messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many solutions does the equation 3(-2(3e^(-1((2x + 3)/(-3x - 2))) - 1)^2 + 3(3e^(-1((2x + 3)/(-3x - 2))) - 1) + 3)^2 - 5(-2(3e^(-1((2x + 3)/(-3x - 2))) - 1)^2 + 3(3e^(-1((2x + 3)/(-3x - 2))) - 1) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 4 | MATH |
[
{
"content": "How many solutions does the equation -2(-2(-2sin(1π(-1x^2 + 5x - 1) + 1) + 3)^2 + 5(-2sin(1π(-1x^2 + 5x - 1) + 1) + 3) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 212 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3π(-3|((2((2x + 1)/(2x - 3)) + 2)/(-3((2x + 1)/(2x - 3)) - 1))| - 2) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3|(1(-3|(5x) + 2| + 1) + 2)| - 3 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) = 2cos(3π((-1((2(-1|x| + 2))/(2(-1|x| + 2) - 1)) + 2)/(-3((2(-1|x| + 2))/(2(-1|x| + 2) - 1)) + 1)) - 2) - 2 equals zero.\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) = -3|((-1(5(-4x^2 - 2x + 3)^2 + 3(-4x^2 - 2x + 3) - 3) + 3)/(-2(5(-4x^2 - 2x + 3)^2 + 3(-4x^2 - 2x + 3) - 3) - 2)) - 3| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(2π(-4((3(-4x^2 - 1x - 4) - 3)/(-2(-4x^2 - 1x - 4))) + 1) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1π(5((-3((1x - 2)/(-1x - 3)) - 1)/(-3((1x - 2)/(-1x - 3)))) - 3) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3((-2(-1|(4x + 2) - 1| + 1) - 1)/(-2(-1|(4x + 2) - 1| + 1) + 3))^2 - 4((-2(-1|(4x + 2) - 1| + 1) - 1)/(-2(-1|(4x + 2) - 1| + 1) + 3)) + 2 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(3cos(1π((-3x + 3)/(-2x + 3))) - 3)^2 + 2(3cos(1π((-3x + 3)/(-2x + 3))) - 3))^2 + 5(1(3cos(1π((-3x + 3)/(-2x + 3))) - 3)^2 + 2(3cos(1π((-3x + 3)/(-2x + 3))) - 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 13 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1π(-2((-1(-2x^2 + 4x + 4) - 1)/(-1(-2x^2 + 4x + 4) - 3))^2 + 3((-1(-2x^2 + 4x + 4) - 1)/(-1(-2x^2 + 4x + 4) - 3)) - 1) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|((2(-3(-3cos(3πx - 2) - 1)^2 + 5(-3cos(3πx - 2) - 1) - 3) - 2)/(2(-3(-3cos(3πx - 2) - 1)^2 + 5(-3cos(3πx - 2) - 1) - 3) + 3)) + 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 120 | MATH |
[
{
"content": "How many solutions does the equation -3(3cos(2π(1|((1x - 1)/(-3x - 3)) + 3| + 2) - 1) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4((-2(-3cos(2π(4x^2 + 4x - 1)) - 1) + 1)/(1(-3cos(2π(4x^2 + 4x - 1)) - 1) + 1))^2 - 2((-2(-3cos(2π(4x^2 + 4x - 1)) - 1) + 1)/(1(-3cos(2π(4x^2 + 4x - 1)) - 1) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 1132 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(-2|(-3(4x - 3)^2 + 4(4x - 3)) + 2| + 1) + 1)/(-1(-2|(-3(4x - 3)^2 + 4(4x - 3)) + 2| + 1) - 3) 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(-3sin(1π(4x - 4) + 2) - 2) - 1)/(1(-3sin(1π(4x - 4) + 2) - 2) + 3)) 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) = -3|((3(-4(2x^2 + 2x + 1)^2 + 3(2x^2 + 2x + 1) + 5) + 2)/(2(-4(2x^2 + 2x + 1)^2 + 3(2x^2 + 2x + 1) + 5) + 2)) + 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(1π(3|(3(2|x + 3| - 2)^2 - 4(2|x + 3| - 2) - 1)| - 2) + 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1071 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(1(-3cos(1π(-4x^2 - 1x + 1) - 2) - 