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algebra_func_zeros_train_0200
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 1(2(-1e^(-1(-2|x + 2| - 1)) + 3) + 3)^2 + 5(2(-1e^(-1(-2|x + 2| - 1)) + 3) + 3) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0201
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 3|(-3sin(1π(-3((-3x + 2)/(-1x))^2 - 5((-3x + 2)/(-1x)) - 3)) - 3) + 2| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
47
math
algebra_func_zeros_train_0202
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = -4(-2sin(1π((1(-3|x| - 1) + 2)/(-1(-3|x| - 1) + 2)) + 3) + 2)^2 + 3(-2sin(1π((1(-3|x| - 1) + 2)/(-1(-3|x| - 1) + 2)) + 3) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0203
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = 2((2(2|(1x + 1) + 2| - 2) + 1)/(2(2|(1x + 1) + 2| - 2) - 1))^2 - 3((2(2|(1x + 1) + 2| - 2) + 1)/(2(2|(1x + 1) + 2| - 2) - 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0204
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = -2sin(2π((-2(5x + 1) - 1)/(1(5x + 1) + 3)) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
48
math
algebra_func_zeros_train_0205
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation -3(3x + 3)^2 + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0206
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = 1(-2sin(1πx + 1) + 2)^2 - 3(-2sin(1πx + 1) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
20
math
algebra_func_zeros_train_0207
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 1(2|((1x + 3)/(-1x)) - 2| + 3)^2 - 4(2|((1x + 3)/(-1x)) - 2| + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0208
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = -2cos(1π(3(5x + 5)^2 - 1(5x + 5) - 5) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1585
math
algebra_func_zeros_train_0209
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 2cos(1π((2x - 3)/(-3x + 4)) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
13
math
algebra_func_zeros_train_0210
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 2(-3((-2(-1|x + 2| + 3) + 3)/(-2(-1|x + 2| + 3) + 1)) - 2)^2 - 5(-3((-2(-1|x + 2| + 3) + 3)/(-2(-1|x + 2| + 3) + 1)) - 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_0211
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = (3(3e^(-2(1|(-1x - 5) - 3| + 1))) - 1)/(3(3e^(-2(1|(-1x - 5) - 3| + 1))) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0212
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 1(-1|((-1(1x^2 + 5x - 1) - 1)/(-1(1x^2 + 5x - 1) + 3)) - 2| - 2) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0213
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = -2sin(1π(2(2|((-2x + 1)/(-1x)) - 3| - 3) - 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
66
math
algebra_func_zeros_train_0214
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = 2(1sin(3π(2|(-1x^2 + 3x + 3) + 1|) - 1) - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1080
math
algebra_func_zeros_train_0215
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 4(3sin(2πx + 2) - 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_0216
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = -3sin(1π((3x + 1)/(-1x - 2)) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
77
math
algebra_func_zeros_train_0217
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = -1cos(1π(1|(5x + 2) + 3| - 3) - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
49
math
algebra_func_zeros_train_0218
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = (-3(3|(-5x - 3) + 2| - 1) - 2)/(3(3|(-5x - 3) + 2| - 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0219
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = (1(2cos(1πx - 2)) + 2)/(-1(2cos(1πx - 2)) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
10
math
algebra_func_zeros_train_0220
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = 1((2x + 3)/(-3x + 2))^2 + 4((2x + 3)/(-3x + 2)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0221
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation (3(-1(-2|(4x + 5)| + 2)^2 + 2(-2|(4x + 5)| + 2) + 1) - 3)/(1(-1(-2|(4x + 5)| + 2)^2 + 2(-2|(4x + 5)| + 2) + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
3
math
algebra_func_zeros_train_0222
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 5(-2|(-5x + 2) + 3| + 3)^2 + 4(-2|(-5x + 2) + 3| + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0223
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = -2cos(1π((-1(3(2x - 3)^2 + 2(2x - 3) - 2) - 1)/(-1(3(2x - 3)^2 + 2(2x - 3) - 2) - 2)) - 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
13
math
algebra_func_zeros_train_0224
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 4(1|((2(-4x^2 + 3x + 5) + 2)/(-1(-4x^2 + 3x + 5) + 2)) - 3| - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0225
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = 1((-3x - 1)/(-2x + 3))^2 - 5((-3x - 1)/(-2x + 3)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0226
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = -3(-1sin(3πx - 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
60
math
algebra_func_zeros_train_0227
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = (3(-2|x + 2| + 3))/(-3(-2|x + 2| + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0228
