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) = 5((-3(-2(-2sin(1π(3(2|x + 3| + 2)^2 - 4(2|x + 3| + 2) + 4) - 3) - 2)^2 + 3(-2sin(1π(3(2|x + 3| + 2)^2 - 4(2|x + 3| + 2) + 4) - 3) - 2) + 4) + 1)/(-2(-2(-2sin(1π(3(2|x + 3| + 2)^2 - 4(2|x + 3| + 2) + 4) - 3) - 2)^2 + 3(-2sin(1π(3(2|x + 3| +... | 231 | MATH |
[
{
"content": "How many solutions does the equation 3((2(1|(2(1((3x + 2)/(-2x)) + 4)^2 + 3(1((3x + 2)/(-2x)) + 4) - 1) - 3| - 3) + 2)/(-3(1|(2(1((3x + 2)/(-2x)) + 4)^2 + 3(1((3x + 2)/(-2x)) + 4) - 1) - 3| - 3) + 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3π(1(-2|(4(-2(-1x^2 + 5x + 2)^2 + 3(-1x^2 + 5x + 2) - 3)^2 + 4(-2(-1x^2 + 5x + 2)^2 + 3(-1x^2 + 5x + 2) - 3) + 2) - 3|)^2 - 2(-2|(4(-2(-1x^2 + 5x + 2)^2 + 3(-1x^2 + 5x + 2) - 3)^2 + 4(-2(-1x^2 + 5x + 2)^2 + 3(-1x^2 + 5x + 2) - 3) + 2... | 44 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3((-2(3(-3|((-3(1|x - 2| + 1) + 2)/(-1(1|x - 2| + 1) - 3)) - 1|) + 3) - 3)/(1(3(-3|((-3(1|x - 2| + 1) + 2)/(-1(1|x - 2| + 1) - 3)) - 1|) + 3) - 3)) - 2)/(-3((-2(3(-3|((-3(1|x - 2| + 1) + 2)/(-1(1|x - 2| + 1) - 3)) - 1|) + 3) - 3)/(1(3(-3|((-3(1|x - 2| + 1) ... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5((1(2(1(-5(-1|x|) + 1) - 3)^2 - 3(1(-5(-1|x|) + 1) - 3) + 4) - 3)/(-2(2(1(-5(-1|x|) + 1) - 3)^2 - 3(1(-5(-1|x|) + 1) - 3) + 4) - 3)) + 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((3((3((1x + 1)/(2x - 1)) - 3)/(-1((1x + 1)/(2x - 1)) + 3)) + 3)/(1((3((1x + 1)/(2x - 1)) - 3)/(-1((1x + 1)/(2x - 1)) + 3)) + 3)) - 1) + 3| - 1)^2 + 4(3|(3((3((3((1x + 1)/(2x - 1)) - 3)/(-1((1x + 1)/(2x - 1)) + 3)) + 3)/(1((3((1x + ... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(2(2cos(2π(2|(3(4x^2 - 5x + 5)^2 - 1(4x^2 - 5x + 5) + 2) + 3| - 3) + 2) - 3) + 2)^2 - 4(2(2cos(2π(2|(3(4x^2 - 5x + 5)^2 - 1(4x^2 - 5x + 5) + 2) + 3| - 3) + 2) - 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 726 | MATH |
[
{
"content": "How many solutions does the equation 2|(1(2(3((-3(2sin(1πx + 3) + 2) + 3)/(2(2sin(1πx + 3) + 2) + 2))^2 - 2((-3(2sin(1πx + 3) + 2) + 3)/(2(2sin(1πx + 3) + 2) + 2)) + 1) - 2)^2 + 2) - 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-2|(1(2(-2|((-1x - 3)/(-2x - 1)) - 3| + 1)^2 - 4) - 4)| + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -1(-3e^(2((-2(-4(1(-5x^2 + 5x + 1)^2 - 5(-5x^2 + 5x + 1))) + 2)/(2(-4(1(-5x^2 + 5x + 1)^2 - 5(-5x^2 + 5x + 1))) + 2))) + 2)^2 - 5(-3e^(2((-2(-4(1(-5x^2 + 5x + 1)^2 - 5(-5x^2 + 5x + 1))) + 2)/(2(-4(1(-5x^2 + 5x + 1)^2 - 5(-5x^2 + 5x + 1))) + 2))) + 2) = 0 have i... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(2sin(3π((-1(3(1(-3|x - 3| + 2)^2 - 4(-3|x - 3| + 2) + 3) - 1) + 3)/(-2(3(1(-3|x - 3| + 2)^2 - 4(-3|x - 3| + 2) + 3) - 1) + 3)) + 2) - 2) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 10 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-3sin(1π(1(2|((1(2x^2 + 3x - 3) - 3)/(-3(2x^2 + 3x - 3) - 1)) - 1|) + 4) - 1) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "How many solutions does the equation -2(-1(-2|((-2(1|(3x^2 - 5x - 4) + 2| - 1) - 2)/(-1(1|(3x^2 - 5x - 4) + 2| - 1) + 2)) + 1| + 1)^2 - 4(-2|((-2(1|(3x^2 - 5x - 4) + 2| - 1) - 2)/(-1(1|(3x^2 - 5x - 4) + 2| - 1) + 2)) + 1| + 1) - 1) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTe... | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(-5(2sin(1π(-5((-3(-4x^2 - 4x + 4))/(1(-4x^2 - 4x + 4) + 2))^2 - 2((-3(-4x^2 - 4x + 4))/(1(-4x^2 - 4x + 4) + 2)) - 5) + 1) - 2) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 185 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(3sin(2π(-2|(-1|(3|(3|x - 3| + 2)| - 3) + 2| + 1) - 1| + 3) + 2) + 1)| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 720 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1((2(1((3(4((-3x - 1)/(1x - 3))^2 + 4((-3x - 1)/(1x - 3))))/(-3(4((-3x - 1)/(1x - 3))^2 + 4((-3x - 1)/(1x - 3))) - 1))^2 + 1((3(4((-3x - 1)/(1x - 3))^2 + 4((-3x - 1)/(1x - 3))))/(-3(4((-3x - 1)/(1x - 3))^2 + 4((-3x - 1)/(1x - 3))) - 1)) - 4) ... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(1cos(2π(1(5(-2(-3x^2 + 5x - 1) - 1)^2 - 3(-2(-3x^2 + 5x - 1) - 1) + 1)^2 - 4(5(-2(-3x^2 + 5x - 1) - 1)^2 - 3(-2(-3x^2 + 5x - 1) - 1) + 1) + 2) + 1)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 128 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3(2((-2(-2cos(1π((-1x - 3)/(-2x - 1)) + 3) + 2) - 1)/(-1(-2cos(1π((-1x - 3)/(-2x - 1)) + 3) + 2) - 1)) - 2) + 2)^2 - 4(3(2((-2(-2cos(1π((-1x - 3)/(-2x - 1)) + 3) + 2) - 1)/(-1(-2cos(1π((-1x - 3)/(-2x - 1)) + 3) + 2) - 1)) - 2) + 2) + 2 e... | 27 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(-2cos(2π(3(-4(1((2x + 2)/(1x + 3))^2 + 1((2x + 2)/(1x + 3)) + 1)^2 + 5(1((2x + 2)/(1x + 3))^2 + 1((2x + 2)/(1x + 3)) + 1) + 3) + 4) - 3) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 746 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(1((-1(4(2e^(1((1x - 3)/(1x - 2))) - 3)^2 + 4(2e^(1((1x - 3)/(1x - 2))) - 3) - 5) - 2)/(-1(4(2e^(1((1x - 3)/(1x - 2))) - 3)^2 + 4(2e^(1((1x - 3)/(1x - 2))) - 3) - 5) - 1)))^2 - 1(1((-1(4(2e^(1((1x - 3)/(1x - 2))) - 3)^2 + 4(2e^(1((1x - 3)/(1x - 2))) - 3) - ... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(-3sin(1π((-1(-2((-3(2|x + 1|) + 1)/(-1(2|x + 1|) + 3)) + 2))/(-1(-2((-3(2|x + 1|) + 1)/(-1(2|x + 1|) + 3)) + 2) + 3)) - 2) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(4(-2|(-1(-2((2x)/(-2x - 1)) - 3)^2 - 1(-2((2x)/(-2x - 1)) - 3) + 2) + 3| + 1) + 4) + 2)/(-1(4(-2|(-1(-2((2x)/(-2x - 1)) - 3)^2 - 1(-2((2x)/(-2x - 1)) - 3) + 2) + 3| + 1) + 4)) equals zero.\n\nPresent the answer in LaTex format: \\boxed... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(2|(-3|(-1(1|(-1x + 2) + 2| + 3) + 4) + 2| + 3) - 2| - 3) + 2)/(-1(2|(-3|(-1(1|(-1x + 2) + 2| + 3) + 4) + 2| + 3) - 2| - 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1|(-2(5(-1(-1x^2 + 5x) - 1)^2 + 5(-1(-1x^2 + 5x) - 1) - 1) - 3) - 3| - 2) + 3)/(3(1|(-2(5(-1(-1x^2 + 5x) - 1)^2 + 5(-1(-1x^2 + 5x) - 1) - 1) - 3) - 3| - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(1((-1(2cos(3π(-1(-5x - 1) + 2) + 1) + 1))/(2(2cos(3π(-1(-5x - 1) + 2) + 1) + 1) - 1))^2 - 2) + 3)/(-2(1((-1(2cos(3π(-1(-5x - 1) + 2) + 1) + 1))/(2(2cos(3π(-1(-5x - 1) + 2) + 1) + 1) - 1))^2 - 2) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answ... | 260 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(4((-3(-1|((2(2x^2 - 3x - 2) + 2)/(2(2x^2 - 3x - 2) - 3))| + 2) + 2)/(1(-1|((2(2x^2 - 3x - 2) + 2)/(2(2x^2 - 3x - 2) - 3))| + 2)))^2 + 4((-3(-1|((2(2x^2 - 3x - 2) + 2)/(2(2x^2 - 3x - 2) - 3))| + 2) + 2)/(1(-1|((2(2x^2 - 3x - 2) + 2)/(2(2x^2 - 3x - 2) - 3))|... | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(2((2((3(1cos(3π(3x - 2))) - 2)/(-3(1cos(3π(3x - 2))))) - 3)/(3((3(1cos(3π(3x - 2))) - 2)/(-3(1cos(3π(3x - 2)))))))^2 - 4) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3cos(3π(2(1(5(1|x - 1| - 2)^2 + 5(1|x - 1| - 2) + 2)^2 - 5(5(1|x - 1| - 2)^2 + 5(1|x - 1| - 2) + 2) - 2)^2 + 3) + 1)) + 2)/(-1(3cos(3π(2(1(5(1|x - 1| - 2)^2 + 5(1|x - 1| - 2) + 2)^2 - 5(5(1|x - 1| - 2)^2 + 5(1|x - 1| - 2) + 2) - 2)^2 + ... | 361 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4((2(-2sin(3π((2(1(-1x + 1) + 2))/(1(1(-1x + 1) + 2) - 3)) - 3) + 2) + 1)/(-3(-2sin(3π((2(1(-1x + 1) + 2))/(1(1(-1x + 1) + 2) - 3)) - 3) + 2) + 4)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 91 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3((2(-1(-2sin(2π(4(-2|x - 2| + 3)^2 - 5(-2|x - 2| + 3) + 3) + 2) - 3)^2 - 4(-2sin(2π(4(-2|x - 2| + 3)^2 - 5(-2|x - 2| + 3) + 3) + 2) - 3) - 2) + 1)/(1(-1(-2sin(2π(4(-2|x - 2| + 3)^2 - 5(-2|x - 2| + 3) + 3) + 2) - 3)^2 - 4(-2sin(2π(4(-2|x - 2|... | 89 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(3((-1((2(1|((1x + 3)/(-1x)) + 3| - 2) + 1)/(-3(1|((1x + 3)/(-1x)) + 3| - 2) + 4)) + 3)/(3((2(1|((1x + 3)/(-1x)) + 3| - 2) + 1)/(-3(1|((1x + 3)/(-1x)) + 3| - 2) + 4)) - 2))^2 - 2((-1((2(1|((1x + 3)/(-1x)) + 3| - 2) + 1)/(-3(1|((1x + 3)/(-1x)) + 3| - 2) + 4)... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1((-2((-1(-2e^(-2(-2|(2x^2 - 5) - 3|)) - 1) - 2)/(-3(-2e^(-2(-2|(2x^2 - 5) - 3|)) - 1) + 2)) + 1)/(3((-1(-2e^(-2(-2|(2x^2 - 5) - 3|)) - 1) - 2)/(-3(-2e^(-2(-2|(2x^2 - 5) - 3|)) - 1) + 2)) - 1)) + 2 equals zero.\n\nPresent the answer in LaT... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1|(2sin(1π((2((1(-1x + 4) + 1)/(-2(-1x + 4))))/(-1((1(-1x + 4) + 1)/(-2(-1x + 4))) + 2)) + 1) - 1) - 1|) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(-4(-5(-3cos(3π(1(-1|x - 1| + 1)^2 - 1(-1|x - 1| + 1) - 2) + 2) + 3)^2 + 4(-3cos(3π(1(-1|x - 1| + 1)^2 - 1(-1|x - 1| + 1) - 2) + 2) + 3) + 3) + 3)| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 27 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1sin(2π(2|((-3((-3(4x^2 + 1x - 4) - 1)/(-2(4x^2 + 1x - 4) - 1)) + 1)/(-3((-3(4x^2 + 1x - 4) - 1)/(-2(4x^2 + 1x - 4) - 1)) + 2)) - 1| + 2) + 2) + 1) + 3)/(3(1sin(2π(2|((-3((-3(4x^2 + 1x - 4) - 1)/(-2(4x^2 + 1x - 4) - 1)) + 1)/(-3((-3(4x... | 14 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(4(-4(3|((-1(-1x) + 2)/(1(-1x))) - 2|) + 1) - 1)^2 + 5(4(-4(3|((-1(-1x) + 2)/(1(-1x))) - 2|) + 1) - 1) - 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) = (-2(3|(-1(-1((3(3x + 4) + 2)/(2(3x + 4) - 1))^2 + 5((3(3x + 4) + 2)/(2(3x + 4) - 1)) + 3)^2 + 1(-1((3(3x + 4) + 2)/(2(3x + 4) - 1))^2 + 5((3(3x + 4) + 2)/(2(3x + 4) - 1)) + 3) - 2) + 3| - 2) - 1)/(-3(3|(-1(-1((3(3x + 4) + 2)/(2(3x + 4) - 1... | 5 | MATH |
[
{
"content": "How many solutions does the equation -1(3(-1(2|(-2sin(3π(2|x + 3| - 2) + 2) - 2) - 2| - 1)^2 + 5(2|(-2sin(3π(2|x + 3| - 2) + 2) - 2) - 2| - 1) - 5)^2 + 3(-1(2|(-2sin(3π(2|x + 3| - 2) + 2) - 2) - 2| - 1)^2 + 5(2|(-2sin(3π(2|x + 3| - 2) + 2) - 2) - 2| - 1) - 5) - 4)^2 + 2(3(-1(2|(-2sin(3π(2|x + 3| -... | 243 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(1π(-1|(1|(-1|(4(-1x^2 - 3x - 1) - 4) + 3| - 3) - 3| + 2) + 1| + 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 818 | MATH |
