messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "How many solutions does the equation 2((3(-3sin(1π(2|x| + 2) - 2)) + 1)/(-1(-3sin(1π(2|x| + 2) - 2))))^2 + 4((3(-3sin(1π(2|x| + 2) - 2)) + 1)/(-1(-3sin(1π(2|x| + 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": "Find the number of x-intercepts of the function f(x) = 2|(-5((1(-3sin(1πx - 1) + 2) - 3)/(-2(-3sin(1πx - 1) + 2) - 3)) + 4) + 3| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "How many solutions does the equation 1cos(2π(-1(5x + 4)^2 - 5(5x + 4) - 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1124 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1((1(1sin(3π(-1|x - 2|) + 3) + 1) + 1)/(-2(1sin(3π(-1|x - 2|) + 3) + 1) + 3)) - 4 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) = -2sin(2π(5(-3x^2 - 5x - 2)) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1335 | MATH |
[
{
"content": "How many solutions does the equation 2|(-1cos(1π(3((2x + 2)/(2x + 1)) + 2) - 1) - 3) + 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(3sin(2π((-3(-3|x + 2| + 3))/(-2(-3|x + 2| + 3) - 1)) + 3) - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((-1(2cos(1πx)))/(-3(2cos(1πx)) - 1)) + 1| + 1 equals zero.\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) = 3cos(2π(5((3(-2x - 5))/(-2(-2x - 5) + 3))^2 - 4((3(-2x - 5))/(-2(-2x - 5) + 3)) - 1) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 173 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-2sin(3π(3x^2 - 1x - 3) - 2) - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1442 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3((-2(1sin(3πx + 2) + 1) + 2)/(-2(1sin(3πx + 2) + 1) + 1)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1cos(3π((1x - 1)/(-1x + 2)) - 3))^2 - 2(1cos(3π((1x - 1)/(-1x + 2)) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1((-2(3cos(3πx + 1)))/(-2(3cos(3πx + 1)) - 1))^2 - 5((-2(3cos(3πx + 1)))/(-2(3cos(3πx + 1)) - 1)) + 3 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 -3sin(1π(5((3(-3|x| - 1) - 3)/(-3(-3|x| - 1) - 1)) + 1) + 2) = 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) = -2|(4(-3sin(3π(5x^2 - 3x - 2)) + 2) + 3) + 2| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1079 | MATH |
[
{
"content": "How many solutions does the equation (3(-1(1sin(3π(3|x| - 3) - 2))^2 + 3(1sin(3π(3|x| - 3) - 2))) - 2)/(2(-1(1sin(3π(3|x| - 3) - 2))^2 + 3(1sin(3π(3|x| - 3) - 2))) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many solutions does the equation (-1(1(2cos(3π(2|x + 1| + 2) - 2) + 3)) + 2)/(-2(1(2cos(3π(2|x + 1| + 2) - 2) + 3)) + 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 4((-1(-1sin(2π(-1|x| - 3) - 1) - 1) - 2)/(3(-1sin(2π(-1|x| - 3) - 1) - 1) + 2))^2 - 3((-1(-1sin(2π(-1|x| - 3) - 1) - 1) - 2)/(3(-1sin(2π(-1|x| - 3) - 1) - 1) + 2)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(3sin(1π(-1(-5x^2 - 5x + 4) + 4) + 1) + 2) - 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 578 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(3cos(1π((-2(-3|x| + 2) - 1)/(-3(-3|x| + 2) + 2)) + 3) + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "How many solutions does the equation 3|(4(-3cos(2π((3x)/(1x + 1)) + 1) + 2) - 2) - 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(3π(4(-4(1|x| + 1) + 1)^2 - 1(-4(1|x| + 1) + 1) - 3) + 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1250 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(3π(-3(3(-1|x + 3| + 2)^2 + 5(-1|x + 3| + 2) + 2) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1460 | MATH |
[
{
