id
stringlengths 43
43
| setting_key
stringclasses 1
value | setting_name
stringclasses 0
values | messages
listlengths 1
1
| ground_truth
stringclasses 22
values | dataset
stringclasses 1
value |
|---|---|---|---|---|---|
algebra_func_intersection_coords_train_0000
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (3(2(-1|x + 1| - 1)^2) - 2)/(2(2(-1|x + 1| - 1)^2) + 2) and g(x) = 1|(3x + 1) - 1| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0001
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (2(2|x + 1| - 2) - 2)/(-1(2|x + 1| - 2) + 3) and g(x) = 2|x - 3| + 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-3
|
math
|
algebra_func_intersection_coords_train_0002
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5((-2(3x - 5) + 2)/(1(3x - 5)))^2 + 1((-2(3x - 5) + 2)/(1(3x - 5))) and g(x) = 1sin(1π(-2|x - 2| - 1) + 1) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_intersection_coords_train_0003
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-2(-1(1x + 4)^2 + 1(1x + 4) + 1) + 1)/(1(-1(1x + 4)^2 + 1(1x + 4) + 1) + 2) and g(x) = 2((-2x + 3)/(-1x - 2))^2 + 1((-2x + 3)/(-1x - 2)) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-5
|
math
|
algebra_func_intersection_coords_train_0004
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer value closest to the x-coordinate where f(x) = -2e^(2((-2x - 3)/(3x - 2))) + 3 and g(x) = -1|x - 2| + 1 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0005
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the largest x-value where the functions f(x) = -1(1x - 4)^2 + 3(1x - 4) - 3 and g(x) = -1x - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
math
|
algebra_func_intersection_coords_train_0006
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-1(-5(-3|(-2cos(3πx - 1) - 1) - 1| + 3)^2 - 5(-3|(-2cos(3πx - 1) - 1) - 1| + 3) - 4) - 3)/(-2(-5(-3|(-2cos(3πx - 1) - 1) - 1| + 3)^2 - 5(-3|(-2cos(3πx - 1) - 1) - 1| + 3) - 4) - 1) and g(x) = 1|(-5(2x + 2)^2 - 4(2x + 2)) - 1| - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0007
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-1(2|(4x^2 - 1x - 3) - 1| + 1) - 3)/(-1(2|(4x^2 - 1x - 3) - 1| + 1) + 3) and g(x) = -1(-3|x + 3|)^2 + 1(-3|x + 3|) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0008
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "If you add up all the x-coordinates where the functions f(x) = 1|(2(-2x^2 - 4x) - 2) + 2| + 2 and g(x) = 3(-1x)^2 - 5(-1x) + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-5
|
math
|
algebra_func_intersection_coords_train_0009
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 2(-2e^(-2((3(3|x| + 3) - 1)/(3(3|x| + 3)))) - 1) - 5 and g(x) = -2|(4((-2x)/(2x + 2)) + 5) - 1| intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0010
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer value closest to the x-coordinate where f(x) = -1(-2(1sin(3πx + 1) - 1) + 3)^2 + 1(-2(1sin(3πx + 1) - 1) + 3) - 2 and g(x) = (-1(-5x + 3) - 1)/(1(-5x + 3) + 3) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0011
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 4(-1|(-1cos(2π((-2x - 1)/(2x + 1))) - 3) - 1| + 3)^2 + 1(-1|(-1cos(2π((-2x - 1)/(2x + 1))) - 3) - 1| + 3) - 1 and g(x) = (-3(5(-2|x - 3| + 3) - 5) + 3)/(3(5(-2|x - 3| + 3) - 5) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_intersection_coords_train_0012
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -4(5((1(-1|x - 2| - 1) - 2)/(2(-1|x - 2| - 1) + 1))^2 - 5((1(-1|x - 2| - 1) - 2)/(2(-1|x - 2| - 1) + 1))) + 1 and g(x) = (-2(-5(5x^2 - 4x - 3) + 2) + 1)/(3(-5(5x^2 - 4x - 3) + 2) - 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0013
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer value closest to the x-coordinate where f(x) = 1(2e^(-2((3x + 1)/(-1x - 2))) - 2)^2 + 5(2e^(-2((3x + 1)/(-1x - 2))) - 2) - 2 and g(x) = (-1(-2e^(-2x) - 3) + 2)/(1(-2e^(-2x) - 3) + 1) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0014
