messages listlengths 1 1 | ground_truth stringclasses 24 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (3(-5(-2|((1(-3x + 2) + 2)/(2(-3x + 2) + 1)) - 2| - 1)^2 - 2(-2|((1(-3x + 2) + 2)/(2(-3x + 2) + 1)) - 2| - 1) - 5) - 1)/(1(-5(-2|((1(-3x + 2) + 2)/(2(-3x + 2) + 1)) - 2| - 1)^2 - 2(-2|((1(-3x + 2) + 2)/(2(-3x + 2) + 1)) ... | 2 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -5((2(4(5(5x - 3) + 1)^2 - 4(5(5x - 3) + 1) + 1) + 1)/(-1(4(5(5x - 3) + 1)^2 - 4(5(5x - 3) + 1) + 1) + 2)) + 5 and g(x) = 3|(-1(2(-3e^(1x) - 2) - 5) + 3) + 2| + 1 meet in the interval [-10, 10].\n\nPresent the answer in La... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -2|(1(-5(3((-3x + 3)/(-2x + 3))^2 + 2((-3x + 3)/(-2x + 3)) + 1)^2 - 2(3((-3x + 3)/(-2x + 3))^2 + 2((-3x + 3)/(-2x + 3)) + 1) + 3) + 5) + 2| - 1 and g(x) = 3(-3(3|(-3cos(1πx + 2) + 1) + 2|... | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 1(-1|(-2((-1(1cos(3πx)) + 3)/(-2(1cos(3πx)) + 3)) + 4) - 3| + 3) - 5 and g(x) = (-3(-4((1((-1x)/(-3x - 2)) + 1)/(-1((-1x)/(-3x - 2)) + 3)) + 2) + 1)/(-2(-4((1((-1x)/(-3x - 2)) + 1)/(-1((-1x)/(-3x - 2)) + 3)) + 2) + 3) intersect in the... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3|(-1((-3(1((2x - 1)/(1x - 2)) + 2) - 2)/(1(1((2x - 1)/(1x - 2)) + 2) + 1)) - 1) - 3| + 2 and g(x) = (-2(-1((3((1x + 2)/(1x + 3)) - 2)/(1((1x + 2)/(1x + 3)) + 3)) + 5) + 1)/(-1(-1((3((1x + 2)/(1x + 3)) - 2)/(1((1x +... | -3 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2cos(1π(3(-2(-2(-5x)^2 - 3(-5x) + 4) - 4)^2 - 2(-2(-2(-5x)^2 - 3(-5x) + 4) - 4) + 4) - 1) + 3 and g(x) = -3e^(-1(-5(-3((-2x + 1)/(-1x + 3))^2 - 4((-2x + 1)/(-1x + 3)) + 5) - 3)) + 1 intersect in the interval [-10, 10]... | -13 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (2(-4((1((2(2x + 2) - 1)/(3(2x + 2) - 1)) - 3)/(-1((2(2x + 2) - 1)/(3(2x + 2) - 1)) + 2)) - 1) - 3)/(-3(-4((1((2(2x + 2) - 1)/(3(2x + 2) - 1)) - 3)/(-1((2(2x + 2) - 1)/(3(2x + 2) - 1)) + 2)) - 1) - 1) and g(x) = (3(-5((2(4x^2 + 4x + 3) + 1)/(... | -1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1(-4(-2(-4(-1|x + 2|)^2 - 1(-1|x + 2|) + 2) - 3) - 5) + 1 and g(x) = (-1(3(-3((1x + 2)/(-1x - 2)) + 2)^2 + 2(-3((1x + 2)/(-1x - 2)) + 2) + 2))/(-3(3(-3((1x + 2)/(-1x - 2)) + 2)^2 + 2(-3((1x + 2... | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(4(5(1|(2|x + 3|) + 1| + 3) - 5) + 2) + 5 and g(x) = -2e^(-2(-3(5(-3x + 3)^2 + 4(-3x + 3) + 1) + 5)) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1|((-1(-5((-2(5x - 4) - 2)/(1(5x - 4) - 2)) - 1))/(3(-5((-2(5x - 4) - 2)/(1(5x - 4) - 2)) - 1) - 1)) + 1| + 1 and g(x) = -1|((1(-3cos(2π(-5x + 5) - 1) - 2) + 2)/(-3(-3cos(2π(-5x + 5) - 1) - 2) + 2)) + 1| + 1 intersect i... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -5(3|(1e^(1(2|((3x - 3)/(-1x + 2)) - 1| - 3)) + 2) + 1| + 2)^2 + 1(3|(1e^(1(2|((3x - 3)/(-1x + 2)) - 1| - 3)) + 2) + 1| + 2) - 1 and g(x) = -3|(-3|(2e^(-2(-3|x| - 1)) + 1) + 3|) + 1| intersect in the interval [-10, 10]?\... | 2 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3((-1((-1(1(1e^(1x) - 3) + 3) + 2)/(2(1(1e^(1x) - 3) + 3) - 1)))/(-2((-1(1(1e^(1x) - 3) + 3) + 2)/(2(1(1e^(1x) - 3) + 3) - 1)) + 3))^2 + 2((-1((-1(1(1e^(1x) - 3) + 3) + 2)/(2(1(1e^(1x) - 3) + 3) - 1)))/(-2((-1(1(1e^(1x... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 4(-1(-2((-1(-1x))/(-3(-1x) + 1))^2 - 3((-1(-1x))/(-3(-1x) + 1)) - 5)^2 + 3(-2((-1(-1x))/(-3(-1x) + 1))^2 - 3((-1(-1x))/(-3(-1x) + 1)) - 5) + 4) + 1 and g(x) = -1|((1(3|(-2|x| + 1) + 2|) + 2)/(2(3|(-2|x| + 1) + 2|) - 1)) - 3| + 3 intersect in ... | 2 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -2e^(-1(-1(1((2((2x - 3)/(2x - 3)) - 2)/(-3((2x - 3)/(2x - 3)))) + 5)^2 + 3(1((2((2x - 3)/(2x - 3)) - 2)/(-3((2x - 3)/(2x - 3)))) + 5) - 5)) + 3 and g(x) = -5(-5(1|(5x - 1) - 1| + 2)^2 - 3(1|(5x - 1) - 1| + 2))^2 - 2(-5(1|(... | 3 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -1|(-4((2(5((-3x - 1)/(-2x)) - 3))/(-1(5((-3x - 1)/(-2x)) - 3) - 1))^2 - 4((2(5((-3x - 1)/(-2x)) - 3))/(-1(5((-3x - 1)/(-2x)) - 3) - 1)) - 5)| - 1 and g(x) = -5(1(1|(-2|x|) - 1| + 1) - 4)^2 - 4(1(1|(-2|x|)... | -1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-1(1((1(3(3|x + 3| + 2) - 2) + 1)/(-2(3(3|x + 3| + 2) - 2) + 3))^2 - 3((1(3(3|x + 3| + 2) - 2) + 1)/(-2(3(3|x + 3| + 2) - 2) + 3)) - 3) - 1)/(-1(1((1(3(3|x + 3| + 2) - 2) + 1)/(-2(3(3|x + 3| + 2) - 2) + 3))^2 - 3((1(3(3|x ... | -3 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 4(1sin(1π((3(1(4x + 1)^2 + 1) + 3)/(3(1(4x + 1)^2 + 1) + 2)) - 1) - 1)^2 - 2(1sin(1π((3(1(4x + 1)^2 + 1) + 3)/(3(1(4x + 1)^2 + 1) + 2)) - 1) - 1) + 2 and g(x) = (1(3|(2(-1x + 5) + 4) + 2| - 1) + 3)/(3(3|(2(-1x + 5) + 4... | 16 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 5(2|((3(3e^(-1(2x^2 - 2x + 2)) + 3) + 3)/(3(3e^(-1(2x^2 - 2x + 2)) + 3)))| - 2)^2 - 1(2|((3(3e^(-1(2x^2 - 2x + 2)) + 3) + 3)/(3(3e^(-1(2x^2 - 2x + 2)) + 3)))| - 2) - 2 and g(x) = (1(2(2(1x - 4) + 4)^2 + 4(2(1x - 4)... | 1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 2(3(2e^(-2(2(2|x|) - 4)))^2 - 1(2e^(-2(2(2|x|) - 4))))^2 + 2(3(2e^(-2(2(2|x|) - 4)))^2 - 1(2e^(-2(2(2|x|) - 4)))) and g(x) = 3e^(-1((1((-1(2|x - 2| + 2) + 3)/(-3(2|x - 2| + 2) + 4)))/(-2((-1(2|x - 2| + 2) + 3)/(-3(2|x - 2| + 2) + 4))))... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 2((1(3sin(3π((3(-2x + 5) + 1)/(-2(-2x + 5) + 3)) + 3) - 3))/(1(3sin(3π((3(-2x + 5) + 1)/(-2(-2x + 5) + 3)) + 3) - 3) + 3)) and g(x) = 3|(-5(4(-5x) - 2)^2 - 1(4(-5x) - 2) - 5)| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in ... | 0 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -5(-3(-1(3|(-2|x - 2| + 1) + 2|) - 1) - 3) + 4 and g(x) = -1(-3|(5(4x - 2) + 4)| - 2)^2 - 2(-3|(5(4x - 2) + 4)| - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 4(3(-3(-1|((-1x - 1)/(-3x - 3)) + 2|) - 4)^2 - 4(-3(-1|((-1x - 1)/(-3x - 3)) + 2|) - 4)) + 4 and g(x) = 3((-2((-3(1|x| - 2) - 3)/(-1(1|x| - 2) - 2)))/(2((-3(1|x| - 2) - 3)/(-1(1|x| - 2) - 2)) + 1)) - 1 meet in the interval [-10, 10] an... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 3(-2(-4(1(3sin(2πx - 1) + 2)^2 + 4(3sin(2πx - 1) + 2) + 5)^2 - 2(1(3sin(2πx - 1) + 2)^2 + 4(3sin(2πx - 1) + 2) + 5) + 2)^2 + 1(-4(1(3sin(2πx - 1) + 2)^2 + 4(3sin(2πx - 1) + 2) + 5)^2 - 2(1(3sin(2πx - 1) + 2)^2 + 4(3sin(2πx - 1) + 2) +... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(2|((-3(-3|((-2x + 2)/(1x - 2)) + 3| + 2) - 3)/(3(-3|((-2x + 2)/(1x - 2)) + 3| + 2) + 1))| - 2) + 3)/(1(2|((-3(-3|((-2x + 2)/(1x - 2)) + 3| + 2) - 3)/(3(-3|((-2x + 2)/(1x - 2)) + 3| + 2) + 1))| - 2) - 3) and g(x... | 4 | MATH |
[
{
