messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-3sin(1π(-5x^2 - 5x + 4) - 1) - 3)^2 + 2(-3sin(1π(-5x^2 - 5x + 4) - 1) - 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 761 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(2sin(2π(5x^2 - 2x + 1) - 3) - 1) - 1)/(3(2sin(2π(5x^2 - 2x + 1) - 3) - 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 920 | MATH |
[
{
"content": "How many solutions does the equation -1|(2cos(2π(2|x + 2| + 2)) - 3) - 2| + 3 = 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(-3cos(1π(3x + 5) - 3) - 3) - 1)/(-3(-3cos(1π(3x + 5) - 3) - 3) - 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 -1(-2|(-3sin(2πx - 1) + 2) - 2| + 1)^2 + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(1π(2|(5x) - 1| - 2) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2((2(2|x - 2| - 1) + 1)/(3(2|x - 2| - 1) + 3))^2 - 3((2(2|x - 2| - 1) + 1)/(3(2|x - 2| - 1) + 3)) + 2 equals zero.\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) = -2(5(-1cos(2πx + 1)) + 5) + 4 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|(-1(-2x^2 + 4x + 5) + 5)| - 1 where -10 ≤ x ≤ 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((1(-2x^2 - 2x + 4) + 1)/(3(-2x^2 - 2x + 4) - 1))^2 - 2 where -10 ≤ x ≤ 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) = 3cos(2π(1(-2x^2 + 5x - 1)^2 + 4(-2x^2 + 5x - 1) + 4)) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 997 | MATH |
[
{
"content": "How many solutions does the equation 3cos(2π(2|(1|x - 3| + 2)| - 2) - 2) - 2 = 0 have in the range [-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) = (2(2cos(1π(-2x - 4) - 3) + 1) + 1)/(-3(2cos(1π(-2x - 4) - 3) + 1) - 1) 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) = -5(-3(2cos(1πx - 2) + 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) = -2sin(3π(-2(4x^2 - 1x + 2) + 2) - 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1071 | MATH |
[
{
"content": "How many solutions does the equation -2(-3(-3x^2 + 3x + 2) - 5)^2 - 4(-3(-3x^2 + 3x + 2) - 5) + 4 = 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) = (-1(2cos(2π(-1|x|) - 3) + 1) - 1)/(3(2cos(2π(-1|x|) - 3) + 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation -3cos(1π(3(-1x - 1)^2 - 3(-1x - 1) - 5) + 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 603 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(-1|((-1x + 2)/(-2x - 2)) - 2|) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(2(-2x^2 - 3x + 4)^2 + 5(-2x^2 - 3x + 4) - 4) - 1)/(-3(2(-2x^2 - 3x + 4)^2 + 5(-2x^2 - 3x + 4) - 4)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(3sin(2π(-5x^2 - 3x - 1) + 2) + 2) + 2)/(-1(3sin(2π(-5x^2 - 3x - 1) + 2) + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 832 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2(1cos(3π(-3|x + 2| - 2)) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many solutions does the equation (-1(1(2sin(2πx + 3) + 1)^2 - 5(2sin(2πx + 3) + 1) - 4) - 2)/(-2(1(2sin(2πx + 3) + 1)^2 - 5(2sin(2πx + 3) + 1) - 4) - 1) = 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) = 5(2cos(1π(2x^2 - 1x - 1) + 3) - 2)^2 + 4(2cos(1π(2x^2 - 1x - 1) + 3) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((3(-3cos(3πx + 3) - 3) + 3)/(2(-3cos(3πx + 3) - 3) - 1)) - 1)/(1((3(-3cos(3πx + 3) - 3) + 3)/(2(-3cos(3πx + 3) - 3) - 1)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(-4(-1x^2 + 3x + 3)^2 + 3(-1x^2 + 3x + 3) + 4) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1333 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3π(-5((-2x + 2)/(-1x - 1))^2 - 3((-2x + 2)/(-1x - 1)) - 4) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 294 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2π(2(4x - 2)^2 + 3(4x - 2) - 2) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1526 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(-3sin(3π(-2|x + 2| + 2) - 3) + 2) - 3 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) = (-1(-5(-1|x + 3| + 3)^2 + 2(-1|x + 3| + 3) + 3) - 2)/(-2(-5(-1|x + 3| + 3)^2 + 2(-1|x + 3| + 3) + 3) - 1) where -10 ≤ x ≤ 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) = -1(-3|(-3|x + 3| + 1) + 2| - 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 -3sin(3π((-2(-2|x - 2|) + 1)/(-2(-2|x - 