[
{
"content": "How many solutions does the equation 1(-5((-3(3|(-3((1x + 2)/(-3x - 3)) - 3) + 3| - 2))/(-2(3|(-3((1x + 2)/(-3x - 3)) - 3) + 3| - 2) - 3))^2 + 4((-3(3|(-3((1x + 2)/(-3x - 3)) - 3) + 3| - 2))/(-2(3|(-3((1x + 2)/(-3x - 3)) - 3) + 3| - 2) - 3)) + 5)^2 + 5(-5((-3(3|(-3((1x + 2)/(-3x - 3)) - 3) + 3| - ... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1((3(2cos(2π(-3|(2((2x)/(3x - 2)) + 5) + 1| + 1) + 3) - 1) + 2)/(-3(2cos(2π(-3|(2((2x)/(3x - 2)) + 5) + 1| + 1) + 3) - 1) + 4)) - 1)/(1((3(2cos(2π(-3|(2((2x)/(3x - 2)) + 5) + 1| + 1) + 3) - 1) + 2)/(-3(2cos(2π(-3|(2((2x)/(3x - 2)) + 5) + 1| + 1) + 3) - 1) +... | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1π(4((-1(-2|(4(-1x) - 2) + 1| + 3) - 3)/(1(-2|(4(-1x) - 2) + 1| + 3))) - 2) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75 | MATH |
[
{
"content": "How many solutions does the equation (2(-1cos(1π((1((2(-5(-1x - 3) + 5))/(-2(-5(-1x - 3) + 5) - 2)) + 3)/(-1((2(-5(-1x - 3) + 5))/(-2(-5(-1x - 3) + 5) - 2)) - 2))) + 1) - 3)/(1(-1cos(1π((1((2(-5(-1x - 3) + 5))/(-2(-5(-1x - 3) + 5) - 2)) + 3)/(-1((2(-5(-1x - 3) + 5))/(-2(-5(-1x - 3) + 5) - 2)) - 2)... | 16 | MATH |
[
{
"content": "How many solutions does the equation 1(-1(-4(2cos(3π((1((1x - 2)/(2x + 2)) - 2)/(1((1x - 2)/(2x + 2)) + 1)) - 2) - 2)^2 - 1(2cos(3π((1((1x - 2)/(2x + 2)) - 2)/(1((1x - 2)/(2x + 2)) + 1)) - 2) - 2) + 1)^2 - 4(-4(2cos(3π((1((1x - 2)/(2x + 2)) - 2)/(1((1x - 2)/(2x + 2)) + 1)) - 2) - 2)^2 - 1(2cos(3π(... | 79 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(1sin(3π(3(-2|(-1(-1x - 5)^2 - 1(-1x - 5) + 2) + 1| - 2)^2 - 2(-2|(-1(-1x - 5)^2 - 1(-1x - 5) + 2) + 1| - 2) - 2) + 3) - 1))/(1(1sin(3π(3(-2|(-1(-1x - 5)^2 - 1(-1x - 5) + 2) + 1| - 2)^2 - 2(-2|(-1(-1x - 5)^2 - 1(-1x - 5) + 2) + 1| - 2) - 2) ... | 1293 | MATH |
[
{
"content": "How many solutions does the equation (-1(5(-3cos(2π((-3(4((-3x - 1)/(-2x + 3)) - 1))/(2(4((-3x - 1)/(-2x + 3)) - 1) - 3)) + 2) - 1) + 5) + 3)/(-3(5(-3cos(2π((-3(4((-3x - 1)/(-2x + 3)) - 1))/(2(4((-3x - 1)/(-2x + 3)) - 1) - 3)) + 2) - 1) + 5) - 3) = 0 have in the range [-10, 10]?\n\nPresent the ans... | 43 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2((-2(-2((-2(-5(-3|x| + 3)^2 - 1(-3|x| + 3) + 1) + 2)/(2(-5(-3|x| + 3)^2 - 1(-3|x| + 3) + 1) - 1)) - 4))/(3(-2((-2(-5(-3|x| + 3)^2 - 1(-3|x| + 3) + 1) + 2)/(2(-5(-3|x| + 3)^2 - 1(-3|x| + 3) + 1) - 1)) - 4) + 1)) equals zero.\n\nPresent the... | 4 | MATH |
[
{
"content": "How many solutions does the equation -4(2|(5(-3cos(2π(2|(2x + 4) + 2|) - 1) + 2) - 3) - 2| - 3)^2 - 4(2|(5(-3cos(2π(2|(2x + 4) + 2|) - 1) + 2) - 3) - 2| - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 239 | MATH |
[
{
"content": "How many solutions does the equation (1(2sin(2π((-2(4(1|(2x + 2) - 3| - 3)^2 + 2(1|(2x + 2) - 3| - 3) - 2) + 1)/(2(4(1|(2x + 2) - 3| - 3)^2 + 2(1|(2x + 2) - 3| - 3) - 2))) - 3) + 1) - 3)/(-2(2sin(2π((-2(4(1|(2x + 2) - 3| - 3)^2 + 2(1|(2x + 2) - 3| - 3) - 2) + 1)/(2(4(1|(2x + 2) - 3| - 3)^2 + 2(1|(... | 30 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-3(-3|(3cos(2π(1((3x - 1)/(-1x - 1)) - 4) + 3) + 1) + 1|) - 4)^2 + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 115 