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = -1e^(1(-2|x - 1| - 2)) - 3 and g(x) = (-2x + 1)/(-2x) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0015
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -2((-2(2|x| + 2))/(-2(2|x| + 2) - 2)) + 2 and g(x) = 1(-2e^(-1x) + 3)^2 + 4(-2e^(-1x) + 3) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0016
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "If you add up all the x-coordinates where the functions f(x) = 2((-3(-1|(-5x + 1) - 1| + 3) + 1)/(-1(-1|(-5x + 1) - 1| + 3) - 2))^2 - 3((-3(-1|(-5x + 1) - 1| + 3) + 1)/(-1(-1|(-5x + 1) - 1| + 3) - 2)) - 3 and g(x) = (1(5(3x + 5)^2 + 2(3x + 5) + 2) - 3)/(-2(5(3x + 5)^2 + 2(3x + 5) + 2) - 3) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0017
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (3(1x^2 + 4x + 2) - 3)/(2(1x^2 + 4x + 2) + 3) and g(x) = -5x + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0018
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2(3e^(-1((3x + 2)/(-2x))) + 3) - 5 and g(x) = 1((-1x - 3)/(3x - 1)) + 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0019
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 2e^(2(-2|(-1x + 3) + 2| + 3)) - 2 and g(x) = 1cos(2π((-3x + 1)/(-3x - 1)) - 2) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_func_intersection_coords_train_0020
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (2(-5(-2x)^2 - 4) - 2)/(2(-5(-2x)^2 - 4) + 3) and g(x) = (-1(-1x + 4) + 1)/(2(-1x + 4) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_intersection_coords_train_0021
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 5((2(1x^2 - 3x - 4) - 2)/(3(1x^2 - 3x - 4) + 1)) - 4 and g(x) = 4((1x - 3)/(2x)) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0022
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 4((-3x + 1)/(-2x)) + 1 and g(x) = -4x intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0023
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-1(1(2|(-3x^2 - 2x - 3) + 3| + 3) - 2) + 2)/(2(1(2|(-3x^2 - 2x - 3) + 3| + 3) - 2) + 2) and g(x) = -2((-1(2|x - 2|) - 1)/(-1(2|x - 2|) + 2)) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
math
|
algebra_func_intersection_coords_train_0024
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 1(-3|(-3x^2 + 4x + 4) - 3| - 3) - 3 and g(x) = -4((-2x + 1)/(-3x + 1)) - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0025
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the largest x-value where the functions f(x) = (1(-3x^2 - 2) + 1)/(-1(-3x^2 - 2) - 2) and g(x) = -3|x - 1| - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0026
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (2(2(2cos(2πx + 3) + 3)^2 - 2(2cos(2πx + 3) + 3) + 4) + 1)/(-1(2(2cos(2πx + 3) + 3)^2 - 2(2cos(2πx + 3) + 3) + 4) - 2) and g(x) = 2(-2x^2 + 1x + 2) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0027
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1(2e^(1(1|(-3x^2 - 1x - 5) + 2| - 3)) - 3) + 1)/(-1(2e^(1(1|(-3x^2 - 1x - 5) + 2| - 3)) - 3) + 2) and g(x) = -3|((-1(-5x) - 3)/(1(-5x) - 3)) + 1| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0028
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2|((-1(1sin(1πx - 3) - 3) + 1)/(-2(1sin(1πx - 3) - 3) + 3)) + 2| + 1 and g(x) = -3|((-1x + 1)/(-2x - 2)) + 3| - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0029
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2(-3e^(-1(5x + 5)) + 3)^2 + 1(-3e^(-1(5x + 5)) + 3) - 5 and g(x) = -5(2|x - 1| - 2) + 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0030
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer value closest to the x-coordinate where f(x) = -1cos(2π((1x + 2)/(-1x + 3)) - 3) + 2 and g(x) = (-2x - 2)/(2x + 3) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0031
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "If you add up all the x-coordinates where the functions f(x) = 2e^(-1(3((1x + 3)/(-3x - 3))^2 + 2((1x + 3)/(-3x - 3)) + 1)) and g(x) = -2(-3x - 1)^2 + 5(-3x - 1) - 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0032