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 2cos(1π(-2(-1|(-1x + 1) + 3| + 3)^2 + 2(-1|(-1x + 1) + 3| + 3) + 5) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
316
math
algebra_func_zeros_train_0229
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = (-1(-3(3|x + 2| - 2) + 1) + 2)/(-2(-3(3|x + 2| - 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_0230
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 3cos(2π(-3x + 4) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
120
math
algebra_func_zeros_train_0231
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = -3e^(-1(-1(4(-1|x + 2| + 1)^2 - 1(-1|x + 2| + 1) - 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_0232
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = 2(4((3(-2|x + 3| + 1))/(1(-2|x + 3| + 1) + 1))^2 + 3((3(-2|x + 3| + 1))/(1(-2|x + 3| + 1) + 1)) - 4) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0233
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = -2|(5((3(-3x + 3) + 1)/(-3(-3x + 3) - 3))^2 - 1((3(-3x + 3) + 1)/(-3(-3x + 3) - 3))) - 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0234
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = (3(3(1sin(3π(5x^2 + 1x - 3) - 3) + 1) - 5) - 2)/(2(3(1sin(3π(5x^2 + 1x - 3) - 3) + 1) - 5) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
987
math
algebra_func_zeros_train_0235
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = -1(1cos(1π(3(-1|x - 1| + 3) - 4) + 3))^2 - 4(1cos(1π(3(-1|x - 1| + 3) - 4) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
60
math
algebra_func_zeros_train_0236
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1π(-2|x + 3| - 3) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
40
math
algebra_func_zeros_train_0237
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = -3((1(-2(1|x + 3| + 2)^2 + 4(1|x + 3| + 2) + 2) - 2)/(-3(-2(1|x + 3| + 2)^2 + 4(1|x + 3| + 2) + 2) - 3)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0238
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = 2((3(-1|(2x^2 - 5x) - 1| + 2))/(-2(-1|(2x^2 - 5x) - 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_0239
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 1e^(1(1|x - 1| - 2)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0240
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = (-1(1(3|(5x - 1) - 3| - 1)^2 + 3(3|(5x - 1) - 3| - 1) + 2) + 2)/(2(1(3|(5x - 1) - 3| - 1)^2 + 3(3|(5x - 1) - 3| - 1) + 2) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0241
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = 3sin(2π(3((2x + 2)/(-2x + 3))^2 + 4((2x + 2)/(-2x + 3)) + 1) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
231
math
algebra_func_zeros_train_0242
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 3cos(3π(-1((1(-2|x - 2| - 1) + 1)/(-2(-2|x - 2| - 1))) - 4) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0243
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 2cos(1π((-3(-1(-1x - 3)^2 - 4(-1x - 3) + 3) + 1)/(1(-1(-1x - 3)^2 - 4(-1x - 3) + 3) + 3)) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
85
math
algebra_func_zeros_train_0244
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = (-2(3sin(2πx - 1)) + 3)/(-1(3sin(2πx - 1)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
40
math
algebra_func_zeros_train_0245
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = -1|(2e^(-2x) - 1) - 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0246
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = (-1(1cos(1π(4x - 2) + 3)))/(3(1cos(1π(4x - 2) + 3)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
80
math
algebra_func_zeros_train_0247
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = (-1(2x^2 - 4x - 3) + 2)/(1(2x^2 - 4x - 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0248
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = 3(-1sin(1πx) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
10
math
algebra_func_zeros_train_0249
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation -4((-1(3|(4x^2 + 4x - 3) + 2| - 3) - 1)/(-1(3|(4x^2 + 4x - 3) + 2| - 3) + 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0250
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 3|((2(-2(-2x^2 + 3x - 1) - 2) - 1)/(3(-2(-2x^2 + 3x - 1) - 2) + 2)) - 1| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0251
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 3(-2|(2((-2x)/(1x + 3)) - 4) - 1| + 3)^2 + 3(-2|(2((-2x)/(1x + 3)) - 4) - 1| + 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0252
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation (-1(1|(2cos(3πx + 3))| - 1))/(1(1|(2cos(3πx + 3))| - 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
120
math
algebra_func_zeros_train_0253
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation (-3(2(-4x + 5)^2 - 4(-4x + 5) - 2))/(-2(2(-4x + 5)^2 - 4(-4x + 5) - 2) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0254
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = 1((1(-3x + 5) - 2)/(2(-3x + 5) - 3))^2 - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0255
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = 1|(1e^(-2x) - 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_0256
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 3(3|x + 2| - 2)^2 + 3(3|x + 2| - 2) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0257
