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) = -1sin(2π(-2|(-5x + 2) - 1| + 1)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 399 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(1(-1|x + 2| + 3)^2 + 4(-1|x + 2| + 3) - 2) + 5 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((-1(-4x^2 + 4x + 3) + 1)/(2(-4x^2 + 4x + 3) - 3))^2 - 2((-1(-4x^2 + 4x + 3) + 1)/(2(-4x^2 + 4x + 3) - 3)) - 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) = -3sin(3π(2(5x + 1)^2 + 1(5x + 1) + 1)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1194 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(-3(2cos(2πx - 3) + 1) + 5) + 1)/(1(-3(2cos(2πx - 3) + 1) + 5) - 2) have in the interval [-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) = 3|(3((3x - 1)/(2x + 3))^2 + 3((3x - 1)/(2x + 3)) - 3) + 1| - 2 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) = 4(1e^(-1(4x^2 + 3x - 2)) - 3)^2 - 2(1e^(-1(4x^2 + 3x - 2)) - 3) - 1 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) = 3cos(1π(-1|(5x^2 - 2x - 3) - 2| + 2)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 434 | MATH |
[
{
"content": "How many solutions does the equation -2|(-3(2x + 1)^2 - 2(2x + 1) + 5) + 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 zeros does the function f(x) = -2cos(1π(5(5x - 2) - 5) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 225 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(1π(-1((2x - 2)/(-2x + 1)) - 4) + 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) = 1((3(2sin(1πx + 2) + 2) - 3)/(-2(2sin(1πx + 2) + 2) + 3))^2 - 5((3(2sin(1πx + 2) + 2) - 3)/(-2(2sin(1πx + 2) + 2) + 3)) - 1 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(2cos(2π(-5x^2 + 1x + 1) + 1) + 1) - 1)/(-1(2cos(2π(-5x^2 + 1x + 1) + 1) + 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 899 | MATH |
[
{
"content": "How many solutions does the equation 4(-2cos(1π(-3x^2 + 5x - 1) + 3) + 1)^2 - 2(-2cos(1π(-3x^2 + 5x - 1) + 3) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 465 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(-3((-2x - 3)/(3x + 3))^2 + 3((-2x - 3)/(3x + 3)) + 5) + 3| - 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 2cos(3π(-3((3x - 3)/(-1x + 2)) - 1) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 105 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(4(2cos(1πx + 3) - 2) + 5) + 1)/(-1(4(2cos(1πx + 3) - 2) + 5) + 3) 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(2(4x^2 - 4x - 4)^2 - 4(4x^2 - 4x - 4) + 2) + 3)/(2(2(4x^2 - 4x - 4)^2 - 4(4x^2 - 4x - 4) + 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 solutions does the equation -2(-2|(-2cos(3πx + 3) + 1) - 3| + 1)^2 - 5(-2|(-2cos(3πx + 3) + 1) - 3| + 1) - 2 = 0 have in the range [-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) = 4(3(1|x|) - 4)^2 - 1(3(1|x|) - 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(2(2x^2 + 3x + 1) - 4)^2 + 1(2(2x^2 + 3x + 1) - 4) 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(-1|x - 1| + 2)^2 - 4(-1|x - 1| + 2) + 4)^2 - 5(4(-1|x - 1| + 2)^2 - 4(-1|x - 1| + 2) + 4) + 5 = 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) = -2|((-3(5x^2 + 2x - 4) + 3)/(2(5x^2 + 2x - 4) - 1)) - 1| + 2 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) = -4(-4(3sin(1πx - 3) - 1) - 2)^2 + 1(-4(3sin(1πx - 3) - 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) = 3cos(1π((3((-1x - 3)/(2x + 1)))/(-2((-1x - 3)/(2x + 1)) - 3)) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3π(3(-1x) + 5) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3(1(4x^2 - 4x - 3)^2 - 5(4x^2 - 4x - 3) + 4)^2 - 5(1(4x^2 - 4x - 3)^2 - 5(4x^2 - 4x - 3) + 4) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π(-3(-5x + 2) - 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 901 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(3sin(3π(-2x + 5) - 1) + 3) - 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3|(-5(-3|x - 1| + 2)) - 1| - 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|((2(-3x^2 + 2x + 1) - 2)/(-2(-3x^2 + 2x + 1) - 2)) + 3| + 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) = -3|(-1(-1x^2 - 4x + 5)^2 - 2(-1x^2 - 4x + 5) + 4) + 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3sin(3π((3x + 1)/(2x)) + 2) - 3) + 2)/(1(3sin(3π((3x + 1)/(2x)) + 2) - 3)) equals zero.