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3e^(1(-3(-3|x - 3| + 2) + 3)) - 2 and g(x) = -4((2x - 2)/(3x - 2)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6
|
math
|
algebra_func_intersection_coords_train_0033
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (2(1(-1e^(1(1|x + 1| - 2))) + 2) + 3)/(-3(1(-1e^(1(1|x + 1| - 2))) + 2) + 1) and g(x) = (2(-4(-3|x + 1| - 2)^2 - 1(-3|x + 1| - 2) - 2) + 2)/(2(-4(-3|x + 1| - 2)^2 - 1(-3|x + 1| - 2) - 2) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0034
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-3(3x^2 + 5x + 5) + 2)/(2(3x^2 + 5x + 5) + 1) and g(x) = 2x + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0035
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer value closest to the x-coordinate where f(x) = -1e^(1(5x - 5)) - 3 and g(x) = -3x^2 - 1x + 2 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0036
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = 1(-3|(-1e^(2((-1x + 3)/(1x - 2))) + 2) - 1| + 1) and g(x) = (-3(1(2|x + 1| + 2) - 5))/(1(1(2|x + 1| + 2) - 5) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_intersection_coords_train_0037
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1(1(-3|((-3x - 3)/(3x)) + 3| - 2) - 4)^2 - 5(1(-3|((-3x - 3)/(3x)) + 3| - 2) - 4) and g(x) = -2|(-1((1x - 1)/(2x + 3))) + 1| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-3
|
math
|
algebra_func_intersection_coords_train_0038
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "If you add up all the x-coordinates where the functions f(x) = 2(4x - 5)^2 + 1(4x - 5) - 4 and g(x) = -2|x - 2| - 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_intersection_coords_train_0039
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1sin(1π(-1(3|x + 1| + 3) + 5) + 2) + 3 and g(x) = (2(-1x^2 + 3x + 2) - 3)/(-2(-1x^2 + 3x + 2) - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_intersection_coords_train_0040
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -2sin(2π(4((1x)/(1x)) - 1) + 2) + 3 and g(x) = (1(5x^2 - 3x - 4) - 3)/(2(5x^2 - 3x - 4)) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0041
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -1|((-2(5(-1x^2 - 2x + 1) - 2) - 3)/(-2(5(-1x^2 - 2x + 1) - 2) - 3)) - 1| - 2 and g(x) = -4(-2|((2x - 3)/(3x + 2))| + 3) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0042
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(2e^(2x) + 2))/(2(2e^(2x) + 2) - 1) and g(x) = 1x - 3 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_intersection_coords_train_0043
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (3(1x^2 + 5x - 1) + 2)/(-3(1x^2 + 5x - 1)) and g(x) = (2x + 3)/(-3x - 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0044
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1|(-1x^2 - 3x + 4) + 2| - 1 and g(x) = 3x - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0045
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "When ordered from left to right, what is the third x-coordinate (rounded to the nearest integer) where f(x) = -1|((-1(-5x) - 1)/(-2(-5x) + 1))| - 3 and g(x) = -2|((-2x - 3)/(1x)) - 2| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0046
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2(-2e^(-2(3|x - 2| - 3)) - 1) - 4 and g(x) = 5(-2|x - 3|) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_intersection_coords_train_0047
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 2sin(1π((-2(2|(-2x^2 - 5x - 2) + 1| + 3) - 1)/(3(2|(-2x^2 - 5x - 2) + 1| + 3) - 1))) - 1 and g(x) = 1((-2(2x^2 - 2x - 4) + 3)/(3(2x^2 - 2x - 4) - 2)) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0048
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5((2(-1x^2 + 2) + 2)/(-3(-1x^2 + 2))) and g(x) = (2(-2e^(1x) + 1))/(-1(-2e^(1x) + 1) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0049