2|) - 3)) + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "How many solutions does the equation 4((1(-1cos(3πx + 1) + 2) - 2)/(2(-1cos(3πx + 1) + 2) - 1))^2 + 2((1(-1cos(3πx + 1) + 2) - 2)/(2(-1cos(3πx + 1) + 2) - 1)) - 1 = 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) = -3(-1sin(2π(-1x - 1) + 1) - 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3e^(-1(5(-1|x + 2| + 3)^2 + 4(-1|x + 2| + 3) - 4)) 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 3((-2(3x^2 - 4x - 3) + 3)/(3(3x^2 - 4x - 3) - 1))^2 + 4((-2(3x^2 - 4x - 3) + 3)/(3(3x^2 - 4x - 3) - 1)) - 5 = 0 have in the range [-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) = 1sin(1π((3(3|x + 3| - 3))/(-1(3|x + 3| - 3) + 3)) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-1sin(3π(2|x - 2| - 1) + 2) - 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) = 3cos(1π((-1(1x + 5) - 2)/(-3(1x + 5))) + 2) - 3 have in the interval [-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) = -3sin(2π(-5(3|x + 3| + 3) + 4) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1sin(3π(-3|(-1|x + 1| - 1) - 3|) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-1cos(3π(-3|x - 2|) + 3) - 2) + 3)/(1(-1cos(3π(-3|x - 2|) + 3) - 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3π((-2((3x - 2)/(3x)))/(1((3x - 2)/(3x)) + 2))) - 2 equals zero.\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) = -2|(-2cos(2π((2x)/(-2x + 3)) + 1) + 2) - 1| + 1 where -10 ≤ x ≤ 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) = -3(-3(1|x + 1|)^2 - 5(1|x + 1|) + 2)^2 + 1(-3(1|x + 1|)^2 - 5(1|x + 1|) + 2) + 1 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(-3sin(2π(-3|x - 1| - 2) - 3) - 2))/(-2(-3sin(2π(-3|x - 1| - 2) - 3) - 2) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation -1(-4(-2cos(1πx - 2))^2 + 5(-2cos(1πx - 2)) + 3) - 1 = 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) = (2(5(-3cos(1πx) - 2)^2 - 1(-3cos(1πx) - 2) - 4) + 1)/(-3(5(-3cos(1πx) - 2)^2 - 1(-3cos(1πx) - 2) - 4) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(-5(-3x - 4)^2 - 3(-3x - 4) + 5)| + 3 where -10 ≤ x ≤ 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) = -2(-5(2x + 2)^2 + 1(2x + 2) + 2)^2 + 1(-5(2x + 2)^2 + 1(2x + 2) + 2) + 3 where -10 ≤ x ≤ 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) = -2cos(3π(5(1|x + 2| - 3)^2 - 3(1|x + 2| - 3) - 3) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1218 | MATH |
[
{
"content": "How many solutions does the equation 4(3sin(3π(1x + 2) - 3) + 1) + 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) = (-3(-3(3cos(3πx + 3) - 3) - 3) + 3)/(-1(-3(3cos(3πx + 3) - 3) - 3) + 3) 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) = -1(-3(1e^(1x) - 2)^2 + 4)^2 - 3(-3(1e^(1x) - 2)^2 + 4) + 5 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 3sin(2π(3|(4x^2 - 2x - 1) + 3| - 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1632 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(-2|(-3cos(2πx + 3) - 1) + 3| - 2) + 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) = -2sin(1π(3|(5x^2 - 4x) + 1| - 3) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1457 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(3(-1cos(2πx + 2) - 1) + 5) + 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) = 4(2cos(1π((-2x)/(3x + 2)) + 1) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-2sin(3π(-3x) - 2) - 2) - 3)/(-1(-2sin(3π(-3x) - 2) - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3(-1x^2 + 5))^2 - 2(3(-1x^2 + 5)) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(5((-1x - 1)/(-2x)) - 4) + 3) + 3 = 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) = 3cos(1π(4(-3x - 2)^2 - 4(-3x - 2) - 5) + 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1485 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(2π(-3(-3x^2 - 4x - 2)^2 - 4(-3x^2 - 4x - 2) + 5)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1334 | MATH |
[
{