"content": "When ordered from left to right, what is the third x-coordinate (rounded to the nearest integer) where f(x) = (-1((-3(-2|(-3(3|x - 2| + 3) + 2)|) - 3)/(-1(-2|(-3(3|x - 2| + 3) + 2)|) + 2)) - 3)/(2((-3(-2|(-3(3|x - 2| + 3) + 2)|) - 3)/(-1(-2|(-3(3|x - 2| + 3) + 2)|) + 2)) + 3) and g(x) = 2|(-1|(2e^... | -4 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(1|((-1(-1e^(-1(-4x + 2)) - 1) - 3)/(1(-1e^(-1(-4x + 2)) - 1) - 2)) - 2|) + 3| and g(x) = 4(-5((2((1x - 3)/(-2x - 3)) - 3)/(1((1x - 3)/(-2x - 3)) + 1))^2 - 4((2((1x - 3)/(-2x - 3)) - 3)/(1((1x - 3)/(-2x - 3)) + 1)) ... | 0 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|((-2((2(3|(-3x^2 + 3x - 4) - 1| - 2) - 3)/(-1(3|(-3x^2 + 3x - 4) - 1| - 2) - 2)) + 2)/(-1((2(3|(-3x^2 + 3x - 4) - 1| - 2) - 3)/(-1(3|(-3x^2 + 3x - 4) - 1| - 2) - 2)) - 1)) + 1| - 2 and g(x) = -1|((2(-2((-1x + 2)/(1x... | -6 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -2(-1(5((2((3x + 3)/(1x)) + 1)/(-3((3x + 3)/(1x)) - 1)) - 4) - 4) + 4 and g(x) = 1|((-3(-1((2x + 2)/(-2x - 3)) + 4) - 2)/(-1(-1((2x + 2)/(-2x - 3)) + 4))) - 1| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 4(1(-1|(-1|(-1x^2 + 3x - 1) - 1|) - 3| + 3) + 2) - 5 and g(x) = (-3(-1cos(3π((-2(1|x - 2| - 1) - 2)/(-2(1|x - 2| - 1) - 2)) + 2) + 3) + 2)/(-2(-1cos(3π((-2(1|x - 2| - 1) - 2)/(-2(1|x - 2| - 1) - 2)) + 2) + 3)) intersec... | 3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 3(2(1(-2|(-5x^2 + 3x + 1) - 1| - 1)^2 + 5(-2|(-5x^2 + 3x + 1) - 1| - 1) - 3) - 4) + 2 and g(x) = (-2(3((1(-2|x + 1| - 1) + 3)/(-1(-2|x + 1| - 1) - 2)) - 1) - 1)/(1(3((1(-2|x + 1| - 1) + 3)/(-1(-2|x + 1| - 1) - 2)) - 1)) mee... | 1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (3(5((-2(-1(-1|x - 3|) + 2) + 1)/(-2(-1(-1|x - 3|) + 2) + 1)) - 2) - 3)/(2(5((-2(-1(-1|x - 3|) + 2) + 1)/(-2(-1(-1|x - 3|) + 2) + 1)) - 2) - 1) and g(x) = (2(-5(-2e^(1(-2|x - 3| + 2)) + 3) - 3) - 2)/(3(-5... | 4 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -1|(2|((3(3|((2x - 2)/(-3x - 2)) + 1|) + 2)/(-3(3|((2x - 2)/(-3x - 2)) + 1|))) + 1| - 1) + 1| + 1 and g(x) = (-2((1(1|(-4x^2 + 5) + 2| + 1) + 2)/(2(1|(-4x^2 + 5) + 2| + 1) + 1)) + 3)/(-1((1(1|(-4x^2 + 5) + 2| + 1) + 2)/(2(1|(-4x^2 + 5)... | -11 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3((2((2(-3(2x + 5) - 3) + 3)/(-1(-3(2x + 5) - 3))) + 1)/(1((2(-3(2x + 5) - 3) + 3)/(-1(-3(2x + 5) - 3))))) - 3)/(-3((2((2(-3(2x + 5) - 3) + 3)/(-1(-3(2x + 5) - 3))) + 1)/(1((2(-3(2x + 5) - 3) + 3)/(-1(-3(2x + 5) - 3... | -3 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (1(-2|(3|((-1(2x + 2) - 3)/(3(2x + 2))) + 1| + 1) - 3| - 3) - 1)/(-2(-2|(3|((-1(2x + 2) - 3)/(3(2x + 2))) + 1| + 1) - 3| - 3)) and g(x) = -2|(-3|((3(5x + 1))/(-2(5x + 1) - 1))| + 2) - 1| + 3 in the interv... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 2(1|(2(-4(-3x - 1) + 5) + 4) - 2| + 1) - 2 and g(x) = (-3((-2(-3|(3x^2 - 5x - 3) + 1| - 1) + 2)/(-2(-3|(3x^2 - 5x - 3) + 1| - 1) - 2)) - 2)/(-3((-2(-3|(3x^2 - 5x - 3) + 1| - 1) + 2)/(-2(-3|(3x^2 - 5x - 3) + 1| - 1) - 2))) m... | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 4(1|(1(-1e^(1(3x^2 + 4x + 2)) + 3) + 5) - 1| - 2)^2 + 3(1|(1(-1e^(1(3x^2 + 4x + 2)) + 3) + 5) - 1| - 2) - 2 and g(x) = -1((1(2|(2x^2 + 1x - 5) + 3| - 1) - 3)/(1(2|(2x^2 + 1x - 5) + 3| - 1) - 2)) - 5 intersect in the interval [-10, 10]?\n\nPre... | -1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3(2|((-3(-3sin(2π(-3x) + 1) + 2) + 1)/(1(-3sin(2π(-3x) + 1) + 2) - 3)) - 3| + 2) - 3 and g(x) = -4(-2((1(5x^2 + 4x - 2) + 1)/(2(5x^2 + 4x - 2) + 1)) - 2) - 1 meet in the interval [-10, 10]?\n\n... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (2((1((-1(-3(3x^2 - 1x - 2)) - 3)/(2(-3(3x^2 - 1x - 2)))) + 2)/(1((-1(-3(3x^2 - 1x - 2)) - 3)/(2(-3(3x^2 - 1x - 2)))) + 3)) + 2)/(-2((1((-1(-3(3x^2 - 1x - 2)) - 3)/(2(-3(3x^2 - 1x - 2)))) + 2)/(1((-1(-3(3x^2 - 1x - 2)) - 3)... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -2(-2|(-3|(-1((-1x + 1)/(-2x + 3)) - 2) + 3| - 3) - 2| + 3) + 4 and g(x) = -1(-4((-2(-1x^2 - 5x + 5) + 2)/(-1(-1x^2 - 5x + 5) - 1)) - 1) + 3 intersect in the interval [-10, 10]?\n\nPresen... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1((-1(-5(3e^(1((3x - 2)/(-2x - 1))))^2 + 5(3e^(1((3x - 2)/(-2x - 1)))) - 3) + 2)/(1(-5(3e^(1((3x - 2)/(-2x - 1))))^2 + 5(3e^(1((3x - 2)/(-2x - 1)))) - 3)))^2 - 5((-1(-5(3e^(1((3x - 2)/(-2x - 1))))^2 + 5(3e^(1((3x - 2)/(-... | 3 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1(-1(1|(-2(-4x + 2)) + 2| + 1)^2 - 3(1|(-2(-4x + 2)) + 2| + 1) - 4)^2 - 2(-1(1|(-2(-4x + 2)) + 2| + 1)^2 - 3(1|(-2(-4x + 2)) + 2| + 1) - 4) - 4 and g(x) = -4(3|(3(-2x^2 + 2) - 1) + 1| - 2) + 3 intersect in the interval ... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-2(1(-3|((-1(-1sin(1πx + 2) + 3) + 1)/(-2(-1sin(1πx + 2) + 3) - 2)) + 1| + 1) - 5) - 3)/(-2(1(-3|((-1(-1sin(1πx + 2) + 3) + 1)/(-2(-1sin(1πx + 2) + 3) - 2)) + 1| + 1) - 5) - 3) and g(x) = (3((1(5((-1x + 2)/(1x + 1))... | 5 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -2e^(2((1(2((-3(-1|x - 1| + 2) + 3)/(-1(-1|x - 1| + 2) + 2)) + 1))/(-2(2((-3(-1|x - 1| + 2) + 3)/(-1(-1|x - 1| + 2) + 2)) + 1) + 1))) - 2 and g(x) = (-2(3(1(-2x^2 + 4x + 1)^2 + 4(-2x^2 + ... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(-3cos(3π((3(1(3x^2 + 2x + 4)) - 1)/(-1(1(3x^2 + 2x + 4)) - 2)) + 1) + 2) + 4 and g(x) = -1(2|((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) - 1| - 3) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in L... | -2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1(-2((-1(-3|(1x^2 + 1x) + 1| + 3) - 2)/(-2(-3|(1x^2 + 1x) + 1| + 3))) + 4) - 3 and g(x) = -4(-3|((-3(-2x^2 + 4x + 5))/(2(-2x^2 + 4x + 5) - 1)) + 3| - 3) + 4 meet in the interval [-10, 10] and round to the nearest integer, what do you g... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (3((1(-1(2|(1|x - 3| + 3) - 2|) + 5) + 1)/(-2(-1(2|(1|x - 3| + 3) - 2|) + 5) - 1)) + 3)/(-2((1(-1(2|(1|x - 3| + 3) - 2|) + 5) + 1)/(-2(-1(2|(1|x - 3| + 3) - 2|) + 5) - 1)) + 3) and g(x) =... | 5 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (2(4(5(3((3x - 1)/(2x + 1))^2 + 4((3x - 1)/(2x + 1)) - 2) - 4)) - 3)/(1(4(5(3((3x - 1)/(2x + 1))^2 + 4((3x - 1)/(2x + 1)) - 2) - 4)) + 2) and g(x) = (2((1((-1((-1x)/(1x - 3)) - 1)/(-2((-1x)/(1x - 3)) + 3)) + 2)/(-3((-1... | 3 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (3((1(1(-2((2x + 1)/(3x - 2)) - 3) - 1))/(-3(1(-2((2x + 1)/(3x - 2)) - 3) - 1) + 4)) - 1)/(3((1(1(-2((2x + 1)/(3x - 2)) - 3) - 1))/(-3(1(-2((2x + 1)/(3x - 2)) - 3) - 1) + 4)) + 1) and g(x) = (-3((2(-3((-2x - 3)/(3x... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1((3((-2(3(1|x - 2| - 3)^2 - 2(1|x - 2| - 3) + 5) + 3)/(-3(3(1|x - 2| - 3)^2 - 2(1|x - 2| - 3) + 5) + 1)) - 2)/(1((-2(3(1|x - 2| - 3)^2 - 2(1|x - 2| - 3) + 5) + 3)/(-3(3(1|x - 2| - 3)^2 - 2(1|x - 2| - 3) + 5) + 1)))) - 1... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2(3(-5(-2(1x - 5) - 4) + 5)^2 + 4(-5(-2(1x - 5) - 4) + 5) - 5) - 4 and g(x) = 5((-2(3|(5x^2 - 5x - 4) + 3| + 1) + 1)/(-2(3|(5x^2 - 5x - 4) + 3| + 1) - 2))^2 - 5 intersect in the interval [-10, 10]?