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1(-1|((-1x - 2)/(-2x - 3)) + 1| - 2) + 3 and g(x) = (3(-3x - 4) + 1)/(2(-3x - 4) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0050
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1(1|x + 2| + 2) - 4 and g(x) = 1x^2 - 4x + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_intersection_coords_train_0051
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -3(-5x - 4)^2 + 2(-5x - 4) and g(x) = 4x - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0052
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2(3x + 2)^2 + 2(3x + 2) and g(x) = (-1x - 3)/(-3x + 4) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0053
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 3(5x)^2 + 5(5x) - 2 and g(x) = -3x - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0054
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -2|((3(-2e^(-1(-4x - 5)) + 2) + 2)/(-2(-2e^(-1(-4x - 5)) + 2) + 3)) - 1| + 1 and g(x) = (-2(-2(1cos(2πx - 1) - 3) + 5) - 2)/(3(-2(1cos(2πx - 1) - 3) + 5) + 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0055
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1(1|x - 2| - 3)^2 - 4(1|x - 2| - 3) - 4 and g(x) = (3x)/(2x + 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-6
|
math
|
algebra_func_intersection_coords_train_0056
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1((-2x)/(-1x + 2))^2 - 2((-2x)/(-1x + 2)) + 2 and g(x) = -2x^2 - 5x - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-3
|
math
|
algebra_func_intersection_coords_train_0057
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = -1|(3e^(1(-4x + 5)) - 2) + 2| - 2 and g(x) = -1(2|x + 3| + 3) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0058
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the largest x-value where the functions f(x) = -2(1x^2 + 2x + 4) + 5 and g(x) = -1|x - 3| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0059
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = -2|((3x)/(-2x - 3)) - 3| + 3 and g(x) = (1x + 2)/(1x + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0060
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 4(-3|((-3(1x - 5))/(3(1x - 5))) + 2| + 3)^2 - 4(-3|((-3(1x - 5))/(3(1x - 5))) + 2| + 3) and g(x) = -5(-2e^(1((-3x + 1)/(-2x - 3))) + 3) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_intersection_coords_train_0061
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3((-3(-3(3|x - 3|) + 4) + 2)/(2(-3(3|x - 3|) + 4) - 3))^2 + 3((-3(-3(3|x - 3|) + 4) + 2)/(2(-3(3|x - 3|) + 4) - 3)) - 1 and g(x) = 1e^(-2((1(-1x^2 - 3x + 1) - 1)/(1(-1x^2 - 3x + 1) + 1))) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-3
|
math
|
algebra_func_intersection_coords_train_0062
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = 3sin(1π((-1(3|x - 3| + 1) - 2)/(-2(3|x - 3| + 1))) + 1) + 3 and g(x) = 1((1x - 2)/(-3x)) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0063
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2e^(-1(3|x + 2|)) - 3 and g(x) = 2x - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0064
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -5(2|x + 1| - 3) + 3 and g(x) = 2|x| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0065
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the largest x-value where the functions f(x) = -1((-3(-3(2|x + 1| + 1)^2 + 1(2|x + 1| + 1) + 1) - 3)/(-3(-3(2|x + 1| + 1)^2 + 1(2|x + 1| + 1) + 1))) + 5 and g(x) = (2(-2(-4x^2 + 2x + 2) - 3) + 2)/(-1(-2(-4x^2 + 2x + 2) - 3)) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0066
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 3((2(-3|x - 3| + 1) + 3)/(-2(-3|x - 3| + 1) + 1))^2 + 5((2(-3|x - 3| + 1) + 3)/(-2(-3|x - 3| + 1) + 1)) - 2 and g(x) = -3((-3x - 3)/(-2x + 3))^2 - 1((-3x - 3)/(-2x + 3)) + 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0067