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2cos(1π(5(3|(-5(1x^2 + 5x + 5)^2 - 4(1x^2 + 5x + 5) - 2) + 2| + 1)^2 - 5(3|(-5(1x^2 + 5x + 5)^2 - 4(1x^2 + 5x + 5) - 2) + 2| + 1) - 3)) + 1)^2 + 1(2cos(1π(5(3|(-5(1x^2 + 5x + 5)^2 - 4(1x^2 + 5x + 5) - 2) + 2| + 1)^2 - 5(3|(-5(1x^2 + 5x ... | 198 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(2sin(3π(4(2((-2((2x)/(-2x - 3)) + 2)/(3((2x)/(-2x - 3))))^2 + 4((-2((2x)/(-2x - 3)) + 2)/(3((2x)/(-2x - 3)))) + 1) - 3) + 3)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 216 | MATH |
[
{
"content": "How many solutions does the equation 4((-3(-3(2|(4(-5x^2 + 4x - 1)^2 - 1(-5x^2 + 4x - 1) - 5)| + 1) + 4) + 2)/(-1(-3(2|(4(-5x^2 + 4x - 1)^2 - 1(-5x^2 + 4x - 1) - 5)| + 1) + 4) + 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) = 1(1((1(5(3|(-4x + 2) - 3| - 1)^2 - 2(3|(-4x + 2) - 3| - 1) - 3) - 3)/(-1(5(3|(-4x + 2) - 3| - 1)^2 - 2(3|(-4x + 2) - 3| - 1) - 3) - 1))^2 - 4((1(5(3|(-4x + 2) - 3| - 1)^2 - 2(3|(-4x + 2) - 3| - 1) - 3) - 3)/(-1(5(3|(-4x + 2) - 3| - 1)^2 - ... | 8 | MATH |
[
{
"content": "How many solutions does the equation (2(2sin(1π(-2(3(5((2x - 2)/(-2x - 2)) - 1)^2 + 2(5((2x - 2)/(-2x - 2)) - 1) + 1)^2 - 3(3(5((2x - 2)/(-2x - 2)) - 1)^2 + 2(5((2x - 2)/(-2x - 2)) - 1) + 1) + 4) + 1) - 2))/(1(2sin(1π(-2(3(5((2x - 2)/(-2x - 2)) - 1)^2 + 2(5((2x - 2)/(-2x - 2)) - 1) + 1)^2 - 3(3(5(... | 1031 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-3((-3(5(-1(3x^2 - 4x + 4)^2 + 2(3x^2 - 4x + 4) + 5)^2 - 2(-1(3x^2 - 4x + 4)^2 + 2(3x^2 - 4x + 4) + 5) - 1) - 2)/(-3(5(-1(3x^2 - 4x + 4)^2 + 2(3x^2 - 4x + 4) + 5)^2 - 2(-1(3x^2 - 4x + 4)^2 + 2(3x^2 - 4x + 4) + 5) - 1) + 4))^2 + 5((-3(5(-1(3x... | 8 | MATH |
[
{
"content": "How many solutions does the equation (-3(2(-3(2sin(1π((3(-1|x + 1| + 1) + 3)/(-2(-1|x + 1| + 1) - 3)) + 1) - 2) - 5)^2 + 3(-3(2sin(1π((3(-1|x + 1| + 1) + 3)/(-2(-1|x + 1| + 1) - 3)) + 1) - 2) - 5) - 4) - 2)/(2(2(-3(2sin(1π((3(-1|x + 1| + 1) + 3)/(-2(-1|x + 1| + 1) - 3)) + 1) - 2) - 5)^2 + 3(-3(2si... | 14 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|(2(3e^(-2(1|(-5(-5x^2 + 2x + 3) + 1)|))) - 2) - 1| + 3 have in the interval [-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) = (-1((3(4((-1((1(-2sin(1πx + 2) + 1) - 1)/(2(-2sin(1πx + 2) + 1) + 2)))/(-1((1(-2sin(1πx + 2) + 1) - 1)/(2(-2sin(1πx + 2) + 1) + 2)) + 3))^2 + 5((-1((1(-2sin(1πx + 2) + 1) - 1)/(2(-2sin(1πx + 2) + 1) + 2)))/(-1((1(-2sin(1πx + 2) + 1) - 1)/(... | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|((1(-1|((1(-1|(-2sin(3πx) + 2) - 3| + 1) - 3)/(-2(-1|(-2sin(3πx) + 2) - 3| + 1) - 2))| + 3) - 1)/(-3(-1|((1(-1|(-2sin(3πx) + 2) - 3| + 1) - 3)/(-2(-1|(-2sin(3πx) + 2) - 3| + 1) - 2))| + 3) + 1))| - 3 have in the interval [-10, 10]?\n\nPresent the answer in... | 188 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(2π(-2((2(-2(-1((-2x + 3)/(1x - 2))^2 - 5((-2x + 3)/(1x - 2)) - 4)^2 - 3(-1((-2x + 3)/(1x - 2))^2 - 5((-2x + 3)/(1x - 2)) - 4) - 3) - 2)/(-1(-2(-1((-2x + 3)/(1x - 2))^2 - 5((-2x + 3)/(1x - 2)) - 4)^2 - 3(-1((-2x + 3)/(1x - 2))^2 - 5((-2x + 3)/(1x - 2)) ... | 41 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3π(-1(-1|(1((1(2x^2 - 1) + 2)/(-3(2x^2 - 1) - 3))^2 - 4((1(2x^2 - 1) + 2)/(-3(2x^2 - 1) - 3)) + 1)| + 1)^2 + 5(-1|(1((1(2x^2 - 1) + 2)/(-3(2x^2 - 1) - 3))^2 - 4((1(2x^2 - 1) + 2)/(-3(2x^2 - 1) - 3)) + 1)| + 1) + 2)) - 1 equals zero.