"content": "How many solutions does the equation -1(-5((-1(-3cos(1πx + 2) + 2) + 3)/(2(-3cos(1πx + 2) + 2) - 3)) + 4)^2 - 3(-5((-1(-3cos(1πx + 2) + 2) + 3)/(2(-3cos(1πx + 2) + 2) - 3)) + 4) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 40 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(-1(-3sin(1πx))^2 - 3(-3sin(1πx)) + 1) - 2| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(-3sin(1π(-1|(-2x - 5) + 3| - 2)) + 1)^2 - 1(-3sin(1π(-1|(-2x - 5) + 3| - 2)) + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 78 | MATH |
[
{
"content": "How many solutions does the equation -4(2(-1sin(2πx - 3) + 1)^2 - 2(-1sin(2πx - 3) + 1) - 2) + 5 = 0 have in the range [-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) = 1cos(2π(1(2|x + 1| - 1)^2 + 3(2|x + 1| - 1) - 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1424 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3π((2(3(1|x| - 3) + 2) - 3)/(3(3(1|x| - 3) + 2) - 2)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(1π(-4(-5x^2 - 2x + 1) + 1) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1168 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5(1cos(3π(4x - 1) + 2))^2 - 3(1cos(3π(4x - 1) + 2)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2π(-2|(3x^2 + 3x - 2) - 2| + 2)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1523 | MATH |
[
{
"content": "How many solutions does the equation -3(-1|(-1sin(3πx + 3) + 3) - 3| - 1)^2 - 5(-1|(-1sin(3πx + 3) + 3) - 3| - 1) - 1 = 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) = -3(3sin(3π(4((3x - 1)/(1x + 3))^2 - 1) - 1) - 2) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 673 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1(-2|(1cos(1πx) - 2) + 2| + 2)^2 - 4(-2|(1cos(1πx) - 2) + 2| + 2) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|((-1(-2cos(2πx - 3) - 1) - 3)/(1(-2cos(2πx - 3) - 1))) - 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) = -4(3cos(3π(-2|(-4x - 5) + 1| + 1) - 1))^2 + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|((-3(4(3sin(2πx - 2)) + 2) - 3)/(1(4(3sin(2πx - 2)) + 2))) - 2| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "How many solutions does the equation 2(3sin(1π((1x - 3)/(-1x - 3)) + 1) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3π((-1(-4x + 1))/(3(-4x + 1) + 3)) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many solutions does the equation (2(-1(-1|(-2sin(2πx + 2) - 3) + 1| - 3)^2 - 3(-1|(-2sin(2πx + 2) - 3) + 1| - 3) + 2) + 2)/(2(-1(-1|(-2sin(2πx + 2) - 3) + 1| - 3)^2 - 3(-1|(-2sin(2πx + 2) - 3) + 1| - 3) + 2) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Y... | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1((2(1cos(1πx + 3)) - 1)/(3(1cos(1πx + 3)) - 2)) + 3) + 3| - 3 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) = -1cos(2π(-2|((-2(-5x + 1) - 1)/(-1(-5x + 1) + 3)) + 1| + 3) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(-3sin(1π(-4x - 2) - 2) - 2) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "How many solutions does the equation -3sin(3π(-3(-2|x + 1| + 1) + 2) - 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 177 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(3π((-2(3|x| - 2) - 3)/(2(3|x| - 2) - 3)) - 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "How many solutions does the equation 2|(-3cos(2π(-1x + 5) + 2) + 1) + 1| - 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 solutions does the equation 4(1sin(1π(1|x - 1| + 2) - 3)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(1((1x + 2)/(3x + 2))^2 + 3((1x + 2)/(3x + 2)) + 2) - 2) - 1 = 0 have in the range [-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) = -2|(-2sin(1π(-3(-3x)^2 - 1(-3x) - 3) + 1) + 3) - 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1000 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(2π(-1|(-5(4x^2 + 3x - 5) + 1) - 3| + 1) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1518 | MATH |