"content": "How many solutions does the equation 2|(-1cos(1π(1x + 1) + 1) - 3) + 2| = 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) = 5(-3sin(3π(-3|x + 3| - 1) + 2)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(1π(1(1x + 3) - 1) - 2) + 3 have in the interval [-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) = -4(-5(-5x^2 - 3x + 2) + 1)^2 + 4 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) = 1(2(2sin(3πx + 3) + 2)) - 1 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) = -5(-3(1cos(1πx + 3))^2 - 4(1cos(1πx + 3)) - 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(-1|(2cos(3πx) + 1)| - 3) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-2sin(3π(1|x + 2| + 3) + 3)) - 3)/(-3(-2sin(3π(1|x + 2| + 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) = 2|(2cos(3π(3|x - 1| - 1) + 3)) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(2cos(3π((-2x + 2)/(2x + 1)) + 1) - 1) + 1)/(-3(2cos(3π((-2x + 2)/(2x + 1)) + 1) - 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "How many solutions does the equation -5((2(1cos(3πx + 3)) + 2)/(-3(1cos(3πx + 3)) - 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 solutions does the equation (-2((2(-3sin(1πx - 2)))/(-3(-3sin(1πx - 2)) - 1)) - 2)/(-3((2(-3sin(1πx - 2)))/(-3(-3sin(1πx - 2)) - 1)) - 1) = 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) = (-1(3cos(2π(-3x^2 - 1)) - 2) - 3)/(1(3cos(2π(-3x^2 - 1)) - 2) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1132 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(4(3sin(1πx - 1) + 1)^2 - 1(3sin(1πx - 1) + 1) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation 3|((-2(3sin(2πx) + 3) + 3)/(2(3sin(2πx) + 3) - 1))| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3π(1(-1x^2 - 3x + 2) + 2)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 614 | MATH |
[
{
"content": "How many solutions does the equation (2(-3cos(1π(1x - 5) - 2) - 1) - 3)/(-3(-3cos(1π(1x - 5) - 2) - 1) - 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) = 2sin(1π(-4(5x - 3)^2 + 2(5x - 3)) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1423 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(3π(-2|(-3|x| + 3) - 1| - 2) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1π((-2((-3x + 3)/(-3x - 3)) - 2)/(-2((-3x + 3)/(-3x - 3)) - 3)) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(-2((1x - 3)/(3x - 1))^2 + 1) + 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 zeros does the function f(x) = 4(4((1x - 1)/(-3x))^2 + 4((1x - 1)/(-3x)) - 1)^2 + 2(4((1x - 1)/(-3x))^2 + 4((1x - 1)/(-3x)) - 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) = (3(-5(3cos(3πx - 3) - 1)) + 1)/(-1(-5(3cos(3πx - 3) - 1)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π(4(-4x^2 + 3x - 5)^2 - 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 733 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π(2((-1x + 1)/(1x - 3))^2 - 5((-1x + 1)/(1x - 3)) - 1) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 213 | MATH |
[
{
"content": "How many solutions does the equation (2((-3(3sin(1πx + 2) + 1) + 2)/(-3(3sin(1πx + 2) + 1) - 3)))/(-2((-3(3sin(1πx + 2) + 1) + 2)/(-3(3sin(1πx + 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": "Find the number of x-intercepts of the function f(x) = 3|((3(2x^2 - 3x - 2) - 2)/(-1(2x^2 - 3x - 2) + 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(-3sin(1π(1|x + 3|) + 3) - 1) + 5 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) = 2(4((3x + 3)/(1x - 2))^2 - 1((3x + 3)/(1x - 2)) - 1)^2 - 4(4((3x + 3)/(1x - 2))^2 - 1((3x + 3)/(1x - 2)) - 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 zeros does the function f(x) = -3cos(1π((-2(3|x - 1| - 3) + 3)/(2(3|x - 1| - 3) + 3)) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(1π(-1(3|x - 2| + 3)^2 + 1(3|x - 2| + 3) - 3) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 897 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((-3(2sin(1πx + 2) + 1) - 2)/(-3(2sin(1πx + 2) + 1) - 3))| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation -4(1cos(3π((-3x - 2)/(-2x + 1)) + 3) - 1)^2 - 4(1cos(3π((-3x - 2)/(-2x + 1)) + 3) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1sin(2π(-2((3x - 3)/(-3x)) + 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(4(-4x^2 - 3x + 4) + 1)^2 - 3(4(-4x^2 - 3x + 4) + 1) + 1 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(2sin(3π((-3x + 2)/(3x + 1)) - 2) - 3)^2 + 3(2sin(3π((-3x + 2)/(3x + 1)) - 2) - 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
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