\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) = (1(-2sin(2π((3x - 1)/(-2x + 3)) - 2)) + 2)/(2(-2sin(2π((3x - 1)/(-2x + 3)) - 2))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(1sin(3π(-2|x + 2|) - 2)) + 1 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 5(-1(-1x^2 - 4x + 4)^2 - 5(-1x^2 - 4x + 4)) - 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 solutions does the equation 1(2sin(1π(-1|x + 1| - 1)) - 2) = 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) = 3(-3(3x^2 + 2x - 5) + 2)^2 - 2 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(-5(-1cos(2πx - 3) - 1)^2 - 3(-1cos(2πx - 3) - 1)) + 5 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) = -3sin(3π(1(5x^2 + 3x - 1) + 4) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1567 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(1(1|x + 1| - 1)^2 + 1(1|x + 1| - 1) - 3)^2 - 2(1(1|x + 1| - 1)^2 + 1(1|x + 1| - 1) - 3) - 4 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|(2|(-4x^2 - 3x + 2)| - 2) - 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(2π(-4(-1|x + 1|)^2 + 3(-1|x + 1|) - 2) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 730 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π(-1|((-3x - 2)/(-1x - 2)) + 3| + 2) + 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(5(5x)^2 - 4(5x) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1572 | MATH |
[
{
"content": "How many solutions does the equation 1sin(1π(3|(-2|x - 1| - 3) + 3| + 3) + 1) + 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) = 1sin(1π(4((-1x + 3)/(2x - 1)) + 2) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "How many solutions does the equation (2(-5(-1sin(1πx - 1))^2 - 3(-1sin(1πx - 1)) + 1) - 2)/(3(-5(-1sin(1πx - 1))^2 - 3(-1sin(1πx - 1)) + 1) - 2) = 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) = -3|(-3sin(3π(1x^2 - 3x - 4) - 1) - 3) + 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 822 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(3(1x^2 - 5)^2 - 2(1x^2 - 5) + 1) - 4 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) = -1cos(3π(1|(5x - 1) - 1| + 3)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(-3cos(1π(1|x| - 1) + 3) + 2) + 2 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) = 3e^(-1(5(2x^2 - 3x - 4)^2 - 4(2x^2 - 3x - 4) - 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 -3sin(1π(4(5x + 1)^2 + 1(5x + 1) - 1) - 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1166 | MATH |
[
{
"content": "How many solutions does the equation -3cos(3π(-5(-2x - 4)^2 - 4(-2x - 4) + 2)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1170 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(-3|(-3|x + 1| + 3) - 1| + 2) - 1| - 1 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) = 2(3cos(3π((-2x - 2)/(2x)) + 1) + 1)^2 + 5(3cos(3π((-2x - 2)/(2x)) + 1) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(-1((2x - 1)/(3x)) - 5) + 1) - 3 = 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(5((3x + 2)/(-2x - 1))^2 - 4((3x + 2)/(-2x - 1)) - 4)^2 + 2(5((3x + 2)/(-2x - 1))^2 - 4((3x + 2)/(-2x - 1)) - 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) = 1|((-2(-2cos(2πx + 3) + 1) - 3)/(2(-2cos(2πx + 3) + 1))) - 3| - 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) = 2cos(2π((1(-4x^2 + 3x))/(1(-4x^2 + 3x) + 1)) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(2cos(1π(-4x^2 - 4x - 3)) + 1) + 1)/(-2(2cos(1π(-4x^2 - 4x - 3)) + 1) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 365 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(3π(-2|((-2x - 1)/(2x)) + 1| - 3) + 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(1|(3x^2 - 5x - 2) - 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 solutions does the equation -1sin(2π(-1|(-5x + 5) - 1| - 1) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3(1cos(1π(2|x + 3| + 3) + 2) + 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) = (2(-3sin(3π(1x - 4) - 1) - 1) - 2)/(-3(-3sin(3π(1x - 4) - 1) - 1) + 1) 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) = (-2(-3|(2|x - 3| - 1) - 1| + 3) - 3)/(-3(-3|(2|x - 3| - 1) - 1| + 3) + 2) 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) = -1sin(2π(-1(-1|x + 3| - 3) + 1) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(4(-1x^2 - 1x + 3)^2 - 1(-1x^2 - 1x + 3) - 5) + 1)/(2(4(-1x^2 - 1x + 3)^2 - 1(-1x^2 - 1x + 3) - 5) - 1) 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) = (-1(-3(3sin(3πx + 1) - 3)^2 - 2(3sin(3πx + 1) - 3) + 2) - 2)/(-2(-3(3sin(3πx + 1) - 3)^2 - 2(3sin(3πx + 1) - 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) = 1|(1(-3cos(3πx - 3) - 3) + 5) - 2| - 1 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|(-1|(-1x + 1) - 1| - 1) + 3| + 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) = 2sin(3π(1(-1|x - 1|)^2 + 5(-1|x - 1|) + 1) - 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 182 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3|(1sin(2π(2x^2 + 1x - 3) + 3) + 1)| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 759 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(2π(-4(5x^2 - 4x - 5)^2 + 3)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1117 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3|((-2(-2sin(2πx - 2) - 3) - 3)/(2(-2sin(2πx - 2) - 3) + 2))| - 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) = -4(-1(3sin(1πx - 1) - 2)^2 - 1(3sin(1πx - 1) - 2) + 2)^2 - 4(-1(3sin(1πx - 1) - 2)^2 - 1(3sin(1πx - 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 zeros does the function f(x) = -3cos(2π(1|(2|x - 3| - 2) - 1|) - 2) - 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) = 2(-1(1sin(2πx - 2) + 1)^2) + 1 have in the interval [-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((-3(3sin(3πx - 3) + 3) + 3)/(-1(3sin(3πx - 3) + 3) + 2)) + 5 equals zero.\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) = -1cos(1π(4(1x^2 + 4x) - 4)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 832 | MATH |
[
{
"content": "How many solutions does the equation -3|((2(-3x^2 - 5x) - 2)/(1(-3x^2 - 5x))) + 1| + 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) = -3((1(-3cos(2πx) + 1) + 3)/(-2(-3cos(2πx) + 1) - 2)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation -2(-4(-1|x - 3| + 3)^2 - 2(-1|x - 3| + 3) + 2) + 4 = 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(-5(3x^2 - 4x) + 3)^2 - 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(2π(-2(-5x^2 - 5x - 1) + 3) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1538 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(1cos(2π(-2|x - 2| - 2) + 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) = 1sin(1π(1|(-5x - 4) - 3| + 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(1(-3|x + 3|)^2 + 3(-3|x + 3|) + 5) - 3)/(-2(1(-3|x + 3|)^2 + 3(-3|x + 3|) + 5)) 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(3π((-2(3x^2 - 5x + 3) - 1)/(1(3x^2 - 5x + 3) + 2)) + 1) + 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) = (1(3|(3x^2 + 4x - 5) - 3| - 1) - 2)/(-2(3|(3x^2 + 4x - 5) - 3| - 1) - 1) 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) = -5(2sin(3π(1x + 1)) - 1) equals zero.\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|(-3|(3x^2 + 2x + 3) - 3| + 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 2(1(2x^2 - 4x - 3)^2 + 3(2x^2 - 4x - 3) + 3) - 5 = 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) = 3|(2cos(1π(2x - 2) - 1) + 2) - 1| 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) = 1(2((1x - 1)/(3x - 2))^2 + 3((1x - 1)/(3x - 2)) - 1)^2 - 1(2((1x - 1)/(3x - 2))^2 + 3((1x - 1)/(3x - 2)) - 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) = -1((-3(-3|x| + 2) - 3)/(-1(-3|x| + 2) + 3))^2 - 4((-3(-3|x| + 2) - 3)/(-1(-3|x| + 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|(4(1|x - 3| - 3) - 4) + 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 -1|((-2(3cos(3πx) - 1))/(2(3cos(3πx) - 1) + 2)) + 3| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
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