\n\nPresent the answer i... | 2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -3|(-1|((1(-1sin(1π((1x - 2)/(-2x + 3))) - 3) - 2)/(1(-1sin(1π((1x - 2)/(-2x + 3))) - 3) + 2)) - 1| + 2) + 3| - 1 and g(x) = 3(2((2(2x + 4) - 1)/(2(2x + 4) + 3)) - 2) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex for... | -3 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3((-1(-4(-2|(2x^2 + 3x - 1) - 3|) - 4))/(-1(-4(-2|(2x^2 + 3x - 1) - 3|) - 4) + 2)) - 5 and g(x) = -2e^(-1(5(-2|(5x - 5)| + 1))) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (1(-4(-1(-1(2x + 3) + 3)^2 - 5(-1(2x + 3) + 3) + 1) + 1) + 3)/(2(-4(-1(-1(2x + 3) + 3)^2 - 5(-1(2x + 3) + 3) + 1) + 1)) and g(x) = (2((-2((-2(2sin(1πx)) - 1)/(2(2sin(1πx)))) + 1)/(2((-2(2sin(1πx)) - 1)/(2... | 3 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3e^(2((-2(-5(1((1x)/(1x + 2))^2 - 5)^2 + 4(1((1x)/(1x + 2))^2 - 5) - 5) + 3)/(-1(-5(1((1x)/(1x + 2))^2 - 5)^2 + 4(1((1x)/(1x + 2))^2 - 5) - 5) - 1))) - 3 and g(x) = (1(-2(2|((-1x - 1)/(1x - 3)) + 2| - 2)^2 + 5(2|((-1x ... | -10 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -3(-1(1(-3|((2x)/(3x - 2)) - 3| - 3)^2 - 4(-3|((2x)/(3x - 2)) - 3| - 3) + 1) + 1) - 2 and g(x) = 2e^(-1((2(1((-2x - 2)/(1x - 3)) + 4))/(3(1((-2x - 2)/(1x - 3)) + 4) + 2))) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in ... | 6 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 1((-1(-1|((1(1sin(3πx - 3)) - 1)/(2(1sin(3πx - 3)) - 3)) - 1|) - 1)/(3(-1|((1(1sin(3πx - 3)) - 1)/(2(1sin(3πx - 3)) - 3)) - 1|) - 2))^2 - 1 and g(x) = -3e^(2((2((-1(5x - 2) + 1)/(1(5x - 2) + 2)) - 1)/(3((-1(5x - 2) + 1)/(1(5x - 2) + 2... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-2((-1((1(-3|((3x + 1)/(-2x - 3)) - 1| + 2) + 2)/(-2(-3|((3x + 1)/(-2x - 3)) - 1| + 2) - 3)) - 1)/(2((1(-3|((3x + 1)/(-2x - 3)) - 1| + 2) + 2)/(-2(-3|((3x + 1)/(-2x - 3)) - 1| + 2) - 3)) + 3)) - 3)/(2((-1((1(-3|((3x + 1... | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1|(-3(1((-1((-1x + 1)/(-2x + 3)) + 2)/(2((-1x + 1)/(-2x + 3)) - 1))^2 - 3((-1((-1x + 1)/(-2x + 3)) + 2)/(2((-1x + 1)/(-2x + 3)) - 1)) + 1) - 5) + 1| - 2 and g(x) = -2|(1(-1|(-4x - 5) - 3| - 1) ... | 2 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 2((1(4(1(2x^2 - 1x)^2 - 1(2x^2 - 1x) - 1) - 1) - 1)/(-1(4(1(2x^2 - 1x)^2 - 1(2x^2 - 1x) - 1) - 1) - 1))^2 - 3((1(4(1(2x^2 - 1x)^2 - 1(2x^2 - 1x) - 1) - 1) - 1)/(-1(4(1(2x^2 - 1x)^2 - 1(2x^2 - 1x) - 1) - 1) - 1)) + 3 and g(... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3(3|((-2(-3|(-4x - 3) + 1| - 3) + 3)/(-1(-3|(-4x - 3) + 1| - 3) - 2)) + 2| + 2) - 1 and g(x) = 2e^(-2(-5(2|((-2x - 2)/(3x)) + 3| - 1) - 1)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 3(2|(1|(1(2x + 2)^2 - 3(2x + 2) - 3) + 2|)| - 2) + 3 and g(x) = 1((3(-1|(-3e^(-1x) + 1) + 3| + 1))/(-3(-1|(-3e^(-1x) + 1) + 3| + 1) - 3)) - 5 intersect in the interval [-10, 10]?\n\nPresen... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -4(4(3|(-2e^(-2(-4x^2 + 5x + 3)) - 1) + 2| - 2) + 2)^2 + 3(4(3|(-2e^(-2(-4x^2 + 5x + 3)) - 1) + 2| - 2) + 2) + 4 and g(x) = 1((-2(-1|(2x - 5)| - 2) + 3)/(1(-1|(2x - 5)| - 2)))^2 - 1((-2(-1|(2x - 5)| - 2) + 3)/(1(-1|(2x - ... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1e^(2(-5(-1|(1(5x^2 + 3x - 1)^2 + 2(5x^2 + 3x - 1) + 4) + 2| - 2)^2 - 5(-1|(1(5x^2 + 3x - 1)^2 + 2(5x^2 + 3x - 1) + 4) + 2| - 2) - 3)) and g(x) = 5(-5(1((-2x)/(-1x + 2)))^2 + 3(1((-2x)/(-1x + 2))) + 4) + 5 intersect in ... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1|(-3(-3|(-1(-3x - 5)^2 - 4(-3x - 5)) - 1| - 3) - 1) - 2| + 1 and g(x) = -2(-3((-2(-2x - 1) - 2)/(-1(-2x - 1) + 2))^2 + 3) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 0 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (-1((1(-1((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3))^2 + 3((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3)) + 3) + 2)/(-3(-1((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3)... | 0 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (3(-2|(-2(2(1|x - 2| + 2) - 1) - 5)| - 3))/(1(-2|(-2(2(1|x - 2| + 2) - 1) - 5)| - 3) + 3) and g(x) = 3|((1((2(2e^(2x) - 3) - 3)/(-1(2e^(2x) - 3) + 2)) + 2)/(3((2(2e^(2x) - 3) - 3)/(-1(2e^(2x) - 3) + 2)) + ... | 0 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 4(-3cos(3π((1(-5(2|x - 1| - 1)^2 - 4(2|x - 1| - 1) - 2) + 3)/(1(-5(2|x - 1| - 1)^2 - 4(2|x - 1| - 1) - 2))) + 1) + 3)^2 - 3(-3cos(3π((1(-5(2|x - 1| - 1)^2 - 4(2|x - 1| - 1) - 2) + 3)/(1(-5(2|x - 1| - 1)^2... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3(-1(1(2(5x - 2) - 1) - 5) - 2) + 2)/(3(-1(1(2(5x - 2) - 1) - 5) - 2) - 2) and g(x) = 1((-1(-3|(-1sin(3πx + 3) - 2) - 1|))/(2(-3|(-1sin(3πx + 3) - 2) - 1|)))^2 + 1((-1(-3|(-1sin(3πx + 3) - 2) - 1|))/(2(-3|(-1sin(3πx... | 1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2(-3(-1((-2((-2x + 3)/(1x + 2)) - 3)/(1((-2x + 3)/(1x + 2)))) - 5) + 4) + 5 and g(x) = -2|(-2sin(2π(-1|(-4x + 3) + 1| + 1) + 2) - 3) + 1| - 3 in the interval [-10, 10], rounded to the nearest integer.\n\... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-1(-3|(3|(-2(1e^(2x) + 1)^2 - 4(1e^(2x) + 1) + 5) + 3| - 2) + 2| - 2) + 3)/(3(-3|(3|(-2(1e^(2x) + 1)^2 - 4(1e^(2x) + 1) + 5) + 3| - 2) + 2| - 2) - 2) and g(x) = -1(3(1|(-1e^(-1x) + 2)| - 3) - 1)^2 + 1(3(1|(-1e^(-1x) + 2)| ... | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(-3(-4(1(-5x^2 + 4x + 2))^2 - 5(1(-5x^2 + 4x + 2)))^2 + 1(-4(1(-5x^2 + 4x + 2))^2 - 5(1(-5x^2 + 4x + 2)))) - 3)/(2(-3(-4(1(-5x^2 + 4x + 2))^2 - 5(1(-5x^2 + 4x + 2)))^2 + 1(-4(1(-5x^2 + 4x + 2))^2 - 5(1(-5x^2 + 4... | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3|(1|(-3|(-4(-1cos(2πx + 2) + 2) + 1)|) - 1| + 3) + 2| + 1 and g(x) = 5(1((3(4x - 5) + 2)/(-2(4x - 5) + 3)) + 2) + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 2 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-3(-3(5(-3(-2|x + 1| - 3) - 5)^2 - 5(-3(-2|x + 1| - 3) - 5) + 4)^2 + 3(5(-3(-2|x + 1| - 3) - 5)^2 - 5(-3(-2|x + 1| - 3) - 5) + 4) - 3))/(3(-3(5(-3(-2|x + 1| - 3) - 5)^2 - 5(-3(-2|x + 1| - 3) - 5) + 4)^2 + 3(5(-3(-2|x + 1| ... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3(4((-2(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 1)/(3(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 3))^2 - 1((-2(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 1)/(3(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x -... | 5 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 1|(-1e^(1(-1((-3(-4x + 2) + 3)/(3(-4x + 2))) - 1)) - 3) - 3| - 1 and g(x) = -5(-4((-3(2x^2 + 2x + 5) + 3)/(-1(2x^2 + 2x + 5) + 2))^2 - 5((-3(2x^2 + 2x + 5) + 3)/(-1(2x^2 + 2x + 5) + 2)) - 2) - 5 intersect in the range -10 ≤ x ≤ 10.\n\... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-3((-3(2cos(1π(3|((-2x + 2)/(3x - 1)) - 1| - 3) - 1) + 3) - 3)/(-3(2cos(1π(3|((-2x + 2)/(3x - 1)) - 1| - 3) - 1) + 3) - 1)) - 1)/(-1((-3(2cos(1π(3|((-2x + 2)/(3x - 1)) - 1| - 3) - 1) + 3) - 3)/(-3(2cos(1π(3|((-2x ... | 1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1(-2e^(2(-4(-2((-3x - 3)/(1x))^2 - 4((-3x - 3)/(1x)) + 3) - 1)) + 2) + 1 and g(x) = -2|((-1(1((-1x - 2)/(3x - 2)) + 4) + 2)/(-3(1((-1x - 2)/(3x - 2)) + 4) - 3)) - 1| + 2 in the interval [-10, 10], rounded... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-2(-5(1(-3|(4x^2 + 1x + 2) - 3|) + 2) - 2))/(-2(-5(1(-3|(4x^2 + 1x + 2) - 3|) + 2) - 2) + 3) and g(x) = 3|(1|(3|(-5x + 3) + 1| - 3) - 3| - 1) + 1| + 3 intersect in the interval [-10, 10]?... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1|(4((3(5(-4x^2 + 3x + 1) - 1) + 1)/(2(5(-4x^2 + 3x + 1) - 1) + 1)) + 3) + 2| and g(x) = -1|(3(-1(-1x + 5)^2 - 4(-1x + 5) - 2) - 1) - 1| meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your ... | 5 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -3(-3|(5(-2cos(1π(-2x + 5) + 3) + 1)^2 - 5(-2cos(1π(-2x + 5) + 3) + 1) - 2) - 2| - 3)^2 + 5(-3|(5(-2cos(1π(-2x + 5) + 3) + 1)^2 - 5(-2cos(1π(-2x + 5) + 3) + 1) - 2) - 2| - 3) + 3 and g(x) = (1((3(-1|(-5x - 1) + 3| + 2) + 3)/(3(-1|(-5x... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (-3((2(1((-2(-3|x - 1| - 3) - 2)/(-1(-3|x - 1| - 3) + 2)) - 4))/(-1(1((-2(-3|x - 1| - 3) - 2)/(-1(-3|x - 1| - 3) + 2)) - 4) - 2)) - 1)/(1((2(1((-2(-3|x - 1| - 3) - 2)/(-1(-3|x - 1| - 3) + 2)) - 4))/(-1(1((-2(-3|x - 1| - 3) - 2)/(-1(-3|... | -1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-2(2(2((1((-1x - 3)/(-1x + 2)) - 3)/(-1((-1x - 3)/(-1x + 2)) + 2))^2 + 4((1((-1x - 3)/(-1x + 2)) - 3)/(-1((-1x - 3)/(-1x + 2)) + 2)) - 2) + 1) + 1)/(3(2(2((1((-1x - 3)/(-1x + 2)) - 3)/(-1((-1x - 3)/(-1x + 2)) + 2))^2 + 4((1((-1x - 3)... | 5 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 3(-2|(-5(-3|(2sin(1πx - 2) + 3) - 3|)^2 - 3(-3|(2sin(1πx - 2) + 3) - 3|) - 4) - 1| + 3) + 1 and g(x) = (1((-1(2|(2|x - 1| - 2) + 1| - 3) + 3)/(-1(2|(2|x - 1| - 2) + 1| - 3) + 2)) + 1)/(-3((-1(2|(2|x - 1| - 2) + 1| - 3) + ... | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3cos(2π(-4(3(1(-1|x + 2| + 1)^2 + 2(-1|x + 2| + 1) + 5) + 5)) - 3) + 2 and g(x) = 5(1(-3((2x + 2)/(-3x - 2)) + 4) - 2)^2 - 2(1(-3((2x + 2)/(-3x - 2)) + 4) - 2) - 1 intersect in the interval [-10, 10].\n\nPresent t... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2(-4((3((2(1x + 1))/(-1(1x + 1) - 1)) + 1)/(-1((2(1x + 1))/(-1(1x + 1) - 1)) + 2)) + 4) - 3 and g(x) = 1((1(-4(2x^2 - 1x + 5) + 3) - 2)/(-3(-4(2x^2 - 1x + 5) + 3) + 4))^2 + 5((1(-4(2x^2 - 1x + 5) + 3) - 2)/(-3(-4(2x... | -1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5(1((1((1(-3x^2 - 5x - 2) + 1)/(-2(-3x^2 - 5x - 2) - 3)) - 1)/(-1((1(-3x^2 - 5x - 2) + 1)/(-2(-3x^2 - 5x - 2) - 3)) - 3)) + 3) + 4 and g(x) = 3|((-1((-2(5x + 2) + 2)/(2(5x + 2) - 1)) + 2)/(-3((... | -1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -4(-2(-2|((-2(2|x + 2| - 2) - 1)/(-1(2|x + 2| - 2) - 3)) + 2| + 3) + 1) - 2 and g(x) = (2(-1e^(1((-3(-3x))/(1(-3x) + 2))) + 2) + 2)/(-2(-1e^(1((-3(-3x))/(1(-3x) + 2))) + 2) + 3) meet in the interval [-10, 10].\n\nPresent t... | -3 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (2(3(3e^(-2(4(1x^2 - 5x - 3) + 5)))^2 - 4(3e^(-2(4(1x^2 - 5x - 3) + 5)))) + 2)/(-1(3(3e^(-2(4(1x^2 - 5x - 3) + 5)))^2 - 4(3e^(-2(4(1x^2 - 5x - 3) + 5))))) and g(x) = 3(-1((-3(5x^2 - 4x + 1) + 3)/(-2(5x^2 - 4x + 1) + 1))^2 ... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (3((2((2((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)) + 2)/(-3((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)))))/(3((2((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)) + 2)/(-3((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)))) -... | 1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2|((-1(-3(2|(2x + 2) + 1| - 2)^2 - 3(2|(2x + 2) + 1| - 2) + 4) + 3)/(1(-3(2|(2x + 2) + 1| - 2)^2 - 3(2|(2x + 2) + 1| - 2) + 4) + 2)) + 3| + 3 and g(x) = 3|(-1e^(-1(3((-1x - 1)/(2x + 1)) + 1)) + 1) - 1| -... | -2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 3((-1(3|(-1((-1x + 1)/(1x + 2)) - 1) - 1| - 2) - 1)/(2(3|(-1((-1x + 1)/(1x + 2)) - 1) - 1| - 2) + 1)) - 1 and g(x) = 1|((-2(2(-5x^2 + 3) + 2) - 2)/(-3(2(-5x^2 + 3) + 2) + 4)) + 3| + 3 meet in th... | -6 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1|(3(-1|((-1(-1|x - 3| + 2) + 3)/(-2(-1|x - 3| + 2) + 1)) - 1| - 2) - 4) + 1| + 1 and g(x) = 2((2(1((-2x + 3)/(3x - 2)) + 2) - 2)/(-2(1((-2x + 3)/(3x - 2)) + 2) - 1)) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex fo... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2|(3|((-1(-1((2x + 3)/(1x)) - 1) + 3)/(3(-1((2x + 3)/(1x)) - 1))) - 1|) + 3| + 2 and g(x) = -4((-2(-5(1x + 5) + 3) - 3)/(-2(-5(1x + 5) + 3))) - 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format:... | -4 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -4(-3e^(1(4(-2((1x)/(2x - 1)) - 2)^2 - 3(-2((1x)/(2x - 1)) - 2) - 3)) + 2) and g(x) = -1|(-3(-1|(3sin(2πx) + 2) - 3| - 1)^2 - 4(-1|(3sin(2πx) + 2) - 3| - 1) - 1) + 2| + 2 meet in the interval [-... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -5(-2|((-2(-1(5x^2 + 3x - 4)) - 2)/(3(-1(5x^2 + 3x - 4)))) - 3|) and g(x) = -1cos(1π((1((1(5x^2 + 5x) + 1)/(1(5x^2 + 5x) + 2)) + 1)/(-1((1(5x^2 + 5x) + 1)/(1(5x^2 + 5x) + 2)) - 1))) + 3 meet in the interval [-10, 10].\n\nPr... | 1 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-2(-3((1(-3cos(2π(1x^2 - 1x - 3)) + 2) + 3)/(-2(-3cos(2π(1x^2 - 1x - 3)) + 2)))^2 + 5((1(-3cos(2π(1x^2 - 1x - 3)) + 2) + 3)/(-2(-3cos(2π(1x^2 - 1x - 3)) + 2)))))/(2(-3((1(-3cos(2π(1x^2 - 1x - 3)) + 2) + 3... | -1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3|(1|(-2|(3|(-3x) - 2| + 1) - 2| + 1) + 2| + 3) + 2| and g(x) = 1|(2(-4(-1|x - 1| - 1) + 3) + 2) - 2| - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(3cos(1π((2(3(3x - 5) + 1) + 3)/(-1(3(3x - 5) + 1) + 2)) + 3) - 2) - 3)/(3(3cos(1π((2(3(3x - 5) + 1) + 3)/(-1(3(3x - 5) + 1) + 2)) + 3) - 2) + 3) and g(x) = -3|(2|(-3|((2x + 2)/(1x - 3)) - 2| + 3) + 2|) + 3| - 2 intersect in the ra... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2|(-3(-3|((-2(1|x - 3| - 1) + 1)/(-3(1|x - 3| - 1) - 1)) + 2| + 3))| + 2 and g(x) = 4(-2((1((1x + 3)/(-2x)) + 3)/(2((1x + 3)/(-2x)) + 3)) - 4) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex forma... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1(1((2(1|(1|x + 3| - 1) - 2| - 2) - 2)/(2(1|(1|x + 3| - 1) - 2| - 2) + 2)) - 4) + 3 and g(x) = (-2(5(-4((2x)/(2x + 3)) - 2)^2 + 5(-4((2x)/(2x + 3)) - 2) + 2) + 3)/(2(5(-4((2x)/(2x + 3)) - 2)^2 + 5(-4((2x)/(2x + 3)) - 2) ... | 3 | MATH |
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