id
stringlengths 29
29
| setting_key
stringclasses 1
value | setting_name
stringclasses 0
values | messages
listlengths 1
1
| ground_truth
stringclasses 186
values | dataset
stringclasses 1
value |
|---|---|---|---|---|---|
algebra_func_zeros_train_0300
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1(-2|(-3cos(3πx - 3) - 2)| + 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
120
|
math
|
algebra_func_zeros_train_0301
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -1((-1(2sin(2πx + 2) + 1) + 2)/(-2(2sin(2πx + 2) + 1)))^2 - 2((-1(2sin(2πx + 2) + 1) + 2)/(-2(2sin(2πx + 2) + 1))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0302
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1(2(3|((2x + 3)/(3x + 3)) - 3| + 1)^2 - 4(3|((2x + 3)/(3x + 3)) - 3| + 1) + 4) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0303
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1e^(-1(2x^2 - 5x - 1)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0304
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(1((-2(3x - 4) + 3)/(3(3x - 4) + 3))^2 + 5((-2(3x - 4) + 3)/(3(3x - 4) + 3)) + 5)| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0305
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2((3(-2(3|x + 3| + 1) + 5) - 3)/(1(-2(3|x + 3| + 1) + 5) + 2))^2 + 4((3(-2(3|x + 3| + 1) + 5) - 3)/(1(-2(3|x + 3| + 1) + 5) + 2)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0306
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1|(-3sin(3πx - 3) + 3) + 2| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
30
|
math
|
algebra_func_zeros_train_0307
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 2sin(1π((-1x + 3)/(-3x + 1)) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0308
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-4(-2((2x + 1)/(-3x + 2)))^2 + 3) + 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_zeros_train_0309
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 3((1x - 1)/(2x - 1))^2 - 5((1x - 1)/(2x - 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0310
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 2e^(2(-3(1|(4x + 4) - 2| + 2)^2 + 1(1|(4x + 4) - 2| + 2) - 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_zeros_train_0311
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -1cos(1π(-2(2|(-5x^2 - 1x - 3) - 1| - 3) + 3) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1159
|
math
|
algebra_func_zeros_train_0312
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-1sin(2πx - 2) + 1) - 2)/(2(-1sin(2πx - 2) + 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0313
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 4(-3|x + 2| + 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0314
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (-3(1(5(-2|x - 1| + 3)^2 - 3(-2|x - 1| + 3) - 1) - 5) - 1)/(2(1(5(-2|x - 1| + 3)^2 - 3(-2|x - 1| + 3) - 1) - 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0315
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -1|(3sin(2π(-3x^2 + 5x) - 3) + 3) - 3| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1128
|
math
|
algebra_func_zeros_train_0316
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1(-3x + 5)^2 + 2(-3x + 5) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0317
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -4(-2|x + 3| + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0318
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -2e^(1(4(5(-1|x - 2| + 3)^2 - 5(-1|x - 2| + 3) - 3) + 5)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0319
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-2|(-4((-2x - 3)/(-3x - 1))^2 - 5((-2x - 3)/(-3x - 1)) + 5) + 1| + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_zeros_train_0320
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 3(3sin(2πx - 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0321
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(1((-2x - 1)/(1x + 3))^2 - 1) - 3| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0322
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 4(4x^2 + 1x - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0323
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 5(-3|x + 1| + 3)^2 + 4(-3|x + 1| + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0324
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 5(4x - 1)^2 + 3(4x - 1) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0325
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (1(1cos(3πx - 1) - 3) + 3)/(2(1cos(3πx - 1) - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_zeros_train_0326
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -5(1|((1(-2x^2 + 3x + 2) - 2)/(3(-2x^2 + 3x + 2) - 2)) - 2| - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0327
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1cos(1π((1x - 3)/(2x)) + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
28
|
math
|
algebra_func_zeros_train_0328
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -4(2x - 1)^2 - 2(2x - 1) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0329
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 3(-2|((-1x)/(1x + 1)) + 2| + 2)^2 + 2(-2|((-1x)/(1x + 1)) + 2| + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_zeros_train_0330
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1π(3|x + 1|) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
62
|
math
|
algebra_func_zeros_train_0331
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2sin(3π(-5((2x + 3)/(2x - 1))^2 - 4((2x + 3)/(2x - 1)) - 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
282
|
math
|
algebra_func_zeros_train_0332
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-3(3(-1sin(3π(2|x - 1| - 3) + 1) - 1)^2 - 5(-1sin(3π(2|x - 1| - 3) + 1) - 1) - 2))/(2(3(-1sin(3π(2|x - 1| - 3) + 1) - 1)^2 - 5(-1sin(3π(2|x - 1| - 3) + 1) - 1) - 2) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