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = 5(3|((1(-3x - 1) + 3)/(2(-3x - 1) + 2)) - 2| - 3)^2 - 1(3|((1(-3x - 1) + 3)/(2(-3x - 1) + 2)) - 2| - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0258
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = (2(-2|(-3x - 5) + 2| + 3))/(1(-2|(-3x - 5) + 2| + 3) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0259
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = 3cos(1π(-1|(5((-3x + 3)/(-3x)) + 3)| + 2) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
80
math
algebra_func_zeros_train_0260
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation -3((-3(-3|(1x - 3) - 1| + 3) + 2)/(-1(-3|(1x - 3) - 1| + 3) + 2))^2 + 2((-3(-3|(1x - 3) - 1| + 3) + 2)/(-1(-3|(1x - 3) - 1| + 3) + 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_0261
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 1(3cos(2π(-3x - 2) - 3) - 3)^2 - 3(3cos(2π(-3x - 2) - 3) - 3) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
120
math
algebra_func_zeros_train_0262
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 2cos(2π((3x + 3)/(1x)) + 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
53
math
algebra_func_zeros_train_0263
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = 5(3|(3cos(3π((-3x + 3)/(3x - 2)) + 1)) + 3| - 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
19
math
algebra_func_zeros_train_0264
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1|(-3cos(3πx - 3) + 2)| + 2) - 3)/(2(-1|(-3cos(3πx - 3) + 2)| + 2) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
60
math
algebra_func_zeros_train_0265
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation -3(-1(-1cos(1πx - 3) - 3)^2 + 4) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
20
math
algebra_func_zeros_train_0266
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 4(1|(-1((2x - 2)/(3x - 1)) - 5)|)^2 - 1(1|(-1((2x - 2)/(3x - 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_0267
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-5x) - 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0268
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = (3(-2(4(2|x + 3| - 3) + 2)^2 - 1(4(2|x + 3| - 3) + 2) + 5) + 3)/(-1(-2(4(2|x + 3| - 3) + 2)^2 - 1(4(2|x + 3| - 3) + 2) + 5) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0269
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 2cos(3π(2|(-4x^2 - 5x - 5) + 3| + 3) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1623
math
algebra_func_zeros_train_0270
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = -2|(4(-2sin(1πx + 2)) + 4) + 1| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
11
math
algebra_func_zeros_train_0271
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = -1|(2(-5(-3cos(3πx - 3) - 1) + 2)^2 + 5(-5(-3cos(3πx - 3) - 1) + 2) + 1) - 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
240
math
algebra_func_zeros_train_0272
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 1sin(2π(-4(-3|x - 3| - 2)^2 + 3(-3|x - 3| - 2) - 4) + 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1199
math
algebra_func_zeros_train_0273
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = 3(-5x^2 - 3x) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0274
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = -3(3x - 3)^2 - 5(3x - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0275
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 1|(1(3(-1cos(1πx + 3)) - 1)^2 + 5) - 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
40
math
algebra_func_zeros_train_0276
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 3(-2x)^2 + 4(-2x) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0277
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation -2|((3(4(-4x^2 - 2x + 4) - 4) + 1)/(-1(4(-4x^2 - 2x + 4) - 4) + 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_0278
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = 3e^(1((-3(1(-2|x + 1| + 3)^2 - 3(-2|x + 1| + 3)) + 3)/(-1(1(-2|x + 1| + 3)^2 - 3(-2|x + 1| + 3)) + 2))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
3
math
algebra_func_zeros_train_0279
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 1cos(2π(-2|(4((1x - 3)/(2x - 1))^2 - 2((1x - 3)/(2x - 1)) + 4) - 2| + 3) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
132
math
algebra_func_zeros_train_0280
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation -2|(-5((-2x - 3)/(2x))^2 - 1((-2x - 3)/(2x)) + 4) - 1| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
3
math
algebra_func_zeros_train_0281
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation 3(1((-1(3|x + 1| - 3) - 2)/(-3(3|x + 1| - 3) + 4))^2 + 5((-1(3|x + 1| - 3) - 2)/(-3(3|x + 1| - 3) + 4)) + 4) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0282
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 4(2|(4x^2 - 1) - 3| - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0283
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = 1(-3(-1cos(3πx))^2 - 1(-1cos(3πx)) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
120
math
algebra_func_zeros_train_0284
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation (1(-3|(-2(-1cos(2πx - 2) - 1)^2 + 1(-1cos(2πx - 2) - 1) + 5) + 1| + 3) + 3)/(-3(-3|(-2(-1cos(2πx - 2) - 1)^2 + 1(-1cos(2πx - 2) - 1) + 5) + 1| + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}...