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "If you add up all the x-coordinates where the functions f(x) = (2(2(-3e^(2(1|x - 1| - 1)) + 3) + 1) - 3)/(-3(2(-3e^(2(1|x - 1| - 1)) + 3) + 1) + 1) and g(x) = -3((1(-1|x + 3| - 2) + 3)/(2(-1|x + 3| - 2) + 1))^2 - 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_intersection_coords_train_0068
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the largest x-value where the functions f(x) = 5(-3e^(-1x) + 1) + 5 and g(x) = 1x + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7
|
math
|
algebra_func_intersection_coords_train_0069
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 5(3((3x - 3)/(3x)))^2 - 3(3((3x - 3)/(3x))) + 1 and g(x) = (-3(-2|x + 3| - 1) - 2)/(-1(-2|x + 3| - 1) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0070
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 4(-2|x| + 3) - 4 and g(x) = 3x + 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0071
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = 3(-1cos(2π(-1x + 3) + 1) + 1)^2 + 5(-1cos(2π(-1x + 3) + 1) + 1) + 4 and g(x) = 5((-3x - 3)/(2x)) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0072
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "If you add up all the x-coordinates where the functions f(x) = 3|((-1(-5(-3x + 4)^2 + 1(-3x + 4)) + 1)/(-1(-5(-3x + 4)^2 + 1(-3x + 4)) + 2))| + 2 and g(x) = 1e^(2(4(2x - 3)^2 - 2(2x - 3) - 2)) + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_intersection_coords_train_0073
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (1(3x^2))/(-1(3x^2) - 1) and g(x) = 5x + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0074
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "If you add up all the x-coordinates where the functions f(x) = 1|(-1((3x + 1)/(1x + 3)) + 3) + 3| - 3 and g(x) = -5((1x)/(1x - 3)) + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-11
|
math
|
algebra_func_intersection_coords_train_0075
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = 3cos(3π((-2x - 3)/(1x + 2))) + 2 and g(x) = 2x - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_intersection_coords_train_0076
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 4(1|((3x - 1)/(2x + 3)) + 1| + 3)^2 - 2 and g(x) = 3|(2x^2 - 3x - 4) - 2| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0077
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -1(1|(-4x + 2) + 2|)^2 + 5 and g(x) = -1(1e^(-1x) + 3)^2 - 2(1e^(-1x) + 3) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0078
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -4(-3|((-3x - 3)/(-1x + 2)) - 2| - 2) + 3 and g(x) = 3|(-1sin(1πx - 1)) - 2| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-7
|
math
|
algebra_func_intersection_coords_train_0079
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = 1(-1|x| + 2)^2 - 2(-1|x| + 2) + 1 and g(x) = (1x + 3)/(2x - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_intersection_coords_train_0080
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3(-1e^(1((1x + 1)/(3x + 3))) + 2) + 2 and g(x) = -5(2x^2 - 2x - 3) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0081
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the largest x-value where the functions f(x) = 1(1|(-5((-1x + 2)/(-3x + 2)) + 4) + 1| - 3)^2 + 4(1|(-5((-1x + 2)/(-3x + 2)) + 4) + 1| - 3) - 4 and g(x) = -4((-2(-3|x - 3| - 3))/(3(-3|x - 3| - 3)))^2 - 4((-2(-3|x - 3| - 3))/(3(-3|x - 3| - 3))) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_intersection_coords_train_0082
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer value closest to the x-coordinate where f(x) = -2(-3|x + 2| - 2) + 5 and g(x) = (-1x - 2)/(2x + 3) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0083
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = -1((1x - 2)/(3x)) - 5 and g(x) = 1x^2 + 3x + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_intersection_coords_train_0084
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = (-2(-2|x + 3| - 2) + 3)/(-2(-2|x + 3| - 2) - 1) and g(x) = 2x intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0085