120
|
math
|
algebra_func_zeros_train_0333
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -1|((-3(5(-1x - 5)^2 - 5(-1x - 5) + 2) + 2)/(-1(5(-1x - 5)^2 - 5(-1x - 5) + 2) + 2)) - 3| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0334
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1π(-5(2|x - 1| - 1) - 4) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
100
|
math
|
algebra_func_zeros_train_0335
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-4(-3cos(1π(-2x - 4)) + 3)^2 - 3(-3cos(1π(-2x - 4)) + 3) - 1) + 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0336
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(3(1sin(2πx + 3) - 2)^2 - 3(1sin(2πx + 3) - 2) - 2) - 3| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0337
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -3|((2(-1x^2 + 5x + 4) - 2)/(3(-1x^2 + 5x + 4) - 1)) + 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0338
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -5(-1|(-3(1cos(1πx - 2) + 1) - 1) - 1| + 1)^2 - 2(-1|(-3(1cos(1πx - 2) + 1) - 1) - 1| + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0339
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 3e^(1(-3((3x - 3)/(2x))^2 - 1((3x - 3)/(2x)) + 3)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0340
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1|((-2(-4x - 2))/(1(-4x - 2) + 3)) + 1| + 1)^2 + 1(-1|((-2(-4x - 2))/(1(-4x - 2) + 3)) + 1| + 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0341
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 3cos(3π((1(-3x + 5) - 2)/(-3(-3x + 5) + 4)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
18
|
math
|
algebra_func_zeros_train_0342
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-2(-2|x + 3| + 2) - 2)/(2(-2|x + 3| + 2) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0343
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (1(-1(-2e^(2(-1x + 1)) + 3)^2 - 5(-2e^(2(-1x + 1)) + 3) + 5) - 1)/(-1(-1(-2e^(2(-1x + 1)) + 3)^2 - 5(-2e^(2(-1x + 1)) + 3) + 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0344
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1cos(2π((-1x + 2)/(-1x)) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
algebra_func_zeros_train_0345
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1(-1|(-3x - 4) + 1| + 3)^2 - 5(-1|(-3x - 4) + 1| + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0346
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -2|(3sin(2π((2(4x^2 + 1x - 5))/(2(4x^2 + 1x - 5) - 1)) + 1) + 2) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
24
|
math
|
algebra_func_zeros_train_0347
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (2(-5(2|x - 3|) + 1))/(-1(-5(2|x - 3|) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0348
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -5(3cos(2π(-1|x + 2| - 1) - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0349
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (-2(-2|(-1cos(1πx + 3) - 1) + 2| + 1) + 1)/(3(-2|(-1cos(1πx + 3) - 1) + 2| + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0350
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1(3|(-1((-2x - 3)/(2x - 3))) + 1| - 2)^2 + 3(3|(-1((-2x - 3)/(2x - 3))) + 1| - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0351
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1|(-2((1(-1x) - 3)/(3(-1x) + 2))^2 - 1((1(-1x) - 3)/(3(-1x) + 2)) - 3) + 1| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0352
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1|(5(3sin(2πx - 2) - 1) + 4) - 2| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
80
|
math
|
algebra_func_zeros_train_0353
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 4(5((1(-2|x + 1| - 1) - 2)/(2(-2|x + 1| - 1) - 1)) - 5)^2 + 2(5((1(-2|x + 1| - 1) - 2)/(2(-2|x + 1| - 1) - 1)) - 5) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0354
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -2(2|((2x + 3)/(-3x + 1)) - 2| - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0355
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (3(2sin(3π(-1|x + 2| - 3) - 2) + 1) - 2)/(-2(2sin(3π(-1|x + 2| - 3) - 2) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_zeros_train_0356
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-5(2cos(1π((2x - 3)/(-1x - 1)) - 2) - 2)^2 + 2(2cos(1π((2x - 3)/(-1x - 1)) - 2) - 2) + 1)| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
71
|
math
|
algebra_func_zeros_train_0357
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -2e^(-1(-3((-3(-1|x + 1| + 1))/(2(-1|x + 1| + 1) + 3)) + 1)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0358
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (2(-2|(-5(3sin(1πx) - 2) - 1)| + 2) + 1)/(1(-2|(-5(3sin(1πx) - 2) - 1)| + 2) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0359
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(1(-5x^2 + 2x - 2) + 5) + 2)/(1(1(-5x^2 + 2x - 2) + 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0360
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 2((-3(-1x - 4))/(-2(-1x - 4) + 3))^2 + 4((-3(-1x - 4))/(-2(-1x - 4) + 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0361
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-1(3sin(3πx - 1) - 1))/(-3(3sin(3πx - 1) - 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_zeros_train_0362
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (2(-2|(1x - 4) - 1| + 1) + 1)/(-2(-2|(1x - 4) - 1| + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0363
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (-1(1|x + 2|) + 2)/(2(1|x + 2|) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0364
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 3sin(3π(-1|(-5x^2 - 4) - 1| + 2) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1316
|
math
|
algebra_func_zeros_train_0365
