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) = -3(1(2sin(2πx + 1) - 1)^2 + 4(2sin(2πx + 1) - 1) - 1) - 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(4(2cos(2πx) - 1)^2 - 2(2cos(2πx) - 1))^2 + 1(4(2cos(2πx) - 1)^2 - 2(2cos(2πx) - 1)) - 4 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) = 1cos(2π((2(-1x - 2) - 2)/(-3(-1x - 2) - 1)) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4((-1(-3sin(1πx - 3) + 2) - 1)/(2(-3sin(1πx - 3) + 2) + 1))^2 + 2((-1(-3sin(1πx - 3) + 2) - 1)/(2(-3sin(1πx - 3) + 2) + 1)) + 5 equals zero.\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(2sin(3πx) - 2)^2 + 2(2sin(3πx) - 2) + 4) + 3)/(-2(1(2sin(3πx) - 2)^2 + 2(2sin(3πx) - 2) + 4) + 3) where -10 ≤ x ≤ 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(-3cos(3π(4x + 5) + 2) - 1) + 3 equals zero.\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) = 2cos(1π(3(-3x^2 + 1x)^2 - 2(-3x^2 + 1x) + 3) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 972 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(2|(-3x + 5) + 3|) - 3) + 2 = 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) = 1sin(2π(-2(-3|x + 1| - 1)) + 2) 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 (2(2|(-4x^2 + 1x + 2) - 1| - 1) + 1)/(1(2|(-4x^2 + 1x + 2) - 1| - 1) + 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 zeros does the function f(x) = -3(3sin(3π(1|x| - 3) + 3) - 1)^2 + 1(3sin(3π(1|x| - 3) + 3) - 1) + 4 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) = 2|(-2e^(2(-2x^2 + 5x - 5)) + 1) - 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(1π(1|(-2|x + 1| + 3) + 1| - 3)) + 1 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 1(2(4x^2 - 5x - 5)^2 - 5(4x^2 - 5x - 5) - 1) + 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) = -2cos(1π(1|(-1|x - 2|) + 1| + 3) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "How many solutions does the equation (-2(-4(-3sin(3πx + 2) - 2)^2 + 5(-3sin(3πx + 2) - 2) + 5) + 1)/(1(-4(-3sin(3πx + 2) - 2)^2 + 5(-3sin(3πx + 2) - 2) + 5) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(1π(3(-1|x - 3| + 3)^2 - 2(-1|x - 3| + 3) + 4) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 420 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π(-2((-1x - 3)/(-3x + 1)) + 5) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(-3(1x^2 - 2x - 1) - 5) + 2| - 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) = 2cos(2π(2(1x - 1)^2 - 1(1x - 1) - 3) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 794 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3π(1|(2x^2 - 2x - 2) + 3|) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 521 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3((-3(1|x - 2| - 3) - 1)/(-1(1|x - 2| - 3) - 3))^2 + 1((-3(1|x - 2| - 3) - 1)/(-1(1|x - 2| - 3) - 3)) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -1(-4(-1x^2 - 3x + 4) + 3)^2 + 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 -2cos(2π(-1(1|x + 2|)^2 - 2(1|x + 2|) - 4)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 496 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(-3cos(3π(-4x - 3) + 1) - 3))/(-1(-3cos(3π(-4x - 3) + 1) - 3) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2sin(3π(1((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1))) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(2sin(1π((-1x - 3)/(3x + 3)) - 1) + 2)^2 + 3(2sin(1π((-1x - 3)/(3x + 3)) - 1) + 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) = 4((2(2cos(2πx - 2)) + 3)/(-3(2cos(2πx - 2)) - 3))^2 + 3((2(2cos(2πx - 2)) + 3)/(-3(2cos(2πx - 2)) - 3)) - 1 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) = -3(5(2x^2 + 2x - 5) + 5)^2 - 4(5(2x^2 + 2x - 5) + 5) + 2 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) = 3(-4(2sin(2πx + 3) + 1)^2 + 1(2sin(2πx + 3) + 1) + 4) - 2 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) = (3(5(-1|x - 2| + 2)^2 - 1(-1|x - 2| + 2)) - 2)/(2(5(-1|x - 2| + 2)^2 - 1(-1|x - 2| + 2)) - 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) = 3|(-2|(-1sin(3πx + 2) - 2) - 1| + 2) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3π(-3|(3|x - 3| + 3) + 2| - 1) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 270 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(-2(-4x + 4)^2 - 5(-4x + 4) + 1)| + 2 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) = 5(-3|(-2sin(2πx + 2) - 2) + 2| + 1) - 1 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(2sin(1π(1x + 3) + 3) + 1) - 1)/(-1(2sin(1π(1x + 3) + 3) + 1) - 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) = (2((-1(-3cos(3πx - 1) + 3))/(2(-3cos(3πx - 1) + 3) - 3)) + 2)/(-3((-1(-3cos(3πx - 1) + 3))/(2(-3cos(3πx - 1) + 3) - 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) = 3cos(3π(-3|(-1x - 5) - 3| - 2) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1π(-2(-2x^2 - 1x - 3) + 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(3π(-3(2|x - 1| + 1) + 5) - 2) - 1 where -10 ≤ x ≤ 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) = -2(-2cos(2π(-1|x + 3|) - 2) - 2) - 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 1|(1sin(3π(-2|x - 3| + 3) + 2) + 2) - 3| - 2 = 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((-1(3x - 3) - 3)/(2(3x - 3) - 1)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-3(-2e^(1x) + 2)^2 - 5(-2e^(1x) + 2))^2 - 1(-3(-2e^(1x) + 2)^2 - 5(-2e^(1x) + 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) = 2(4(-1x + 1)^2 - 3(-1x + 1) - 1)^2 - 5(4(-1x + 1)^2 - 3(-1x + 1) - 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) = (-2(1|(3|x + 1| - 3) - 3| - 3))/(-1(1|(3|x + 1| - 3) - 3| - 3) + 2) 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) = (-1(-2|(-1x^2 - 5x)| - 2) - 3)/(2(-2|(-1x^2 - 5x)| - 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) = 1(-3(-3cos(1πx + 3) - 2) - 2) + 4 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) = -5(-1(-2x^2 + 5x + 5)^2 + 3(-2x^2 + 5x + 5) + 3) 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) = 4(1(3|x + 3| - 3)^2 - 5(3|x + 3| - 3) + 1) + 3 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 2|(-1(-5x + 5)^2 - 5(-5x + 5) - 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 -4(1cos(2π(-4x - 3) - 2) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(-5(2sin(2πx + 1) + 2)^2 + 3(2sin(2πx + 1) + 2) - 3) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(1sin(2π((3x)/(3x - 2)) - 3))^2 - 3(1sin(2π((3x)/(3x - 2)) - 3)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2π(1(1|x - 2| + 1) + 2) + 1) + 2 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) = (-2(3(-1x^2 - 2x + 2)^2 - 5(-1x^2 - 2x + 2) - 1) - 1)/(-3(3(-1x^2 - 2x + 2)^2 - 5(-1x^2 - 2x + 2) - 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) = 4(-1|(3x^2 + 2x)| + 2)^2 - 3(-1|(3x^2 + 2x)| + 2) - 5 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) = -2sin(2π(-1((1x + 3)/(1x - 3))^2 - 3((1x + 3)/(1x - 3)) - 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 297 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(3sin(3π(3|x + 1|) - 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many solutions does the equation 3cos(2π((-1((1x)/(-3x + 4)) + 3)/(-2((1x)/(-3x + 4)) - 2)) - 3) - 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) = (-1((-1(2sin(1πx) - 1) + 1)/(1(2sin(1πx) - 1))) + 1)/(1((-1(2sin(1πx) - 1) + 1)/(1(2sin(1πx) - 1)))) 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(-2|(1|x + 3|)| + 1) + 1) + 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 -2(-2sin(2π(2|x - 1| - 3) - 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 zeros does the function f(x) = -1(-2|(-3|x + 3| + 1) + 2| + 1)^2 - 5(-2|(-3|x + 3| + 1) + 2| + 1) - 5 have in the interval [-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) = (-3(5(2sin(2πx + 1) - 1) - 3) - 3)/(1(5(2sin(2πx + 1) - 1) - 3) - 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) = 2cos(2π((2((-1x - 1)/(1x + 3)) - 2)/(-1((-1x - 1)/(1x + 3)) - 2)) - 3) - 1 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) = 3cos(1π(-4(1|x - 1| - 2)^2 - 5(1|x - 1| - 2) + 4) - 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 602 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(2π((2((-1x - 2)/(3x + 2)) - 2)/(-1((-1x - 2)/(3x + 2)) + 2))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(3π((-3((1x + 2)/(2x)) + 1)/(-3((1x + 2)/(2x))))) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(-3sin(3π((2x - 3)/(-1x + 3)) + 1) - 2) - 2)/(-2(-3sin(3π((2x - 3)/(-1x + 3)) + 1) - 2) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(2π(4(-3|x|)) - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "How many solutions does the equation -4(-3cos(3π(-1|x - 3| - 2) + 1) - 1) - 5 = 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) = 1(-1(-3cos(3πx - 1) + 1)^2 + 3(-3cos(3πx - 1) + 1) - 1) + 2 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(1π(2(5x + 4) - 2) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π(4(3x^2 - 5x - 4) + 4) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1233 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2π(3|(-1x^2 + 3x) - 3|) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 532 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(2π((1(-4x + 2) - 1)/(-3(-4x + 2))) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many solutions does the equation 2|(1cos(2π(-1x^2 - 3x - 5) + 2) + 1) - 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 408 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(-5(-2x^2 + 2)^2 - 1(-2x^2 + 2) - 1) - 1)/(-1(-5(-2x^2 + 2)^2 - 1(-2x^2 + 2) - 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 solutions does the equation -1|((3(-3cos(3πx - 3)) + 3)/(1(-3cos(3πx - 3)) + 2)) - 2| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(1(4x^2 + 5x - 5)) - 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 672 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1cos(3π(-3(-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"
}
] | 1884 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(5(2cos(3πx + 3) + 1)^2 + 3(2cos(3πx + 3) + 1) - 2)^2 + 2(5(2cos(3πx + 3) + 1)^2 + 3(2cos(3πx + 3) + 1) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109 | MATH |
[
{
"content": "How many solutions does the equation -2sin(3π(-3(-4x^2 + 3x - 1) + 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1561 | MATH |
[
{
"content": "How many solutions does the equation (1(-1(-4x^2 + 5x + 2)^2 - 3(-4x^2 + 5x + 2) + 2) + 3)/(2(-1(-4x^2 + 5x + 2)^2 - 3(-4x^2 + 5x + 2) + 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 zeros does the function f(x) = -3sin(3π(-5((2x + 1)/(-1x - 1))^2 + 2((2x + 1)/(-1x - 1)) - 5) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 146 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(2sin(2π(1x^2 + 2x + 1)) - 2))/(-1(2sin(2π(1x^2 + 2x + 1)) - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 193 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2π((-3(1x - 1))/(-2(1x - 1) + 3)) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(3|(-3sin(2πx + 1) - 1)| - 2) - 2)/(2(3|(-3sin(2πx + 1) - 1)| - 2) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "How many solutions does the equation 4(-1(-1|x| - 1) - 2)^2 - 5(-1(-1|x| - 1) - 2) - 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) = 1cos(2π(2|(3|x + 2| + 3) - 1|) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(-1sin(1π(-2x + 5) + 2)) - 1| - 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) = -1sin(2π(-2|(1|x + 1|) + 2| - 2) - 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) = -2(-2|(-2sin(1πx - 1) - 2) + 1| + 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-3cos(1π((1x - 2)/(-2x - 3))) - 1) + 3| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "How many solutions does the equation -3cos(1π(2((-2x + 3)/(2x - 1)) - 2) + 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "How many solutions does the equation -3|(-2|(4x - 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": "Determine the number of values x in [-10, 10] where f(x) = -2(1(1x^2 + 2x + 1) - 4)^2 + 3(1(1x^2 + 2x + 1) - 4) + 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) = 3sin(2π(-5(4x^2 - 2x + 1)^2 - 4(4x^2 - 2x + 1) + 4) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 578 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(2cos(1π(1x)) + 2) + 1)/(2(2cos(1π(1x)) + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
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