[
{
"content": "How many solutions does the equation 3sin(2π(2((-2(1|x| + 2) - 2)/(3(1|x| + 2) - 1))^2 + 1((-2(1|x| + 2) - 2)/(3(1|x| + 2) - 1)) - 4) - 3) + 1 = 0 have in the range [-10, 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) = -3|(2(2cos(1π(1x^2 + 2x - 3)) - 1) - 2) + 3| where -10 ≤ x ≤ 10.\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) = -1sin(3π(-1(-3|x + 1|) + 1) - 2) where -10 ≤ x ≤ 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) = -5(1(-3sin(3πx - 3) - 1)^2 + 1(-3sin(3πx - 3) - 1) - 3) + 1 equals zero.\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|(1(-2cos(3πx + 1) - 1)^2 + 4(-2cos(3πx + 1) - 1) + 2)| equals zero.\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) = 1cos(3π((1(-5(2x^2 + 4x + 2)) - 3)/(3(-5(2x^2 + 4x + 2)))) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1π(3(-3|(-2x^2 + 3x + 5) - 1| - 2) + 5) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1152 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(3π((-2(3|x + 1|) - 3)/(2(3|x + 1|) - 1)) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(1(-3|(3sin(1πx - 2) - 2)| - 1) + 4) - 2)/(-2(1(-3|(3sin(1πx - 2) - 2)| - 1) + 4) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-3sin(2π((-1(2|x| - 3) - 1)/(-3(2|x| - 3) + 4)) - 3) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2sin(1π(-4(-2|((1x + 2)/(-2x + 1)) + 1| + 2) - 4) + 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(3π(4(-2|(2x^2 - 1x + 3) - 2|) - 2) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1146 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(-3sin(1π(1(1x - 1)^2 - 5(1x - 1) - 2) - 3) + 2) + 2)/(-2(-3sin(1π(1(1x - 1)^2 - 5(1x - 1) - 2) - 3) + 2) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 226 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(-2sin(3π((-1(1|x + 1| - 1) - 2)/(2(1|x + 1| - 1) + 2)) + 3) + 2)^2 + 5(-2sin(3π((-1(1|x + 1| - 1) - 2)/(2(1|x + 1| - 1) + 2)) + 3) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 30 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(-1sin(2π(-1((-2x - 1)/(-2x - 2)) + 3) + 3) - 3) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2π(3((2x - 1)/(-1x - 3)) - 3) - 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3π(-5(3((-1x + 2)/(-1x + 3))^2 + 5((-1x + 2)/(-1x + 3)) - 1) - 2) + 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 393 | MATH |
[
{
"content": "How many solutions does the equation 4(2cos(2π(-3|(5x^2 - 1x + 2) + 1| - 2) - 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1365 | MATH |
[
{
"content": "How many solutions does the equation 3cos(2π((1(-5x^2 - 4x + 4) - 3)/(-1(-5x^2 - 4x + 4) - 2)) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-3sin(3π((1(-3|x| + 2) - 2)/(-2(-3|x| + 2) - 2)) - 3) - 1)^2 + 3(-3sin(3π((1(-3|x| + 2) - 2)/(-2(-3|x| + 2) - 2)) - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(5(-2sin(2πx - 3) - 1))| + 2 equals zero.\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) = -2sin(2π((-3(-1(1|x + 1| + 2)^2 + 2(1|x + 1| + 2)) - 2)/(-3(-1(1|x + 1| + 2)^2 + 2(1|x + 1| + 2)) - 3)) - 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|((-2(3cos(1πx + 3) - 2) - 3)/(2(3cos(1πx + 3) - 2) + 2)) + 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(-3cos(1π(-4(1|x - 2|)^2 + 5(1|x - 2|) - 4) - 1) + 1) + 2)/(-2(-3cos(1π(-4(1|x - 2|)^2 + 5(1|x - 2|) - 4) - 1) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 581 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(1π(3|(5x^2 + 2x + 3) - 3| + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1639 | MATH |
