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(3π(-2(2|x + 2| - 2) - 3) + 1) + 2 equals zero.\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) = 2|(2cos(3π((1x + 2)/(-2x - 2)) + 3) - 1) + 2| - 3 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|(-4(1cos(3πx + 1) + 1) - 2) + 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 4(1((1x - 1)/(-3x - 2))^2 - 5((1x - 1)/(-3x - 2)))^2 - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 2|(2cos(2π(2|x - 2| + 3) + 1) - 2)| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(2π(3|(2x^2 - 1x - 3) - 2| - 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1585 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1|(1sin(2πx + 1) - 3) + 1| - 3) + 1| + 3 equals zero.\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|(1sin(1π(5x^2 + 3)))| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1068 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(3π(4(2|x + 2| + 3)^2 - 2(2|x + 2| + 3) + 5) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1506 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(3cos(2π(-1x^2 - 3x + 1) + 3) - 1) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 164 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(-2|(-2|x| + 2) + 2| + 2)^2 - 4(-2|(-2|x| + 2) + 2| + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 3sin(2π(-3|(5x^2 + 4x - 5) - 2| + 3) - 1) + 3 = 0 have in the range [-10, 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(-3cos(2π(2x + 3) + 1) - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(1|(-2|x| + 3) + 2| + 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -3|(5(-3x^2 - 4x + 5) + 4) - 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(3cos(1π(5x - 4) - 2) + 2) - 1)/(3(3cos(1π(5x - 4) - 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 5(-2(3x^2 - 5x - 3)^2 + 5(3x^2 - 5x - 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π((2(-1x^2 + 1x + 2) - 1)/(-1(-1x^2 + 1x + 2) + 2)) + 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3sin(3π(2|x|) + 2)) + 1 equals zero.\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(1π(-2|((2x)/(-2x - 1)) - 3| - 3) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((-2(-1cos(3πx + 3) - 2) - 1)/(-3(-1cos(3πx + 3) - 2) - 3)) - 2| + 3 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) = -1sin(1π(1((-3x - 2)/(1x))^2 - 5((-3x - 2)/(1x)) + 5) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 95 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(3π((-1((2x)/(-3x - 3)) - 3)/(-1((2x)/(-3x - 3)) - 1)) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 125 | MATH |
[
{
"content": "How many solutions does the equation -2sin(3π(-4((-1x - 2)/(1x))^2 - 2((-1x - 2)/(1x)) - 3) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 250 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(5(-2cos(2πx + 3) - 2)^2 + 3(-2cos(2πx + 3) - 2) - 5) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation 5(4(-1|x + 2| + 1)^2 + 1(-1|x + 2| + 1) - 3) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(-3|(-2x^2 + 5x + 4)| + 3))/(2(-3|(-2x^2 + 5x + 4)| + 3) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(5(-4x^2 + 1x + 3) - 2)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(2π(-2|(2|x + 2| - 3) - 1| + 1) + 3) 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) = -2sin(1π(-5(4x^2 + 5x - 1)^2 - 3(4x^2 + 5x - 1) - 1) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 721 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-2(2cos(2πx + 3)) + 1)/(-3(2cos(2πx + 3)) - 2))^2 - 4((-2(2cos(2πx + 3)) + 1)/(-3(2cos(2πx + 3)) - 2)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(-1(3cos(2πx - 1) - 2)^2 + 5(3cos(2πx - 1) - 2) + 2) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1π(-1((-3x - 1)/(3x + 2)) - 4) - 3) + 3 equals zero.\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) = 5(3sin(2π(-1x) - 2) - 2) + 3 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) = 3(-2cos(3π(5x^2 + 5x) + 3))^2 - 2(-2cos(3π(5x^2 + 5x) + 3)) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1490 | MATH |
