messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(2cos(1π(-2(-3|x + 2| + 3) + 3) + 3) + 3)^2 - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(-2(-3x)^2 - 2(-3x) + 5)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1700 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(2sin(2π(4x^2 + 4x - 2) - 3) - 1) - 1)/(-3(2sin(2π(4x^2 + 4x - 2) - 3) - 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 359 | MATH |
[
{
"content": "How many solutions does the equation 2cos(2π(4((-1x - 1)/(1x))) + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "How many solutions does the equation -3cos(1π(2(4x^2 - 2x + 5) - 5) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1214 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(1π(-5(2|x + 3| - 1) + 5) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3((2(2sin(2πx - 3) + 2) - 3)/(1(2sin(2πx - 3) + 2))) + 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) = 4(-3sin(3π(-1|x - 1| + 3) - 3) - 3) + 4 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) = -4(-3cos(3π(2|x + 2| - 2) + 2)) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1sin(1π(5((-1(4x + 4) + 3)/(-1(4x + 4) + 2))^2 - 2((-1(4x + 4) + 3)/(-1(4x + 4) + 2)) + 1) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(3π(-3(5x + 3)^2 - 2(5x + 3) - 1) + 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1219 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1π(-5(3x - 3)^2 + 4(3x - 3) + 1) - 3) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1135 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1π(2((2x + 3)/(3x)) + 4) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(2π((-1(-2|x| + 3) - 3)/(-3(-2|x| + 3) - 3)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "How many solutions does the equation 3|((1(-3sin(3πx + 2) + 1) + 3)/(1(-3sin(3πx + 2) + 1))) + 2| - 2 = 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(-1sin(1π(4x^2 + 1x - 3) - 2)) + 1)/(-2(-1sin(1π(4x^2 + 1x - 3) - 2)) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 794 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(-2|(2(-2sin(2πx - 1) + 1)^2 + 4(-2sin(2πx - 1) + 1) - 2) + 2| + 2) - 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) = (-1(3cos(1π(3(-2|x + 2|) + 5) + 3)) - 2)/(3(3cos(1π(3(-2|x + 2|) + 5) + 3)) - 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) = 3cos(1π(2|(3(1x^2 + 2x) - 2) + 1| + 3) - 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 516 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2sin(2π(-3((3(3x^2 - 5x - 1) + 3)/(-1(3x^2 - 5x - 1) - 2)) - 4) - 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 125 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(-1(2cos(1πx - 3) - 1)) + 1)/(3(-1(2cos(1πx - 3) - 1)) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many solutions does the equation 3cos(3π(-3(-3|x - 1| - 1)^2 + 1(-3|x - 1| - 1)) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1550 | MATH |
[
{
"content": "How many solutions does the equation -3|(5((2(2sin(1πx + 2) + 3) - 3)/(-3(2sin(1πx + 2) + 3) + 2)) - 1) - 2| + 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) = -1(1(3|(-2cos(3πx + 2) - 1) + 1|)^2 - 3(3|(-2cos(3πx + 2) - 1) + 1|) - 4) + 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) = 3cos(3π((2(-2x^2 - 1x + 1) - 3)/(2(-2x^2 - 1x + 1) + 1)) + 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(2π(2|(-3x^2 - 1x + 1) - 3| - 1) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 959 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1π(-2|(-1x + 4) + 1| - 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) = -1|(3sin(2π((2(5x - 3))/(-2(5x - 3) - 1)))) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(-2sin(1π(-3|((-1x + 1)/(2x - 1)) - 2| + 1)) + 1) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(3π((2(1x^2 + 3x + 2) - 3)/(3(1x^2 + 3x + 2) + 3)) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "How many solutions does the equation -2(5(3|(2cos(2πx - 3) + 2) - 3| - 2) + 1)^2 + 4(5(3|(2cos(2πx - 3) + 2) - 3| - 2) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "How many solutions does the equation 2|(4(2sin(1πx + 3) + 2)^2 + 2(2sin(1πx + 3) + 2) - 2) + 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation 2cos(3π(4(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"
}
] | 1424 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(2π(-3|(5x^2 + 1x + 1) + 2| + 2) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1005 | MATH |
[
{