\... | 175 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(3|(1|(1|(2(3sin(3πx) - 1) + 5)|) + 1| - 2)| - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 188 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (2(5(-5(4(-1cos(1π(-4x + 1)))^2 - 2(-1cos(1π(-4x + 1))) - 5) + 3) + 4) - 2)/(-3(5(-5(4(-1cos(1π(-4x + 1)))^2 - 2(-1cos(1π(-4x + 1))) - 5) + 3) + 4)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 32 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(1|(-2cos(2π(3(5((1x + 1)/(1x))^2 - 3)^2 - 5(5((1x + 1)/(1x))^2 - 3) + 4) - 2) + 1)| - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 462 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(2π(-2(1((-1(-4(1|x - 1|) + 1) - 2)/(-2(-4(1|x - 1|) + 1) + 3))^2 - 4((-1(-4(1|x - 1|) + 1) - 2)/(-2(-4(1|x - 1|) + 1) + 3)) - 5)^2 - 3(1((-1(-4(1|x - 1|) + 1) - 2)/(-2(-4(1|x - 1|) + 1) + 3))^2 - 4((-1(-4(1|x - 1|) + 1) - 2)/(-2(-4(1|x - ... | 252 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-2(1(-2((2(4x^2 + 5x) - 3)/(-2(4x^2 + 5x) - 1)) + 2)^2 - 2(-2((2(4x^2 + 5x) - 3)/(-2(4x^2 + 5x) - 1)) + 2) + 3)^2 + 4(1(-2((2(4x^2 + 5x) - 3)/(-2(4x^2 + 5x) - 1)) + 2)^2 - 2(-2((2(4x^2 + 5x) - 3)/(-2(4x^2 + 5x) - 1)) + 2) + 3) + 5)^2 - 3... | 8 | MATH |
[
{
"content": "How many solutions does the equation -3(1((-2(3|(2(-1x^2 - 4x - 2) + 1) - 3| - 3) + 3)/(3(3|(2(-1x^2 - 4x - 2) + 1) - 3| - 3))) + 3)^2 - 4(1((-2(3|(2(-1x^2 - 4x - 2) + 1) - 3| - 3) + 3)/(3(3|(2(-1x^2 - 4x - 2) + 1) - 3| - 3))) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTe... | 6 | MATH |
[
{
"content": "How many solutions does the equation 1|(-4(-3|(2|(-2|(-3|x + 1| - 1) + 2| + 3)| - 3) - 1| - 1)^2 - 5(-3|(2|(-2|(-3|x + 1| - 1) + 2| + 3)| - 3) - 1| - 1) + 1) - 1| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many solutions does the equation -1(1(4((-3(2(2x + 5)^2 - 3(2x + 5)) + 3)/(1(2(2x + 5)^2 - 3(2x + 5)) + 2)) + 1)^2 - 2(4((-3(2(2x + 5)^2 - 3(2x + 5)) + 3)/(1(2(2x + 5)^2 - 3(2x + 5)) + 2)) + 1) + 1)^2 + 5(1(4((-3(2(2x + 5)^2 - 3(2x + 5)) + 3)/(1(2(2x + 5)^2 - 3(2x + 5)) + 2)) + 1)^2 - 2(4((-3(... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(1(1(2(1(-3sin(3πx + 1) - 1)^2 + 4(-3sin(3πx + 1) - 1) - 5) - 5) - 3) - 5) 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) = -4(3(-2|(4(-2|(-4x - 5) + 2| + 3) + 4)| + 1) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(2(1sin(2π(-5(-1(4x^2 - 2x + 3)^2 - 2(4x^2 - 2x + 3) + 5)^2 + 5(-1(4x^2 - 2x + 3)^2 - 2(4x^2 - 2x + 3) + 5) + 3) + 2) + 1) - 5) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4((-1(2(1(2(2cos(2πx - 1) + 3)^2 - 1)^2 - 5(2(2cos(2πx - 1) + 3)^2 - 1) - 3) - 2) + 2)/(-3(2(1(2(2cos(2πx - 1) + 3)^2 - 1)^2 - 5(2(2cos(2πx - 1) + 3)^2 - 1) - 3) - 2) - 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Y... | 14 | MATH |
[
{