80
math
algebra_func_zeros_train_0285
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = 3(2(2|((-1x + 2)/(-1x)) + 1|))^2 + 3(2(2|((-1x + 2)/(-1x)) + 1|)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0286
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 5((1(-2(-3|x - 1| + 3) - 5) - 3)/(3(-2(-3|x - 1| + 3) - 5)))^2 + 1((1(-2(-3|x - 1| + 3) - 5) - 3)/(3(-2(-3|x - 1| + 3) - 5))) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0287
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = (2(-4(2|(-1x - 1) - 1|)^2 - 4(2|(-1x - 1) - 1|) + 4))/(2(-4(2|(-1x - 1) - 1|)^2 - 4(2|(-1x - 1) - 1|) + 4) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0288
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = -4((-2(1x^2 + 4x - 2) + 2)/(-3(1x^2 + 4x - 2) - 2)) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0289
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 1(3(-1|((2x - 3)/(3x + 3)) + 1| - 2)^2 + 5(-1|((2x - 3)/(3x + 3)) + 1| - 2) - 5) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0290
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = 2(-3((3x - 2)/(-2x + 3))^2 - 2((3x - 2)/(-2x + 3)) + 5) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0291
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation -3sin(3π(-1|(2x^2 - 4x - 4) - 3|)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1120
math
algebra_func_zeros_train_0292
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = -2e^(-2(-2((-2x + 2)/(-3x))^2 + 3)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0293
algebra_func_zeros
null
[ { "role": "user", "content": "Find the number of x-intercepts of the function f(x) = -3((-3(-5x + 4) - 1)/(-1(-5x + 4) - 3))^2 + 3((-3(-5x + 4) - 1)/(-1(-5x + 4) - 3)) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0294
algebra_func_zeros
null
[ { "role": "user", "content": "How many zeros does the function f(x) = -3|((2(-5x^2 + 5x + 3) + 2)/(2(-5x^2 + 5x + 3) - 1)) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2
math
algebra_func_zeros_train_0295
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation -2(-2sin(3π(-4(3|x - 2| + 2) + 3) - 1) - 2)^2 + 3(-2sin(3π(-4(3|x - 2| + 2) + 3) - 1) - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
720
math
algebra_func_zeros_train_0296
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1cos(3π(-2|x - 2| - 3)) - 1)^2 - 2(-1cos(3π(-2|x - 2| - 3)) - 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
120
math
algebra_func_zeros_train_0297
algebra_func_zeros
null
[ { "role": "user", "content": "How many solutions does the equation (3(-2cos(3πx - 2) - 2) + 3)/(-1(-2cos(3πx - 2) - 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
60
math
algebra_func_zeros_train_0298
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = -1(2|x + 3|)^2 + 3(2|x + 3|) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math
algebra_func_zeros_train_0299
algebra_func_zeros
null
[ { "role": "user", "content": "Determine the number of values x in [-10, 10] where f(x) = (-2(3|(2(-5x + 4)^2 - 2(-5x + 4) - 3) - 3| - 2) + 3)/(2(3|(2(-5x + 4)^2 - 2(-5x + 4) - 3) - 3| - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4
math