"content": "How many solutions does the equation 2(5(1sin(1πx + 3))^2 + 2(1sin(1πx + 3)) + 1) - 5 = 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((3(-2x + 5) - 1)/(2(-2x + 5)))) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(2π(-3(1|x| - 2) + 4) - 3) + 2 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) = -2sin(3π(-1|(1x + 1)|) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation 3|(-2cos(1π(-4(2x^2 - 5) + 2) + 1) + 2) - 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1196 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2π(1(2|x + 3| + 3)^2 + 2(2|x + 3| + 3) + 1) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1582 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(2cos(2π(2|(3x + 5) - 3| - 1) - 3)) - 2)/(3(2cos(2π(2|(3x + 5) - 3| - 1) - 3)) - 1) 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 -2sin(3π(-1|(1x - 5) + 3| - 1)) + 2 = 0 have in the range [-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) = 2sin(3π(1(2x^2 - 3x - 2) - 4) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1076 | MATH |
[
{
"content": "How many solutions does the equation 1(-1(2|(2cos(2πx - 3) + 2) - 3| - 2))^2 + 3(-1(2|(2cos(2πx - 3) + 2) - 3| - 2)) - 2 = 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|(-1sin(1π(1x + 2))) - 2| + 1 = 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) = -1(2cos(2π(-2|x + 3| - 2) - 2) - 3) - 4 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) = 3cos(3π((2(5x - 2) - 2)/(-1(5x - 2) + 2)) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(1π(4((3(3|x - 1| - 2) + 1)/(1(3|x - 1| - 2) - 3))^2 + 5((3(3|x - 1| - 2) + 1)/(1(3|x - 1| - 2) - 3)) + 4) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 341 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2sin(2π(-2(-4x^2 + 1x - 1)) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1658 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(2π(2|(-5(-1x - 2)^2 + 3(-1x - 2) + 4) + 1| - 3) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1615 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1π((-1(2(-5x + 2)^2 + 2(-5x + 2) - 3) - 3)/(-3(2(-5x + 2)^2 + 2(-5x + 2) - 3))) - 1) - 2 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) = (-2(3cos(1π(2|x + 1| - 2) + 3) - 2) + 1)/(-1(3cos(1π(2|x + 1| - 2) + 3) - 2) + 3) 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) = 1(-2sin(3π(-4((2x + 2)/(-1x))^2 + 4((2x + 2)/(-1x)) + 3) - 1) + 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 190 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(1sin(1π((1x)/(3x + 2)) + 2) + 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3((-3(-2(-1cos(2πx) + 2) + 4) - 3)/(3(-2(-1cos(2πx) + 2) + 4) + 2))^2 + 5((-3(-2(-1cos(2πx) + 2) + 4) - 3)/(3(-2(-1cos(2πx) + 2) + 4) + 2)) - 5 have in the interval [-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) = -2cos(3π((2(-3|x - 3| + 2) + 2)/(2(-3|x - 3| + 2))) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-1(-3sin(1π(1|x - 2|) + 3)) - 2) - 2)/(-2(-1(-3sin(1π(1|x - 2|) + 3)) - 2) + 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(3sin(2π(2|(-2x + 2) - 3| + 1)) + 2) - 2)/(-1(3sin(2π(2|(-2x + 2) - 3| + 1)) + 2) - 3) 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 -1cos(1π(-5(3|x - 3|)^2 + 3(3|x - 3|) - 5) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1068 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3π(4(-1|x + 2|) - 5) + 3) + 1 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) = 5(-3|(-3cos(3πx) + 1) - 3| + 2) + 2 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) = -4(3sin(2π(-4((-1x - 3)/(-3x + 4)) - 4) - 2) + 2)^2 - 4(3sin(2π(-4((-1x - 3)/(-3x + 4)) - 4) - 2) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3π(3((3x + 3)/(1x - 2)) - 5) - 2) - 1 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(1π(-3(-3|x - 3| + 1)^2 - 5(-3|x - 3| + 1) - 2) - 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 981 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(3π(1|(5(-5x - 4)^2 - 3(-5x - 4) - 3) - 1| + 3) + 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1237 | MATH |
[
{
"content": "How many solutions does the equation (2(-2|(-3cos(2πx - 2)) + 3| - 1) + 3)/(1(-2|(-3cos(2πx - 2)) + 3| - 1) + 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|(-1(3sin(2π(5x - 2) + 1) + 3)^2 + 3(3sin(2π(5x - 2) + 1) + 3) - 2) + 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(4(-1cos(2πx - 3) + 1)^2 - 1(-1cos(2πx - 3) + 1) - 5) + 2| + 2 have in the interval [-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) = 5(3cos(1π(4x^2 - 3x - 2) + 2) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 350 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1sin(3π(2|(-5x + 5) - 3| - 3)) - 1))/(-1(1sin(3π(2|(-5x + 5) - 3| - 3)) - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 288 | MATH |