"content": "How many solutions does the equation 2cos(3π(-1|(-2|((-2((-3(1x^2 + 1x - 3) - 2)/(1(1x^2 + 1x - 3))))/(3((-3(1x^2 + 1x - 3) - 2)/(1(1x^2 + 1x - 3))) - 2)) - 3| - 2)| + 3)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(3π(-2|((-3((-1(-1((2x + 3)/(-3x + 2))^2 - 3((2x + 3)/(-3x + 2)) + 2) - 2)/(-2(-1((2x + 3)/(-3x + 2))^2 - 3((2x + 3)/(-3x + 2)) + 2) + 3)) + 2)/(1((-1(-1((2x + 3)/(-3x + 2))^2 - 3((2x + 3)/(-3x + 2)) + 2) - 2)/(-2(-1((2x + 3)/(-3x + 2))^2 - 3((2x + 3)/(-... | 271 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(1(-4(-1(3|(-3|x - 3|) + 2| - 2) - 2) - 5)^2 - 5(-4(-1(3|(-3|x - 3|) + 2| - 2) - 2) - 5) - 5) + 3)/(-2(1(-4(-1(3|(-3|x - 3|) + 2| - 2) - 2) - 5)^2 - 5(-4(-1(3|(-3|x - 3|) + 2| - 2) - 2) - 5) - 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer ... | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(-5(2|(3(3|((-2x + 3)/(1x + 3)) - 2| - 1) + 2) - 2| - 1) + 5) + 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) = -2cos(3π(-4(-5(4((-1(-1x + 4) - 1)/(-2(-1x + 4) + 1))^2 + 5((-1(-1x + 4) - 1)/(-2(-1x + 4) + 1)) - 3) - 4)^2 + 5(-5(4((-1(-1x + 4) - 1)/(-2(-1x + 4) + 1))^2 + 5((-1(-1x + 4) - 1)/(-2(-1x + 4) + 1)) - 3) - 4) + 1) - 2) where -10 ≤ x ≤ 10.\n\nPr... | 1400 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3((-2((3(3|(5(1x^2 - 4x - 4) + 4) - 3| - 1) - 2)/(-1(3|(5(1x^2 - 4x - 4) + 4) - 3| - 1) + 2)) + 2)/(1((3(3|(5(1x^2 - 4x - 4) + 4) - 3| - 1) - 2)/(-1(3|(5(1x^2 - 4x - 4) + 4) - 3| - 1) + 2)) - 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in ... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(1(3|((-2(-2|(5x + 2) - 1|) - 1)/(2(-2|(5x + 2) - 1|) + 2)) - 2| - 3) - 1) - 2 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|(2sin(1π(-2(-2(2(-3x^2 + 2x - 4)^2 + 5(-3x^2 + 2x - 4) + 3) - 2)^2 - 3(-2(2(-3x^2 + 2x - 4)^2 + 5(-3x^2 + 2x - 4) + 3) - 2) + 5) - 3)) + 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 135 | MATH |
[
{
"content": "How many solutions does the equation (3(-3sin(3π(-2(-3(1|(-5x + 3) + 3| - 3) + 4)^2 + 5(-3(1|(-5x + 3) + 3| - 3) + 4) - 3) - 1) + 3) - 3)/(-3(-3sin(3π(-2(-3(1|(-5x + 3) + 3| - 3) + 4)^2 + 5(-3(1|(-5x + 3) + 3| - 3) + 4) - 3) - 1) + 3) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in ... | 1101 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-2(1((3(-3|(-2cos(3πx + 3) - 1)| + 2))/(-2(-3|(-2cos(3πx + 3) - 1)| + 2) - 2))^2 - 5((3(-3|(-2cos(3πx + 3) - 1)| + 2))/(-2(-3|(-2cos(3πx + 3) - 1)| + 2) - 2)))^2 - 4(1((3(-3|(-2cos(3πx + 3) - 1)| + 2))/(-2(-3|(-2cos(3πx + 3) - 1)| + 2) - 2)... | 259 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(2π(-1|((2(1(-3|(5x - 2) - 2| + 3) + 4) - 3)/(2(1(-3|(5x - 2) - 2| + 3) + 4) - 1))| - 3) - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(3π((-2(-1(1(-4(-5x^2 + 4x - 2) - 5)^2 + 1(-4(-5x^2 + 4x - 2) - 5) + 3) + 5) - 2)/(-1(-1(1(-4(-5x^2 + 4x - 2) - 5)^2 + 1(-4(-5x^2 + 4x - 2) - 5) + 3) + 5)))) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 14 | MATH |
[
{
"content": "How many solutions does the equation -1(1e^(1(5(5(1|(1|x + 2| - 2) - 1| - 2)^2 + 1(1|(1|x + 2| - 2) - 1| - 2) - 3)^2 + 5(5(1|(1|x + 2| - 2) - 1| - 2)^2 + 1(1|(1|x + 2| - 2) - 1| - 2) - 3) - 1)) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 16 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1((1(1|(2|(-1(4x + 5)^2 + 5(4x + 5) - 2) - 1|) - 1|) + 1)/(3(1|(2|(-1(4x + 5)^2 + 5(4x + 5) - 2) - 1|) - 1|) - 2))^2 - 4((1(1|(2|(-1(4x + 5)^2 + 5(4x + 5) - 2) - 1|) - 1|) + 1)/(3(1|(2|(-1(4x + 5)^2 + 5(4x + 5) - 2) - 1|) - 1|) - 2)) + 4 e... | 5 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1π(3(-1|(-1(-1|(1x^2 + 3x - 2) - 3|)^2 + 5(-1|(1x^2 + 3x - 2) - 3|) - 4)| + 2) - 4) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1166 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(3(-1sin(1π(3(-3((2x + 3)/(1x + 2))^2 + 2((2x + 3)/(1x + 2)))^2 + 4(-3((2x + 3)/(1x + 2))^2 + 2((2x + 3)/(1x + 2)))) + 2))^2 + 2(-1sin(1π(3(-3((2x + 3)/(1x + 2))^2 + 2((2x + 3)/(1x + 2)))^2 + 4(-3((2x + 3)/(1x + 2))^2 + 2((2x + 3)/(1x + 2)))) + 2)) - 1) - 5... | 459 | MATH |
