(1|(3cos(1πx - 2) + 1) + 1| + 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(-4(-1cos(3π(1x - 3) + 1) + 1)^2 - 1(-1cos(3π(1x - 3) + 1) + 1) + 1) - 2)/(3(-4(-1cos(3π(1x - 3) + 1) + 1)^2 - 1(-1cos(3π(1x - 3) + 1) + 1) + 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1π(1((-1x + 2)/(1x - 3)) - 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2sin(1π((-3(3x^2 + 5x - 5) - 1)/(2(3x^2 + 5x - 5))) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(3((3(2sin(1πx + 2) + 2) + 3)/(3(2sin(1πx + 2) + 2) - 2)) - 4)^2 + 3(3((3(2sin(1πx + 2) + 2) + 3)/(3(2sin(1πx + 2) + 2) - 2)) - 4) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation -1cos(2π((-1(1x - 4) - 2)/(-2(1x - 4) - 1)) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "How many solutions does the equation 2(-2cos(3π(1x^2 + 2x + 5) - 2) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 274 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2(3|(-2sin(2πx + 3) + 2)|)^2 + 3(3|(-2sin(2πx + 3) + 2)|) + 2) - 2)/(-2(-2(3|(-2sin(2πx + 3) + 2)|)^2 + 3(3|(-2sin(2πx + 3) + 2)|) + 2)) 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) = 5(-3sin(3π(4(-3|x - 3| + 2) - 1) - 2))^2 - 4(-3sin(3π(4(-3|x - 3| + 2) - 1) - 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1200 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2π((-3(2x^2 + 5x + 2) - 3)/(3(2x^2 + 5x + 2) - 2)) - 2) + 2 equals zero.\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) = 3sin(3π(-1|(-4x^2 + 1x + 4) - 2| + 1) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 973 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(5(1|(-2sin(1πx - 2) + 1) - 2| - 3)^2 - 3(1|(-2sin(1πx - 2) + 1) - 2| - 3) - 3) - 2 have in the interval [-10, 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) = -3cos(3π(-1((-1x + 1)/(1x + 1))^2 + 5((-1x + 1)/(1x + 1)) + 4) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 204 | MATH |
[
{
"content": "How many solutions does the equation 1|(1cos(3π(5(-1x + 4)^2 - 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"
}
] | 1050 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(1|(-3cos(3πx + 3) - 1) - 2| - 2) - 1)/(1(1|(-3cos(3πx + 3) - 1) - 2| - 2) + 2) 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 3sin(1π(-3|(-1(1x^2 + 5x - 3) - 4)|) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2π(-1(2|x - 3| + 3)^2 + 2(2|x - 3| + 3) - 1) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1500 | MATH |
[
{
"content": "How many solutions does the equation -3cos(3π(-2|((1x + 2)/(2x + 2)) + 2| + 3) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "How many solutions does the equation (2(-2cos(1π(2|(-1x^2 - 2x + 5) - 1| - 2))) + 3)/(2(-2cos(1π(2|(-1x^2 - 2x + 5) - 1| - 2))) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 404 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(4(2cos(2π((1x - 1)/(-2x - 1)) - 2) + 1) + 2)^2 + 4(4(2cos(2π((1x - 1)/(-2x - 1)) - 2) + 1) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(4(1cos(3πx - 2) - 2) + 5) - 2| - 3 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 2sin(3π((2(-2x^2 - 5x + 2) - 2)/(2(-2x^2 - 5x + 2) + 3)) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "How many solutions does the equation -1cos(1π(2((2x + 2)/(-1x + 2)) - 4) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | MATH |
[
{
"content": "How many solutions does the equation -2|(3(2(-2sin(3πx + 2) + 2) - 4)^2 - 5(2(-2sin(3πx + 2) + 2) - 4) - 1) + 2| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2sin(2π(-2|(-3((3x + 1)/(-1x - 1))) + 1| - 2) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 181 | MATH |
[
{
"content": "How many solutions does the equation 4(3|(3(-3cos(1πx - 2) - 1)^2 + 2(-3cos(1πx - 2) - 1) - 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": "How many solutions does the equation -2cos(2π(1(3|(4x - 3) + 1| - 2)^2 - 4(3|(4x - 3) + 1| - 2) - 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1437 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(3sin(2π(-3x^2 - 4x - 3) + 3) + 3) - 1)/(1(3sin(2π(-3x^2 - 4x - 3) + 3) + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1014 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(3π(1(-2((3x - 3)/(3x + 2)) - 1)^2 - 2(-2((3x - 3)/(3x + 2)) - 1) + 5) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3π(5(-1|(3x + 2) + 2| - 3)^2 + 2(-1|(3x + 2) + 2| - 3) - 3) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1428 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(1π(-2(-3|((-2x - 2)/(3x + 2)) - 2| + 2) - 5) + 1) - 1 have in the interval [-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) = (-3(-1sin(1π(-1|(-1x - 3) - 2| - 3) - 3)) - 1)/(3(-1sin(1π(-1|(-1x - 3) - 2| - 3) - 3)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(1|(3sin(1πx - 3)) - 2| - 2)^2 + 4(1|(3sin(1πx - 3)) - 2| - 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) = -1(-2cos(3π(-2(3|x - 3| + 2)) - 3) + 3)^2 + 3(-2cos(3π(-2(3|x - 3| + 2)) - 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "How many solutions does the equation -2|(4(3sin(1π((-1x + 1)/(2x)) - 2) + 1)^2 + 4(3sin(1π((-1x + 1)/(2x)) - 2) + 1) - 1)| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "How many solutions does the equation (1(-3e^(-2(3(-2|x| - 1)^2 + 2(-2|x| - 1) - 2)) + 2) - 2)/(-2(-3e^(-2(3(-2|x| - 1)^2 + 2(-2|x| - 1) - 2)) + 2) - 1) = 0 have in the range [-10, 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) = (2(-4(3|(-2cos(1πx + 3)) - 2| - 2) - 5) + 3)/(3(-4(3|(-2cos(1πx + 3)) - 2| - 2) - 5) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(3(3sin(1π(5x^2 - 3x)) - 3) + 2) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "How many solutions does the equation -3(-1cos(3π((-2x - 1)/(-1x + 3))) - 2)^2 - 1(-1cos(3π((-2x - 1)/(-1x + 3))) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 94 | MATH |
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