3)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "How many solutions does the equation 2|(-4((-3((-3x + 3)/(-1x - 1)))/(-2((-3x + 3)/(-1x - 1)) + 3))^2 - 5((-3((-3x + 3)/(-1x - 1)))/(-2((-3x + 3)/(-1x - 1)) + 3)) + 4)| - 1 = 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) = -4(-4((-1(-1sin(1πx - 3)) + 2)/(-3(-1sin(1πx - 3)) + 1))^2 - 5((-1(-1sin(1πx - 3)) + 2)/(-3(-1sin(1πx - 3)) + 1)) + 1)^2 + 1(-4((-1(-1sin(1πx - 3)) + 2)/(-3(-1sin(1πx - 3)) + 1))^2 - 5((-1(-1sin(1πx - 3)) + 2)/(-3(-1sin(1πx - 3)) + 1)) + 1... | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(3π(-3(-4((-2x + 2)/(-1x - 2))^2 + 1((-2x + 2)/(-1x - 2)) + 3) + 1) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 644 | MATH |
[
{
"content": "How many solutions does the equation 3(1(1(-2|x - 2| + 3)^2 + 4(-2|x - 2| + 3) + 4)^2 - 3(1(-2|x - 2| + 3)^2 + 4(-2|x - 2| + 3) + 4) - 5) - 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) = 3sin(2π((3(-1(3x^2 + 1x - 5) + 2) + 1)/(-1(-1(3x^2 + 1x - 5) + 2) + 2)) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(-1(-2|(1x + 5) - 1| - 2)^2 - 3(-2|(1x + 5) - 1| - 2) + 3) - 2| + 1 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(5((3(-2cos(3πx + 2) + 1) - 1)/(-2(-2cos(3πx + 2) + 1) - 3))^2 + 3((3(-2cos(3πx + 2) + 1) - 1)/(-2(-2cos(3πx + 2) + 1) - 3)) - 5)^2 - 5(5((3(-2cos(3πx + 2) + 1) - 1)/(-2(-2cos(3πx + 2) + 1) - 3))^2 + 3((3(-2cos(3πx + 2) + 1) - 1)/(-2(-2cos(3... | 180 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(-3sin(2π((3((-2x + 2)/(2x + 2)) + 2)/(-1((-2x + 2)/(2x + 2)))) - 3)) - 1)/(2(-3sin(2π((3((-2x + 2)/(2x + 2)) + 2)/(-1((-2x + 2)/(2x + 2)))) - 3)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 51 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(-3|(3cos(1π(5x - 5)) + 2)|) + 3)/(2(-3|(3cos(1π(5x - 5)) + 2)|) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 151 | MATH |
[
{
"content": "How many solutions does the equation 5(1cos(1π(5((3x - 1)/(-2x)) - 1))) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1|(-3(3|x|) + 4) + 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 -2cos(2π(4(-3|(1x + 3) + 2| + 3) - 2) + 1) - 2 = 0 have in the range [-10, 10]?\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) = 1(-1(2|(-2|x + 2|) - 1| - 2) + 3)^2 + 5(-1(2|(-2|x + 2|) - 1| - 2) + 3) - 5 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) = -2cos(3π(-3|(-1(-2|x - 1|)^2 + 5) + 2| - 3) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1074 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3(-5(3|(3|x + 3| - 2) - 2|)^2 + 2(3|(3|x + 3| - 2) - 2|) + 3) - 1)/(-1(-5(3|(3|x + 3| - 2) - 2|)^2 + 2(3|(3|x + 3| - 2) - 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) = 1|((-1(-1cos(3π((-2x - 2)/(2x - 3)) + 2) + 1) + 1)/(2(-1cos(3π((-2x - 2)/(2x - 3)) + 2) + 1) - 3)) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "How many solutions does the equation -2cos(1π(2(2(4x + 1) + 4) + 5) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 154 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(3|(2(-5x^2 + 2x)^2 - 1(-5x^2 + 2x) - 4) + 1| - 2) - 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3((1(1(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 2) + 3)/(2(1(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 2) + 2)) + 3)/(-2((1(1(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 2) + 3)/(2(1(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 2) + 2)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex for... | 4 | MATH |