[
{
"content": "How many solutions does the equation -3(-3sin(3π(-3|((-2(1(1x^2 - 4)^2 + 4(1x^2 - 4) + 2) + 2)/(2(1(1x^2 - 4)^2 + 4(1x^2 - 4) + 2))) + 1|) - 2))^2 + 5(-3sin(3π(-3|((-2(1(1x^2 - 4)^2 + 4(1x^2 - 4) + 2) + 2)/(2(1(1x^2 - 4)^2 + 4(1x^2 - 4) + 2))) + 1|) - 2)) - 2 = 0 have in the range [-10, 10]?\n\nPr... | 38 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1|(-2((2((-2(-3|x + 2| + 3) - 1)/(3(-3|x + 2| + 3))) - 3)/(-1((-2(-3|x + 2| + 3) - 1)/(3(-3|x + 2| + 3))) + 3)) + 3) + 1| + 2) + 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-1sin(3π(-2(-1(3((3x - 1)/(3x + 3))^2 + 4((3x - 1)/(3x + 3)))^2 + 4(3((3x - 1)/(3x + 3))^2 + 4((3x - 1)/(3x + 3))) + 1) + 3) + 2)) - 3)/(3(-1sin(3π(-2(-1(3((3x - 1)/(3x + 3))^2 + 4((3x - 1)/(3x + 3)))^2 + 4(3((3x - 1)/(3x + 3))^2 + 4((3... | 541 | MATH |
[
{
"content": "How many solutions does the equation (3(2sin(2π(-1|(2((2((-2x - 2)/(-3x + 2)) - 2)/(-1((-2x - 2)/(-3x + 2)) - 1))^2 - 2((2((-2x - 2)/(-3x + 2)) - 2)/(-1((-2x - 2)/(-3x + 2)) - 1)) - 4) - 2| + 1)) + 2))/(2(2sin(2π(-1|(2((2((-2x - 2)/(-3x + 2)) - 2)/(-1((-2x - 2)/(-3x + 2)) - 1))^2 - 2((2((-2x - 2)/... | 99 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2((-3(-1(-2sin(2π(-5(-4x^2 - 5x)) + 1) + 3) + 3))/(-1(-1(-2sin(2π(-5(-4x^2 - 5x)) + 1) + 3) + 3) + 2)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1213 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-5(-1((2(1(2x^2 + 4x - 5) - 1))/(-2(1(2x^2 + 4x - 5) - 1) + 3))^2 - 5((2(1(2x^2 + 4x - 5) - 1))/(-2(1(2x^2 + 4x - 5) - 1) + 3)) - 2) - 5)^2 - 4(-5(-1((2(1(2x^2 + 4x - 5) - 1))/(-2(1(2x^2 + 4x - 5) - 1) + 3))^2 - 5((2(1(2x^2 + 4x - 5) - ... | 4 | MATH |
[
{
"content": "How many solutions does the equation -1(-1|((-1(2(-2(2cos(1πx + 1) + 1) + 4)^2 + 5(-2(2cos(1πx + 1) + 1) + 4) + 2) - 1)/(3(2(-2(2cos(1πx + 1) + 1) + 4)^2 + 5(-2(2cos(1πx + 1) + 1) + 4) + 2) + 2)) + 3| - 1) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 72 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(4(-3(-1(1((-1x)/(-1x + 3))^2 - 2((-1x)/(-1x + 3)) - 4) + 1)^2 + 5(-1(1((-1x)/(-1x + 3))^2 - 2((-1x)/(-1x + 3)) - 4) + 1) - 1) + 5)^2 - 3(4(-3(-1(1((-1x)/(-1x + 3))^2 - 2((-1x)/(-1x + 3)) - 4) + 1)^2 + 5(-1(1((-1x)/(-1x + 3))^2 - 2((-1x)/(-1x + 3)) - 4) + ... | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(2π(3(1(-2((1((2x - 1)/(-1x - 3)) - 3)/(-1((2x - 1)/(-1x - 3)))) - 3)^2 + 3(-2((1((2x - 1)/(-1x - 3)) - 3)/(-1((2x - 1)/(-1x - 3)))) - 3) + 1)) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 610 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-1sin(3π((3((-1((-2(1x^2 + 1x - 4) + 2)/(3(1x^2 + 1x - 4) + 2)))/(-2((-2(1x^2 + 1x - 4) + 2)/(3(1x^2 + 1x - 4) + 2)) - 2)) - 2)/(-1((-1((-2(1x^2 + 1x - 4) + 2)/(3(1x^2 + 1x - 4) + 2)))/(-2((-2(1x^2 + 1x - 4) + 2)/(3(1x^2 + 1x - 4) + 2)) - 2... | 110 | MATH |
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