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_0000
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -1((1(2|(3x)| + 2) - 1)/(-1(2|(3x)| + 2) + 2))^2 + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0001
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (3(-3sin(3πx - 3) + 1) + 2)/(-2(-3sin(3πx - 3) + 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_zeros_train_0002
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1((-2(-1|x + 1| - 2) - 1)/(1(-1|x + 1| - 2) + 3)) + 5)^2 + 2(1((-2(-1|x + 1| - 2) - 1)/(1(-1|x + 1| - 2) + 3)) + 5) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0003
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 5(2cos(2π(3|(4x^2 + 1x - 3) - 3| - 3) - 3) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
799
|
math
|
algebra_func_zeros_train_0004
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2π(-1(-1|(-1x + 5) + 2| - 1)^2 - 1(-1|(-1x + 5) + 2| - 1) + 2) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
636
|
math
|
algebra_func_zeros_train_0005
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 2(2((2x)/(1x + 1))^2 - 4((2x)/(1x + 1)) - 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_0006
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -1e^(2(-3((-1(-4x^2 + 3x + 2))/(3(-4x^2 + 3x + 2) + 3)) - 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_0007
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2π((2(-3|x - 2| - 2) - 3)/(-1(-3|x - 2| - 2) + 3))) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0008
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2|((2(-2(-2x^2 - 1x - 5) - 2) - 2)/(1(-2(-2x^2 - 1x - 5) - 2) + 3)) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0009
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2|(1((-1x - 3)/(3x - 2))^2 - 4((-1x - 3)/(3x - 2)) - 3) - 1| - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_zeros_train_0010
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 3cos(3π(-2|((2(-5x^2 + 5) - 3)/(-1(-5x^2 + 5) + 2)) - 1| + 3) - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
64
|
math
|
algebra_func_zeros_train_0011
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3(-1|x - 1| + 1)^2 + 3(-1|x - 1| + 1)) + 1)/(1(3(-1|x - 1| + 1)^2 + 3(-1|x - 1| + 1)) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0012
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-3sin(1πx + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_func_zeros_train_0013
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(3cos(1π(-4x^2 + 2x - 3) + 1) - 3) - 2)/(2(3cos(1π(-4x^2 + 2x - 3) + 1) - 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
497
|
math
|
algebra_func_zeros_train_0014
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 3(3|x + 3|) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0015
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -3(-2|(3x^2 - 1x - 1)| + 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0016
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (-3(2cos(3π(-3|(1x^2 - 3x - 2) - 2|) - 3) + 1) - 1)/(-1(2cos(3π(-3|(1x^2 - 3x - 2) - 2|) - 3) + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1177
|
math
|
algebra_func_zeros_train_0017
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-3|(2cos(1πx + 1) - 3) + 3| + 3) - 1)/(1(-3|(2cos(1πx + 1) - 3) + 3| + 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0018
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(1(-2((3x - 3)/(-2x + 3))^2 + 4((3x - 3)/(-2x + 3)) + 3) - 2) - 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0019
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1(1|(1((3x + 1)/(1x + 1)) + 1) - 1| + 1)^2 - 2(1|(1((3x + 1)/(1x + 1)) + 1) - 1| + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0020
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -1cos(2π(-1x - 2)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21
|
math
|
algebra_func_zeros_train_0021
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-1(2(2(-2|x - 3| + 2)^2 + 1(-2|x - 3| + 2)) - 5))/(-2(2(2(-2|x - 3| + 2)^2 + 1(-2|x - 3| + 2)) - 5) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0022
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1π(-3|(4x^2 + 2x - 1) + 2| - 2) + 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
971
|
math
|
algebra_func_zeros_train_0023
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-2sin(1π(1|x| - 1) - 2) + 1)^2 - 2(-2sin(1π(1|x| - 1) - 2) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0024
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 5(-3((-2x - 3)/(1x + 3))^2 + 1((-2x - 3)/(1x + 3)) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0025
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 3(1|(-2x + 1) + 3|)^2 + 4(1|(-2x + 1) + 3|) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0026
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -5(-4((3(1e^(2x) - 1) - 2)/(-3(1e^(2x) - 1) + 4)))^2 + 3(-4((3(1e^(2x) - 1) - 2)/(-3(1e^(2x) - 1) + 4))) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0027
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3π(-2x^2 - 2x - 4) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1168
|
math
|
algebra_func_zeros_train_0028
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1(3(-1|((2x + 2)/(-3x - 2)) - 2| + 1))^2 - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0029
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -3(-1|(-1e^(-1x) + 2) + 3| + 2)^2 + 3(-1|(-1e^(-1x) + 2) + 3| + 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0030
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-2(2(5(-1|x| + 3)^2 + 5(-1|x| + 3)) - 1) + 1)/(1(2(5(-1|x| + 3)^2 + 5(-1|x| + 3)) - 1)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0031
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 5(-2|((2(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 2| - 1)^2 + 5(-2|((2(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 2| - 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_0032
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3sin(3π(-4x^2 - 1x - 2) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1338