[
{
"content": "How many solutions does the equation -3cos(3π(-5(5((-2x - 1)/(2x - 3)) - 5)^2 + 4(5((-2x - 1)/(2x - 3)) - 5) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1380 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(-3(-3(-3x - 1)^2 + 1(-3x - 1) + 1) - 3) + 1| + 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) = 5((3(3sin(1π(-5x + 4) + 2) - 1) + 2)/(-3(3sin(1π(-5x + 4) + 2) - 1) - 3)) where -10 ≤ x ≤ 10.\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(-3cos(3πx - 1) - 1)^2 + 2(-3cos(3πx - 1) - 1) + 3) - 3| + 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) = -1|((1(-2(1|x + 2| - 1) + 5))/(1(-2(1|x + 2| - 1) + 5) - 3)) + 1| + 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) = -1(-2|(5(-2x + 5)^2 - 2(-2x + 5) - 5) + 2|) - 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(3cos(3π(-5((-1x - 2)/(1x + 3)) + 2) - 3) + 1) + 3)/(-2(3cos(3π(-5((-1x - 2)/(1x + 3)) + 2) - 3) + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "How many solutions does the equation 1(-1(2sin(3π((-1x + 1)/(1x - 3)) + 1) + 2)^2 + 3(2sin(3π((-1x + 1)/(1x - 3)) + 1) + 2) + 5)^2 + 4(-1(2sin(3π((-1x + 1)/(1x - 3)) + 1) + 2)^2 + 3(2sin(3π((-1x + 1)/(1x - 3)) + 1) + 2) + 5) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex forma... | 45 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(3π(-1|(-1(3|x + 1| - 1)^2 + 5(3|x + 1| - 1) - 5) + 1| + 1) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1190 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(1((-2(-4x^2 + 4x + 4) + 2)/(-1(-4x^2 + 4x + 4) + 3))^2 + 5((-2(-4x^2 + 4x + 4) + 2)/(-1(-4x^2 + 4x + 4) + 3)) + 5) + 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 3sin(1π(1((-1((3x)/(-1x - 1)) + 3)/(-2((3x)/(-1x - 1))))^2 + 4((-1((3x)/(-1x - 1)) + 3)/(-2((3x)/(-1x - 1)))) - 1)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(-2cos(1π(-3|(5x^2 + 1x - 1) + 3| + 3) - 2))^2 - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1329 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(4(-3cos(1π(-3|x - 2| + 3) - 3) + 1) + 1)^2 - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 110 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-1sin(3π(-5((-3x)/(-1x - 3))^2 - 1((-3x)/(-1x - 3)) + 2))) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 706 | MATH |
[
{
"content": "How many solutions does the equation -1cos(1π(-3|(4((3x - 3)/(-3x - 1))^2 - 5((3x - 3)/(-3x - 1)) - 3) + 1| - 1) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(-2|(2cos(1π(1x^2 - 4x + 4) - 3)) - 1| + 3) - 3| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 97 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|(-2(2|(-1|x + 1| + 1) + 3|)) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(3π(-2|(-3(1x + 4)^2) - 1| + 3) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1485 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π(1(1|((3x - 3)/(1x + 2)) + 3|) - 4) + 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2|(-1|(3sin(1πx + 2) + 2)| + 1) + 1| + 2) + 1)/(-3(-2|(-1|(3sin(1πx + 2) + 2)| + 1) + 