[
{
"content": "How many solutions does the equation (2(-2cos(3π(-4x^2 - 2x + 2) + 1) - 3) + 2)/(2(-2cos(3π(-4x^2 - 2x + 2) + 1) - 3) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 956 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|((3(1cos(3πx - 1) - 1) - 1)/(2(1cos(3πx - 1) - 1) + 1)) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation (-2(3|(2sin(2πx + 2) - 1) + 3| - 1) - 1)/(1(3|(2sin(2πx + 2) - 1) + 3| - 1) + 3) = 0 have in the range [-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(-1(2sin(3πx) - 1)^2 + 3(2sin(3πx) - 1) + 3) - 2 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) = 1cos(3π(3|(-1x^2 + 1x + 1) - 1|) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 763 | MATH |
[
{
"content": "How many solutions does the equation (-2(1(1sin(2π(-3x + 5) + 1) + 1)^2 + 5(1sin(2π(-3x + 5) + 1) + 1) - 3) - 2)/(-3(1(1sin(2π(-3x + 5) + 1) + 1)^2 + 5(1sin(2π(-3x + 5) + 1) + 1) - 3) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 120 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(-1|(-2(-3cos(1πx - 2) + 1)^2 + 5(-3cos(1πx - 2) + 1) + 2) - 3| - 1) - 2)/(1(-1|(-2(-3cos(1πx - 2) + 1)^2 + 5(-3cos(1πx - 2) + 1) + 2) - 3| - 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 80 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π(-3|(-3x^2 - 1x - 4) + 2| + 3) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1499 | MATH |
[
{
"content": "How many solutions does the equation (-3(4(2sin(1πx + 2) - 1) + 4) - 1)/(-1(4(2sin(1πx + 2) - 1) + 4) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation -2cos(3π(3(1x - 3)^2 - 5(1x - 3) - 3) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 838 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(1cos(2π(2|x + 2| - 1) - 2))^2 + 1(1cos(2π(2|x + 2| - 1) - 2)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2π(1(-1|((-1x + 3)/(-1x + 2)) + 3|) - 5) - 2) - 3 equals zero.\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) = 2cos(1π(-3|(5x - 1) + 1| - 3)) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 149 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(2π((2(5(2|x + 3| - 2) - 3) - 1)/(-1(5(2|x + 3| - 2) - 3) - 2)) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-3|((3(2sin(1πx - 2)) - 3)/(3(2sin(1πx - 2)) + 3)) - 3|)^2 + 5(-3|((3(2sin(1πx - 2)) - 3)/(3(2sin(1πx - 2)) + 3)) - 3|) + 2 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) = 5((-1(3sin(2πx - 3) + 3) + 2)/(3(3sin(2πx - 3) + 3) + 2)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(2((-3(1sin(3πx + 3)) - 1)/(-2(1sin(3πx + 3))))) - 3| + 3 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) = -2cos(2π(-1((1x + 2)/(2x + 3)) + 2) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2π(3(5x - 1)^2 - 1(5x - 1) + 3) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1518 | MATH |
[
{
"content": "How many solutions does the equation (2(-3sin(1π(1x^2 - 5x - 3) + 2) - 1) + 1)/(-1(-3sin(1π(1x^2 - 5x - 3) + 2) - 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 212 | MATH |
[
{
"content": "How many solutions does the equation 3cos(1π((-2(1x^2 + 3x - 4) + 1)/(-1(1x^2 + 3x - 4) - 2)) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1((1(-2sin(1π(2x^2 - 3x - 4) + 1) - 2) - 2)/(3(-2sin(1π(2x^2 - 3x - 4) + 1) - 2) + 2)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 224 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π((-2(3|x| - 3) + 1)/(3(3|x| - 3) + 1))) = 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(-3sin(2π(-3x^2 + 4x + 5) - 1) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1101 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(3π(-1((-1x + 2)/(3x - 2)) - 4) - 1) - 1 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 -3cos(3π(-3((3x - 1)/(-3x - 1)) - 5)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3π(-5(-2|(-1x - 1) - 3| + 3)^2 - 1(-2|(-1x - 1) - 3| + 3) + 3) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1052 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(2(-2cos(3πx - 3) - 3)^2 + 5(-2cos(3πx - 3) - 3) - 3) 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(-2(3sin(3πx - 2) - 3) - 5))/(-2(-2(3sin(3πx - 2) - 3) - 5) + 1))^2 - 2((-2(-2(3sin(3πx - 2) - 3) - 5))/(-2(-2(3sin(3πx - 2) - 3) - 5) + 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 94 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1sin(2π(-1(3((-1x - 3)/(1x + 1)) + 1)^2 + 1(3((-1x - 3)/(1x + 1)) + 1) - 4) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 194 | MATH |
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