|
math
|
algebra_func_zeros_train_0033
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1|((-2(-2(-3sin(3πx + 3) - 1)^2 + 5(-3sin(3πx + 3) - 1) - 1) + 2)/(2(-2(-3sin(3πx + 3) - 1)^2 + 5(-3sin(3πx + 3) - 1) - 1) + 2)) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
146
|
math
|
algebra_func_zeros_train_0034
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 5((-1(-3|(1x + 3) - 1| + 3) - 2)/(2(-3|(1x + 3) - 1| + 3) + 2))^2 - 1((-1(-3|(1x + 3) - 1| + 3) - 2)/(2(-3|(1x + 3) - 1| + 3) + 2)) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0035
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3cos(2π(3|(-3x^2 - 3x + 4) - 2| - 2) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1613
|
math
|
algebra_func_zeros_train_0036
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1π(-5x^2 + 2x - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1000
|
math
|
algebra_func_zeros_train_0037
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 5(-3sin(3πx) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_zeros_train_0038
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2(-3(-2|x - 1|)^2 + 2(-2|x - 1|) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0039
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (-2(-1|(5(-2x^2 + 1x + 3) + 4) - 1| + 2) - 2)/(-2(-1|(5(-2x^2 + 1x + 3) + 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_0040
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (3(1cos(1π(1(-3|x - 3| + 1)^2 - 1(-3|x - 3| + 1) + 1) + 3)))/(-1(1cos(1π(1(-3|x - 3| + 1)^2 - 1(-3|x - 3| + 1) + 1) + 3)) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1412
|
math
|
algebra_func_zeros_train_0041
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1(3cos(3π(5(2|x| - 3)^2 + 2(2|x| - 3) - 5) - 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1041
|
math
|
algebra_func_zeros_train_0042
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-3sin(2πx + 3))^2 - 2(-3sin(2πx + 3)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
80
|
math
|
algebra_func_zeros_train_0043
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (2(1(-2cos(3πx - 1) + 2) - 2) + 3)/(3(1(-2cos(3πx - 1) + 2) - 2) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_zeros_train_0044
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -4(2|(3x^2 - 3x + 2) - 1| - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0045
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (1(-3x^2 + 3x + 3) + 2)/(2(-3x^2 + 3x + 3) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0046
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 3((3(-1x + 2) + 1)/(2(-1x + 2)))^2 + 4((3(-1x + 2) + 1)/(2(-1x + 2))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0047
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 5(-3((-1x + 1)/(3x))^2 - 5((-1x + 1)/(3x)) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0048
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -4((-1(2(2|x - 3| - 1) + 3) + 3)/(1(2(2|x - 3| - 1) + 3) - 2))^2 - 5((-1(2(2|x - 3| - 1) + 3) + 3)/(1(2(2|x - 3| - 1) + 3) - 2)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0049
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1|(-2e^(-2(1(2x^2 + 4x - 2) - 5)) + 2) + 3| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0050
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1((-2(1(1|x| - 2)^2 - 3(1|x| - 2) - 2) + 3)/(-1(1(1|x| - 2)^2 - 3(1|x| - 2) - 2))) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0051
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -2sin(3π((1(-5x^2 - 5x - 2) + 1)/(1(-5x^2 - 5x - 2) - 3))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
algebra_func_zeros_train_0052
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -3(-1|x| + 1)^2 + 3(-1|x| + 1) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0053
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -2cos(3π((-2x - 2)/(-1x + 2)) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
143
|
math
|
algebra_func_zeros_train_0054
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 5(-1x^2 - 5x + 5) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0055
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(2((-3x - 1)/(1x)) - 1) + 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0056
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (-1(3cos(1π(-1|x + 2| - 3) - 1) + 1))/(-2(3cos(1π(-1|x + 2| - 3) - 1) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0057
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2cos(1π(1((-2(-4x^2 - 5x - 4))/(-1(-4x^2 - 5x - 4) - 3)) - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
86
|
math
|
algebra_func_zeros_train_0058
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1cos(2π((2(-3x - 4) - 2)/(-1(-3x - 4) - 3)) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
88
|
math
|
algebra_func_zeros_train_0059
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (1(-1cos(3π(3x - 3) + 2) + 3) - 2)/(1(-1cos(3π(3x - 3) + 2) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
90
|
math
|
algebra_func_zeros_train_0060
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1π(1|x - 1| - 1) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
algebra_func_zeros_train_0061
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((2(-1(-1x + 4)^2 - 5(-1x + 4) + 4) + 3)/(-3(-1(-1x + 4)^2 - 5(-1x + 4) + 4) + 2))| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0062
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(3|(4x^2 - 1x - 5) + 3| - 3) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0063
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3|(-1cos(2πx - 2) - 3) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0064
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -4(2|(-1x^2 - 2x + 3) + 2| - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0065
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (-3(3(-1x - 5)^2 + 5(-1x - 5) + 2) + 1)/(2(3(-1x - 5)^2 + 5(-1x - 5) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0066