[
{
"content": "How many solutions does the equation -2sin(2π(3|(-3|x - 1| - 1) - 2| - 1) - 3) + 1 = 0 have in the range [-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) = 2sin(3π(1((-3x)/(-2x + 3)) + 3) - 3) + 2 where -10 ≤ x ≤ 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) = -1(-2cos(3π(-3x) - 3) + 1)^2 - 2(-2cos(3π(-3x) - 3) + 1) + 2 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) = -1cos(1π(-3|(2|x + 2| - 1) - 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) = (-3(-2|(-5x^2 - 3x - 1) + 1|) - 2)/(3(-2|(-5x^2 - 3x - 1) + 1|) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -3(-1sin(2π(-3x^2 + 4x + 5) - 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 509 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(3(2|x| - 3))^2 - 5(3(2|x| - 3)) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(4(-2|x - 3| + 2)^2 - 5(-2|x - 3| + 2) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 5(-2|((1x - 2)/(-3x + 4))| + 3)^2 + 3(-2|((1x - 2)/(-3x + 4))| + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2sin(3π(2|x + 3| + 1) - 1) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation -4(-1(3sin(1πx + 1) - 2)^2 + 5(3sin(1πx + 1) - 2) - 5) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2((2(1|x + 1| - 3) - 2)/(3(1|x + 1| - 3) - 1))^2 + 3((2(1|x + 1| - 3) - 2)/(3(1|x + 1| - 3) - 1)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5((-1(3x^2 - 2x - 2) + 3)/(-1(3x^2 - 2x - 2) - 3))^2 + 4((-1(3x^2 - 2x - 2) + 3)/(-1(3x^2 - 2x - 2) - 3)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(3π(3|((2x + 2)/(-1x - 2))| + 1) - 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 zeros does the function f(x) = 3cos(1π(-1|((-2x - 1)/(2x - 1))| - 3) - 1) have in the interval [-10, 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) = -3cos(3π(-3(-3|x + 3|)^2 + 1(-3|x + 3|) - 5) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1283 | MATH |
[
{
"content": "How many solutions does the equation 1|(-1|(1sin(3πx + 2) - 2)| - 3) + 2| - 3 = 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) = 3sin(3π(4(-3|x - 2| - 3)^2 - 5(-3|x - 2| - 3) + 3) + 1) - 2 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) = 3(-2sin(2π((2x)/(2x - 3))) - 2)^2 + 5(-2sin(2π((2x)/(2x - 3))) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(-1e^(2(-5x^2 + 4x + 1))) - 1| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(3π(2|(3x^2 + 3x + 5) + 1| - 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1698 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(-4(3sin(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": "How many solutions does the equation 2|((-1(-3cos(1πx + 3) + 2) + 3)/(-3(-3cos(1πx + 3) + 2) - 3)) - 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(2π(-3|((3x - 2)/(-1x + 3)) - 2| + 1) - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 138 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(2((2x + 3)/(-3x - 3))^2 - 2((2x + 3)/(-3x - 3)) - 1) - 3| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(3π(1(1|x + 1| + 3) + 5)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(-1(2x^2 - 5x - 1)^2 + 4)^2 + 3(-1(2x^2 - 5x - 1)^2 + 4) - 3 where -10 ≤ x ≤ 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) = -5(5(3cos(1πx + 2) - 1) - 3)^2 - 3(5(3cos(1πx + 2) - 1) - 3) 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(3(2x^2 - 2x - 3)^2 - 4(2x^2 - 2x - 3) + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(2cos(1π(5x + 2) + 3) - 3) + 2| + 1 equals zero.\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) = -1(-3|(-2|x + 1|) + 3| + 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-5((2x - 2)/(2x - 1))^2 - 1((2x - 2)/(2x - 1)) + 5) + 3| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-3(-3x^2 + 5x + 5) - 1)/(-2(-3x^2 + 5x + 5) - 1))^2 - 2((-3(-3x^2 + 5x + 5) - 1)/(-2(-3x^2 + 5x + 5) - 1)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(3sin(2π(2x + 4) + 2) - 3) + 3)/(1(3sin(2π(2x + 4) + 2) - 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(3π(1|(-1|x - 1| + 3)| - 1) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-2|(-1sin(2πx) + 3) - 2| + 3)| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(3π(-2|(-2|x - 3| + 3) + 3|) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation -1(-2cos(3π(-2x^2 + 2x + 5) - 1) + 2)^2 + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1162 | MATH |