[
{
"content": "How many solutions does the equation -3|(-2cos(1π(5(2x - 3)^2 - 1(2x - 3) - 5) - 2) + 2) - 3| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 175 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(-1|(5(3sin(1πx + 1) + 2)^2 - 4(3sin(1πx + 1) + 2) + 4) - 3| + 3) + 5 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 1cos(3π(4((3x + 1)/(-2x - 1))^2 + 3((3x + 1)/(-2x - 1)) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 85 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2cos(2π(1|x - 2| - 2) + 1) + 3) + 4 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) = 5(-5(1sin(2π((3x + 3)/(-2x)) + 2) + 1)^2 - 1(1sin(2π((3x + 3)/(-2x)) + 2) + 1) + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "How many solutions does the equation (3(3cos(1π(1(4x^2 - 5) - 1)) - 3) + 3)/(1(3cos(1π(1(4x^2 - 5) - 1)) - 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 758 | MATH |
[
{
"content": "How many solutions does the equation (-3(1cos(1π(5x^2 - 5x - 4) + 1)) - 2)/(2(1cos(1π(5x^2 - 5x - 4) + 1)) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 883 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2π(3|(-1x - 1) - 2| - 1) + 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) = 5(3cos(3π(1((1x + 2)/(2x + 1))^2 + 4((1x + 2)/(2x + 1)) + 5) + 2) - 3) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 85 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-3sin(2π((3x - 2)/(2x - 1)) - 1) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(-4(1(2sin(2πx + 2) - 1))^2 + 2)| - 2 where -10 ≤ x ≤ 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) = -4(3(-2sin(1π(-3|x - 3| - 2) + 2) - 1)^2 - 5(-2sin(1π(-3|x - 3| - 2) + 2) - 1) - 1) - 1 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(1(1sin(1πx + 2) + 1) + 2) + 3)/(-3(1(1sin(1πx + 2) + 1) + 2) + 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) = -3((-2(3cos(2πx - 2) + 1) - 2)/(3(3cos(2πx - 2) + 1) + 2))^2 + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many solutions does the equation -4(-3cos(2π(1((-1x - 3)/(-2x - 1))^2 - 4((-1x - 3)/(-2x - 1)) + 3) + 3) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 106 | MATH |
[
{
"content": "How many solutions does the equation (1(-3(-4(-3cos(3πx - 2) - 2)^2 - 5(-3cos(3πx - 2) - 2) - 2) - 3))/(-1(-3(-4(-3cos(3πx - 2) - 2)^2 - 5(-3cos(3πx - 2) - 2) - 2) - 3) + 3) = 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) = 2|(-2sin(3π(1x^2 + 1x - 3) + 3) + 1)| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 602 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(3((-1(3sin(1πx - 1)) + 1)/(-1(3sin(1πx - 1)))) - 2)^2 + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(2π(3(-1(3|x| + 1) + 1)^2 - 1(-1(3|x| + 1) + 1)) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1222 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1sin(1π(2(-2|x| + 2)^2 + 4(-2|x| + 2) + 5) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 510 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(2sin(2π(-1|((-1x)/(-2x - 2)) + 1| - 1) - 1) + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (2(-3sin(2π(-1|x + 2| - 3) - 3) - 3) + 3)/(1(-3sin(2π(-1|x + 2| - 3) - 3) - 3) + 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(-1(-1|(-1sin(1πx - 2)) + 2| - 3) - 5))/(-3(-1(-1|(-1sin(1πx - 2)) + 2| - 3) - 5) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(1(1cos(2πx + 1))^2 + 2(1cos(2πx + 1)) - 1) - 2)/(-3(1(1cos(2πx + 1))^2 + 2(1cos(2πx + 1)) - 1) + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 6