1| + 2)) 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) = (2(3sin(1π((-1(3|x + 1| - 1) + 2)/(1(3|x + 1| - 1))) + 3) + 2))/(3(3sin(1π((-1(3|x + 1| - 1) + 2)/(1(3|x + 1| - 1))) + 3) + 2) + 2) 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) = 1sin(1π(-3|(1(-2x - 5) - 1) - 1| + 2) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(3sin(2π(-1(3x^2 - 4x + 4) + 3) + 2) - 2))/(-2(3sin(2π(-1(3x^2 - 4x + 4) + 3) + 2) - 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 562 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1π(3(-2((2x)/(-3x + 4)) - 2) + 5) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(2cos(1π(2|((2x + 2)/(-3x + 4)) - 3|) + 2) + 2)^2 + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "How many solutions does the equation -2|(-1(2cos(3π(-2|x + 2| - 2) + 1) - 1) - 5) + 2| = 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) = 1sin(2π(-1((-1(-4x + 2) - 3)/(-2(-4x + 2)))^2 - 1((-1(-4x + 2) - 3)/(-2(-4x + 2)))) + 3) equals zero.\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) = 3sin(2π(5(2|(2|x - 1| - 3) + 2|) - 5) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 378 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(1(-2cos(1π((-2x - 2)/(2x - 1)) + 1))^2 + 5(-2cos(1π((-2x - 2)/(2x - 1)) + 1)) - 5)| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(-4((2(-2x^2 - 4x + 5) - 1)/(1(-2x^2 - 4x + 5) + 2))^2 - 3((2(-2x^2 - 4x + 5) - 1)/(1(-2x^2 - 4x + 5) + 2)) + 2)^2 + 3(-4((2(-2x^2 - 4x + 5) - 1)/(1(-2x^2 - 4x + 5) + 2))^2 - 3((2(-2x^2 - 4x + 5) - 1)/(1(-2x^2 - 4x + 5) + 2)) + 2) - 2 have in the interval [... | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(2π(5(2(4x^2 + 1x - 3))^2 - 4(2(4x^2 + 1x - 3)) + 4)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 571 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3((3(-2|(3sin(2πx) + 1)| + 2) + 2)/(-1(-2|(3sin(2πx) + 1)| + 2))) - 3)/(-1((3(-2|(3sin(2πx) + 1)| + 2) + 2)/(-1(-2|(3sin(2πx) + 1)| + 2)))) 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) = 5(-3sin(1π(-1(-3x^2 + 2x + 5)^2 - 2(-3x^2 + 2x + 5) - 2) + 3)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1093 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|((-1(-2sin(2π((1x + 3)/(-3x + 2)) + 1) + 1) - 1)/(1(-2sin(2π((1x + 3)/(-3x + 2)) + 1) + 1)))| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "How many solutions does the equation -4(3((2(2|x + 3| - 2) + 2)/(2(2|x + 3| - 2) - 1)) + 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": "Find the number of x-intercepts of the function f(x) = (3(-2|(2sin(2π(-1x + 3)) - 3) + 2| + 1) + 2)/(1(-2|(2sin(2π(-1x + 3)) - 3) + 2| + 1)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((2(-1(-3cos(3πx))) + 3)/(2(-1(-3cos(3πx))))) - 2)/(-3((2(-1(-3cos(3πx))) + 3)/(2(-1(-3cos(3πx))))) + 4) 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) = 2|(-2(3(-1x - 1)^2 + 3(-1x - 1) + 3) + 4) + 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 1(-3(3|(-2|x + 2| + 1) + 1| + 1) + 5)^2 - 1(-3(3|(-2|x + 2| + 1) + 1| + 1) + 5) = 0 have in the range [-10, 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) = 1sin(3π(-2(3((3x - 3)/(-2x - 1)) - 3)^2 + 1(3((3x - 3)/(-2x - 1)) - 3) + 2) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 445 | MATH |
[
{