[
{
"content": "How many solutions does the equation (2(3(-2|x + 1| + 3)^2 - 1(-2|x + 1| + 3) - 3) + 2)/(-3(3(-2|x + 1| + 3)^2 - 1(-2|x + 1| + 3) - 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-2|(2cos(3πx - 2) + 3) - 1| - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many solutions does the equation -3|(3(-3cos(2πx) - 3)^2 + 3(-3cos(2πx) - 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) = -4(-1(-5x^2 - 2x + 3) + 2)^2 + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 4(2(-2sin(3πx) - 3) + 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation -5(1|(1cos(2πx - 3) + 3) - 2| - 2)^2 - 1(1|(1cos(2πx - 3) + 3) - 2| - 2) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3π(-1((-2x - 1)/(-1x + 2)) - 2) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 141 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π((-1(2x - 1) + 3)/(-1(2x - 1))) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "How many solutions does the equation 2|(-1((3x + 3)/(-1x + 2))^2 + 5((3x + 3)/(-1x + 2)) - 1) + 2| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(3π(1(-1x^2 + 4x + 5)^2 - 4(-1x^2 + 4x + 5) - 4) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1050 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(1π(2(1x^2 - 5x - 1)^2 - 1(1x^2 - 5x - 1) + 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1269 | MATH |
[
{
"content": "How many solutions does the equation 2(-3((-3x + 2)/(3x + 2))^2 - 2((-3x + 2)/(3x + 2)) + 3)^2 + 5(-3((-3x + 2)/(3x + 2))^2 - 2((-3x + 2)/(3x + 2)) + 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -3((2(4x^2 + 3x - 1) + 2)/(3(4x^2 + 3x - 1) - 2))^2 + 3((2(4x^2 + 3x - 1) + 2)/(3(4x^2 + 3x - 1) - 2)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π(-2|((-3x - 3)/(-1x + 2)) + 2| - 2) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 213 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1sin(1π(-3|(-2x^2 - 5x - 2) - 3| - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1166 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(1π(4(5x + 1) - 4) + 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "How many solutions does the equation -1(-2sin(3π(5x - 1) - 3) - 3)^2 - 3(-2sin(3π(5x - 1) - 3) - 3) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(-3|(-5x^2 - 1x + 3) + 2| + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π(-2(1x^2 + 1x - 1) - 5) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 768 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(5(-4x^2 - 2x + 1)^2 - 5(-4x^2 - 2x + 1) + 1)^2 - 3(5(-4x^2 - 2x + 1)^2 - 5(-4x^2 - 2x + 1) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(1sin(3π((1x)/(-3x - 1)) + 3)) + 3)/(1(1sin(3π((1x)/(-3x - 1)) + 3)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(-3cos(3π(2|x| + 1) + 2) + 1) - 1)/(-2(-3cos(3π(2|x| + 1) + 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(1π((2(2x - 1) + 3)/(-1(2x - 1))) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "How many solutions does the equation 2(-3cos(3π(5x^2 + 4x + 4) + 1) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1319 | MATH |
[
{
"content": "How many solutions does the equation 2(3sin(3π(3|x - 1| - 1) + 3) - 3)^2 + 1(3sin(3π(3|x - 1| - 1) + 3) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 182 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(2(5x^2 + 4x)^2 + 4(5x^2 + 4x) - 1)| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation (2(-4(-2sin(2πx - 3)) - 1) + 2)/(2(-4(-2sin(2πx - 3)) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
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