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 2|(1(-5x^2 + 4x + 1) + 4) - 3| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0366
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1(-5x^2 + 4x - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0367
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 2cos(2π(-4x^2 - 4x - 4) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1310
|
math
|
algebra_func_zeros_train_0368
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(5(-2|x + 2| + 1)^2 - 3(-2|x + 2| + 1) - 5) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0369
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -2|(1(2((-2x + 1)/(-2x - 1))^2 - 1((-2x + 1)/(-2x - 1)) - 4) + 5) - 2| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0370
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -2|(1((2x + 1)/(-2x + 3))^2 + 2((2x + 1)/(-2x + 3)) - 5) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0371
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(5(3cos(3πx + 3) - 2)^2 + 2(3cos(3πx + 3) - 2) - 4) + 1| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
240
|
math
|
algebra_func_zeros_train_0372
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (2(1(2x - 4)^2 + 1(2x - 4) - 5))/(3(1(2x - 4)^2 + 1(2x - 4) - 5) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0373
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -2sin(2π((2(-2|x - 1| + 3) - 1)/(2(-2|x - 1| + 3) + 1)) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
70
|
math
|
algebra_func_zeros_train_0374
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3e^(1(-1|((-2x - 2)/(2x + 3)) - 1| + 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0375
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2π(-3(3|x| + 1) + 5) - 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
176
|
math
|
algebra_func_zeros_train_0376
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1(-1|x - 3| + 3)^2 + 2(-1|x - 3| + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0377
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3sin(2π(2|(-5x + 4) - 3| + 2) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
400
|
math
|
algebra_func_zeros_train_0378
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -4(2((-1x - 3)/(-1x))^2 + 3((-1x - 3)/(-1x)) - 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0379
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π(-5(3|x + 2|)^2 - 2(3|x + 2|) + 3) + 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1207
|
math
|
algebra_func_zeros_train_0380
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1|(4((3(-3e^(-1x) + 3) + 2)/(-1(-3e^(-1x) + 3) + 3))^2 + 4((3(-3e^(-1x) + 3) + 2)/(-1(-3e^(-1x) + 3) + 3)) - 2) + 2| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0381
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -2|(-3cos(2π((-3x + 2)/(1x - 3)) - 3) - 1)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
121
|
math
|
algebra_func_zeros_train_0382
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-2|x - 1| + 3) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0383
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-1x^2 - 5x - 1) + 1)/(-2(-1x^2 - 5x - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0384
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 3((2(-1sin(2πx + 1) - 2) + 3)/(-1(-1sin(2πx + 1) - 2))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0385
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1sin(3π(-2|(1((1x + 3)/(-1x - 2))^2 - 1((1x + 3)/(-1x - 2)) - 4) - 3| + 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
82
|
math
|
algebra_func_zeros_train_0386
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3|(-3e^(2((-1(-3x - 5))/(3(-3x - 5) + 2))) + 1) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0387
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1((2x - 1)/(-3x + 1))^2 + 1((2x - 1)/(-3x + 1)) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0388
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -4(3((2x + 3)/(-3x - 3)) + 4)^2 + 1(3((2x + 3)/(-3x - 3)) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0389
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(4(-2x^2 - 2x + 2) - 1) - 2)/(2(4(-2x^2 - 2x + 2) - 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0390
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(3|(3(-2x - 5)^2 + 2(-2x - 5) + 1) - 2|))/(-2(3|(3(-2x - 5)^2 + 2(-2x - 5) + 1) - 2|) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0391
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 3(1cos(3πx + 3)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_zeros_train_0392
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1sin(1π(3|x| - 1) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
30
|
math
|
algebra_func_zeros_train_0393
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 4(2e^(-1x) - 1)^2 - 5(2e^(-1x) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0394
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 2|(2x + 2) + 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0395
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2sin(3π(-1x^2 + 3x - 3)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
611
|
math
|
algebra_func_zeros_train_0396
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -2(-1|(-3cos(1πx + 2) + 1) - 3|)^2 - 5(-1|(-3cos(1πx + 2) + 1) - 3|) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
27
|
math
|
algebra_func_zeros_train_0397
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (1(3|(5(-2x^2 - 2x + 5) + 1) + 2| + 1) - 3)/(2(3|(5(-2x^2 - 2x + 5) + 1) + 2| + 1) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0398
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(4(1e^(-2(-5x^2 + 2x)) - 3) + 2)| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0399
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -3cos(2π((1x - 1)/(2x - 1)) - 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
24
|
math
|
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