"content": "How many solutions does the equation -1(1cos(2π(-1(3x^2 - 5x - 5) - 2) - 1) + 1)^2 + 1(1cos(2π(-1(3x^2 - 5x - 5) - 2) - 1) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1033 | MATH |
[
{
"content": "How many solutions does the equation (-1(-1cos(3π(-1|(-5x - 2) - 3| + 2) + 2) - 1) - 1)/(3(-1cos(3π(-1|(-5x - 2) - 3| + 2) + 2) - 1) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(1|(3(3sin(1πx - 2) - 1)^2 + 5(3sin(1πx - 2) - 1) - 1) + 1| - 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) = -3((-3(-1(-5x^2 - 1x + 4)^2 + 3(-5x^2 - 1x + 4) - 1) + 2)/(3(-1(-5x^2 - 1x + 4)^2 + 3(-5x^2 - 1x + 4) - 1) - 1)) + 5 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) = -2cos(2π(1|(1|((3x + 2)/(2x + 3)) - 3| - 3) + 2| + 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(3π(1|(3(1|x - 3| - 3) + 5) - 3| + 2) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(1π(1(-2|(-3x + 5) + 1|)^2 + 2(-2|(-3x + 5) + 1|)) - 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1242 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1((1(-2cos(3π((2x + 3)/(1x - 3))) + 1))/(2(-2cos(3π((2x + 3)/(1x - 3))) + 1) + 2)) + 3)/(-2((1(-2cos(3π((2x + 3)/(1x - 3))) + 1))/(2(-2cos(3π((2x + 3)/(1x - 3))) + 1) + 2)) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\box... | 127 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1sin(2π(-3(2|(1x - 5)| - 2) + 1) + 3) 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 1(3(-4(3sin(2πx - 3) + 1)) - 5)^2 + 5(3(-4(3sin(2πx - 3) + 1)) - 5) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(5(-2(1x^2 - 3x) + 5)^2 + 3(-2(1x^2 - 3x) + 5) - 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) = 3(-1|((-2(-3x^2 + 4x + 2) - 3)/(3(-3x^2 + 4x + 2))) - 3| + 2) + 1 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) = -2sin(1π(2|(-1(-1|x| - 3) - 1) + 2| - 2) + 2) + 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) = -1|(-3(1(3|x| + 1) - 5) - 4) - 1| + 1 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) = (1((-3((-3(-1sin(3πx - 3)) - 1)/(-1(-1sin(3πx - 3)) + 2)) - 1)/(2((-3(-1sin(3πx - 3)) - 1)/(-1(-1sin(3πx - 3)) + 2)) + 2)) - 2)/(3((-3((-3(-1sin(3πx - 3)) - 1)/(-1(-1sin(3πx - 3)) + 2)) - 1)/(2((-3(-1sin(3πx - 3)) - 1)/(-1(-1sin(3πx - 3)) ... | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(1(3e^(1(2x^2 + 3x - 1)) - 2)^2 - 1(3e^(1(2x^2 + 3x - 1)) - 2) - 2)^2 - 2(1(3e^(1(2x^2 + 3x - 1)) - 2)^2 - 1(3e^(1(2x^2 + 3x - 1)) - 2) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 8 | MATH |
[
{
"content": "How many solutions does the equation 2cos(2π(-4(3((3x)/(-1x + 2)) - 4) + 1) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 393 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3|(2(4x - 2)^2 + 4(4x - 2) - 2) + 2| + 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) = -1|(1|(3(1x^2 + 2x + 1)^2 + 2(1x^2 + 2x + 1) + 2) - 1| - 2) - 3| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -2sin(3π(-1(1(-2|x - 1| - 3)^2 + 3(-2|x - 1| - 3) - 5) - 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1708 | MATH |
[
{
"content": "How many solutions does the equation 5(-2|(-1(1sin(3πx) - 2)^2 + 4) - 2| + 3) = 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) = 5(-1(2|(-1x^2 + 3)| + 1) + 4) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.