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 3|(4(1sin(3πx + 1) - 1)) + 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
120
|
math
|
algebra_func_zeros_train_0067
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -3|(-5(2((-3x + 2)/(3x + 1))^2 + 4((-3x + 2)/(3x + 1))) + 1) - 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0068
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 2sin(3π(-3|((-2x - 1)/(-3x + 4)) - 1| - 3) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
118
|
math
|
algebra_func_zeros_train_0069
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1|((-3(2(-5x - 1)^2 - 5))/(3(2(-5x - 1)^2 - 5) - 2)) + 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0070
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (-1(3(3cos(3πx + 3) + 1)^2 + 4(3cos(3πx + 3) + 1) + 3) + 3)/(-1(3(3cos(3πx + 3) + 1)^2 + 4(3cos(3πx + 3) + 1) + 3) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
120
|
math
|
algebra_func_zeros_train_0071
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 2|((-2(-4(1x^2 + 4x) + 2) + 2)/(-2(-4(1x^2 + 4x) + 2) - 3)) - 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_0072
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2(-2|(5((-2x - 2)/(-1x - 2))^2 + 5((-2x - 2)/(-1x - 2)) - 5) - 1| + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0073
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1|((-1(4(-1x^2 + 5x + 2) - 1) - 2)/(-3(4(-1x^2 + 5x + 2) - 1) + 2)) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0074
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (-2(-2(-1|x + 2| + 3)^2 + 2) - 2)/(-2(-2(-1|x + 2| + 3)^2 + 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_0075
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1x - 1)^2 - 4(1x - 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0076
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2|((-2(-5x - 3) + 2)/(-3(-5x - 3) + 4)) - 1| - 3)^2 - 2(2|((-2(-5x - 3) + 2)/(-3(-5x - 3) + 4)) - 1| - 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0077
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3cos(1π(-4x^2 + 5) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
800
|
math
|
algebra_func_zeros_train_0078
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1e^(2((-2(-4(-1x - 5)^2 + 1(-1x - 5) + 2) + 1)/(3(-4(-1x - 5)^2 + 1(-1x - 5) + 2) - 1))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0079
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -1cos(2π(-2(3(1|x - 3| + 2) + 5)^2 - 1(3(1|x - 3| + 2) + 5) + 5)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1182
|
math
|
algebra_func_zeros_train_0080
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -5(5x + 4)^2 + 5(5x + 4) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0081
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-3(-4(-3sin(3πx) + 2) + 3))/(-1(-4(-3sin(3πx) + 2) + 3) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_zeros_train_0082
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -1((3(4(1|x - 3| - 3)^2 - 2) - 2)/(1(4(1|x - 3| - 3)^2 - 2) - 2)) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0083
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1x - 4) - 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0084
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (-1(-1sin(1πx + 2) - 1) - 1)/(-2(-1sin(1πx + 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_0085
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1|(5x^2 - 4x + 2) - 3| + 3) - 2)/(1(-1|(5x^2 - 4x + 2) - 3| + 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0086
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1(5(-3sin(2π(2|x - 3| + 1) - 1) + 1)^2 + 5(-3sin(2π(2|x - 3| + 1) - 1) + 1) - 2) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
160
|
math
|
algebra_func_zeros_train_0087
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3((-2(2|x + 3| - 2) + 2)/(2(2|x + 3| - 2) + 3)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0088
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (1(-3cos(2π(-3|x| - 3) - 1) + 2) - 3)/(2(-3cos(2π(-3|x| - 3) - 1) + 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
120
|
math
|
algebra_func_zeros_train_0089
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 2|(3((2(5x^2 + 5x + 2) - 3)/(2(5x^2 + 5x + 2) + 2))) + 1| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0090
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1(4x - 3)^2 - 1(4x - 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0091
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -2(1((3x - 2)/(2x - 3))^2 - 1((3x - 2)/(2x - 3)) - 4) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0092
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (2(-3(-1(-1|x + 2| + 2)^2 - 3(-1|x + 2| + 2) + 5)) - 2)/(2(-3(-1(-1|x + 2| + 2)^2 - 3(-1|x + 2| + 2) + 5)) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0093
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1π((-1x - 2)/(-2x + 3)) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
46
|
math
|
algebra_func_zeros_train_0094
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(2(5(-2|x| + 1)^2 + 5(-2|x| + 1) - 2) - 5) + 1)/(-3(2(5(-2|x| + 1)^2 + 5(-2|x| + 1) - 2) - 5) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0095
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1cos(3π(-3x - 4) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
180
|
math
|
algebra_func_zeros_train_0096
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(3|(-2cos(1πx - 1) + 1) - 2|)^2 + 1(3|(-2cos(1πx - 1) + 1) - 2|) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0097
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1cos(2π(1|x - 3|) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0098
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(5((1x - 2)/(-2x + 1)) - 5)^2 - 3(5((1x - 2)/(-2x + 1)) - 5) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0099
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π(1(-3x)^2 - 2(-3x) - 3) - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1376
|
math
|
End of preview. Expand
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