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -2e^(2(3x^2 + 5x + 1)) + 3 and g(x) = (-3x + 1)/(3x - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0086
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = 3(1|x - 1| - 2) + 5 and g(x) = -4x + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0087
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5(-3e^(1((3(1x^2 + 4x + 4) + 3)/(1(1x^2 + 4x + 4) - 3))) - 2) - 3 and g(x) = 1((-3(-3|x + 1| + 3) + 2)/(3(-3|x + 1| + 3) + 1))^2 - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_intersection_coords_train_0088
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the third intersection point (counting from left to right) between the functions f(x) = (-1(5(1sin(1π(1x) + 1) - 2)^2 + 3(1sin(1π(1x) + 1) - 2) - 5) + 2)/(-2(5(1sin(1π(1x) + 1) - 2)^2 + 3(1sin(1π(1x) + 1) - 2) - 5) - 2) and g(x) = -5(-5((-2x + 3)/(-1x - 2)) + 1)^2 - 2(-5((-2x + 3)/(-1x - 2)) + 1) - 5 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_intersection_coords_train_0089
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = -1sin(2π(3|x + 3|)) - 3 and g(x) = (1x)/(2x + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0090
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 4(2|(-5x^2 + 4x - 4) + 1| - 1) - 5 and g(x) = -2(4x^2 - 2x - 5) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0091
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer value closest to the x-coordinate where f(x) = -3(-3e^(-1((-1x + 1)/(1x + 3))) - 3) - 1 and g(x) = (1(-1x - 4) + 1)/(-1(-1x - 4) - 3) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_intersection_coords_train_0092
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2((1(1(-2|x - 3|)^2 + 2) + 2)/(-1(1(-2|x - 3|)^2 + 2) + 2)) + 5 and g(x) = -2|((3(4x^2 + 1x) - 3)/(-1(4x^2 + 1x) + 3)) - 3| - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_intersection_coords_train_0093
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = (-2(-3sin(1π(-1x - 3) + 1) + 3) - 3)/(3(-3sin(1π(-1x - 3) + 1) + 3)) and g(x) = (-3(-5x + 4) - 2)/(-2(-5x + 4) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0094
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "If you add up all the x-coordinates where the functions f(x) = -5((1(2(1|x - 2| + 3)^2 + 2(1|x - 2| + 3) - 4))/(-1(2(1|x - 2| + 3)^2 + 2(1|x - 2| + 3) - 4))) + 2 and g(x) = 2((-3(3|x - 3| - 3) + 3)/(3(3|x - 3| - 3))) - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6
|
math
|
algebra_func_intersection_coords_train_0095
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (2(-1e^(-1x) + 1) + 3)/(3(-1e^(-1x) + 1)) and g(x) = (1x - 1)/(2x + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-9
|
math
|
algebra_func_intersection_coords_train_0096
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 2(3|x + 2| - 2)^2 + 1(3|x + 2| - 2) - 4 and g(x) = 1x^2 + 1x meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-3
|
math
|
algebra_func_intersection_coords_train_0097
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (1(-2(-4x^2 - 3x) - 3))/(2(-2(-4x^2 - 3x) - 3)) and g(x) = (-3(-1x^2 + 3x + 2) - 3)/(2(-1x^2 + 3x + 2) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_intersection_coords_train_0098
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "At what integer value (rounded) do the functions f(x) = (-1(-4(1(-1|x - 3| + 3)^2 + 2(-1|x - 3| + 3) + 3) + 2))/(1(-4(1(-1|x - 3| + 3)^2 + 2(-1|x - 3| + 3) + 3) + 2) + 3) and g(x) = -5(3e^(2((3x - 2)/(-2x - 2))) - 1) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_intersection_coords_train_0099
|
algebra_func_intersection_coords
| null |
[
{
"role": "user",
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3(2e^(2((3x - 3)/(1x + 2))) + 1)^2 - 2(2e^(2((3x - 3)/(1x + 2))) + 1) and g(x) = (2(-3x^2 - 5x) + 3)/(3(-3x^2 - 5x)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
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