messages listlengths 1 1 | ground_truth stringclasses 24 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "At what integer value (rounded) do the functions f(x) = (-3(2e^(-1(4((-3(-5((1x + 3)/(1x - 2)) + 3) + 3)/(-2(-5((1x + 3)/(1x - 2)) + 3) - 3)) - 4))) + 1)/(-2(2e^(-1(4((-3(-5((1x + 3)/(1x - 2)) + 3) + 3)/(-2(-5((1x + 3)/(1x - 2)) + 3) - 3)) - 4))) + 1) and g(x) = -1e^(-2((2(1((2(-1x^2 - 2x + 5) - 1... | 1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 5(-3(3|(-5(-3(-4x^2 + 1x - 2)^2 + 3(-4x^2 + 1x - 2) + 2)^2 + 3(-3(-4x^2 + 1x - 2)^2 + 3(-4x^2 + 1x - 2) + 2) - 2) + 3|) + 2) + 3 and g(x) = -2|(3((3(1|(-3x + 2) - 3| - 2) + 2)/(-1(1|(-3x + 2) - 3| - 2) + 3))^2 + 2((3(1|(-3... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1|(-1(3|(3e^(1((2(3x - 1) - 2)/(2(3x - 1) + 3))) - 3) + 3| + 1)^2 + 2(3|(3e^(1((2(3x - 1) - 2)/(2(3x - 1) + 3))) - 3) + 3| + 1) + 2) + 2| - 3 and g(x) = 3(-4((-2((2(2x^2 - 4x + 4) + 2)/(-3(2x^2 - 4x + 4) - 2)) + 3)/(... | -1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 2cos(2π((-2(4(-1(-3|(-1x^2 - 3x - 4) + 2| + 3) + 4) - 1))/(2(4(-1(-3|(-1x^2 - 3x - 4) + 2| + 3) + 4) - 1) - 1)) - 1) + 1 and g(x) = -1((-3(4((-3((1x + 1)/(-1x - 3)) - 2)/(2((1x + 1)/(-1x - 3)) + 3)) + 4) + 3)/(2(4((-3((1x + 1)/(-1x - ... | -2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -4((-3(-3(3|((-3((-1x)/(2x)) - 3)/(2((-1x)/(2x)) + 1)) + 2| + 2)^2 - 1(3|((-3((-1x)/(2x)) - 3)/(2((-1x)/(2x)) + 1)) + 2| + 2) + 3) + 1)/(-2(-3(3|((-3((-1x)/(2x)) - 3)/(2((-1x)/(2x)) + 1)) + 2| + 2)^2 - 1(3|((-3((-1x)/(2x)) - 3)/(2((-1x)/(2x))... | 2 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -2(4((1(-3(-3(1|x - 2| + 3) - 3) - 4) + 3)/(-1(-3(-3(1|x - 2| + 3) - 3) - 4))) - 3)^2 + 2(4((1(-3(-3(1|x - 2| + 3) - 3) - 4) + 3)/(-1(-3(-3(1|x - 2| + 3) - 3) - 4))) - 3) + 5 and g(x) = -1(-1(1((1((3x)/(-1x + 2)) -... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -3sin(2π((3(2((1(-5(-3|x + 2| - 1)^2 - 3(-3|x + 2| - 1) + 1) - 3)/(2(-5(-3|x + 2| - 1)^2 - 3(-3|x + 2| - 1) + 1) - 3)) + 2) - 1)/(1(2((1(-5(-3|x + 2| - 1)^2 - 3(-3|x + 2| - 1) + 1) - 3)/(2(-5(-3|x + 2| - 1)^2 - 3(-3|x + 2| ... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1(2((2(3(5(-4x - 4) + 5) - 2) - 2)/(1(3(5(-4x - 4) + 5) - 2) + 3)) + 1) - 4 and g(x) = (3((-3(-3|(-3|((-1x - 2)/(2x)) + 3| + 3) + 3|) + 2)/(2(-3|(-3|((-1x - 2)/(2x)) + 3| + 3) + 3|) - 1)) - 2)/(1((-3(-3|(-3|((-1x - 2... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -4(-1|(5(4(3|(-1e^(1x)) + 1| + 2) - 5) + 5) + 3| - 1)^2 + 3(-1|(5(4(3|(-1e^(1x)) + 1| + 2) - 5) + 5) + 3| - 1) + 5 and g(x) = -3(5(-1|(-3((-1x - 3)/(1x + 2))) - 2| + 2) + 1)^2 + 4(5(-1|(-3((-1x - 3)/(1x + 2))) - 2| + 2) + 1) - 4 meet i... | -4 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-1(3(1((3((-2(3|x + 3|) - 1)/(2(3|x + 3|) - 1)))/(-1((-2(3|x + 3|) - 1)/(2(3|x + 3|) - 1)) - 3))^2 - 5((3((-2(3|x + 3|) - 1)/(2(3|x + 3|) - 1)))/(-1((-2(3|x + 3|) - 1)/(2(3|x + 3|) - 1)) - 3)) + 4) - 2) + 1)/(-1(3... | -2 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -3|(-1e^(1((2(1|(3|(2x^2 - 4x + 5) + 2| - 3) + 2|))/(-1(1|(3|(2x^2 - 4x + 5) + 2| - 3) + 2|) + 3))) + 2) - 3| - 3 and g(x) = -3e^(1(-1(-1((3(-3|x - 3|))/(-2(-3|x - 3|) + 3))^2 - 5((3(-3|x... | 4 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -5(-3(1(-1((1((-3x + 2)/(2x + 3)) - 2)/(2((-3x + 2)/(2x + 3)) + 3))^2 - 3((1((-3x + 2)/(2x + 3)) - 2)/(2((-3x + 2)/(2x + 3)) + 3)) + 3) + 3) - 2) - 5 and g(x) = (-2(-5(2|(-1((3x - 2)/(-2x))^2 - 1((3x - 2)/(-2x)) - 2) - 3|... | -3 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (2(-1(2(-1((-3(2|x - 3| + 3))/(1(2|x - 3| + 3) + 2))) + 2)^2 - 4(2(-1((-3(2|x - 3| + 3))/(1(2|x - 3| + 3) + 2))) + 2) + 2) + 2)/(2(-1(2(-1((-3(2|x - 3| + 3))/(1(2|x - 3| + 3) + 2))) + 2)^2 - 4(2(-1((-3(2|x - 3| + 3))/(1(2|x - 3| + 3) ... | 2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -5(3|(-2|(5((1((3x - 2)/(-3x)))/(3((3x - 2)/(-3x)) + 1)) + 2) - 1|) + 1| + 1) + 5 and g(x) = (1(1cos(3π(-5(-1(-5x - 4)^2 + 5(-5x - 4)) + 5) + 1) + 2) - 2)/(2(1cos(3π(-5(-1(-5x - 4)^2 + 5(-5x - 4)) + 5) + 1) + 2) + 3) intersect in the interval... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1|(5(-1((1(1|(3x^2 - 2x - 3) + 3| + 3) - 2)/(2(1|(3x^2 - 2x - 3) + 3| + 3) - 3)) - 2)) + 1| - 1 and g(x) = 1(1((-2(-2e^(2((-3x + 2)/(-1x))) + 1) - 3)/(2(-2e^(2((-3x + 2)/(-1x))) + 1) - 1)) - 4) - 1 meet in the inter... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 4(5(1|(-5((3((-1x + 1)/(-2x + 3)))/(-3((-1x + 1)/(-2x + 3)) - 2))^2 - 3((3((-1x + 1)/(-2x + 3)))/(-3((-1x + 1)/(-2x + 3)) - 2)) + 4) + 2| - 2)^2 + 3(1|(-5((3((-1x + 1)/(-2x + 3)))/(-3((-1x + 1)/(-2x + 3)) - 2))^2 - 3((3(... | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -2(2|((2(-3((1(1|x + 1| + 3))/(-2(1|x + 1| + 3) + 1)) + 4) - 2)/(3(-3((1(1|x + 1| + 3))/(-2(1|x + 1| + 3) + 1)) + 4) - 2)) + 1| + 3)^2 + 3(2|((2(-3((1(1|x + 1| + 3))/(-2(1|x + 1| + 3) + 1)) + 4) - 2)/(3(-3((1(1|x + 1| + 3))/(-2(1|x + ... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (3(1|(-4(5((-2((-1x)/(2x - 1)) - 1)/(-3((-1x)/(2x - 1)) + 4)) - 2)^2 - 2(5((-2((-1x)/(2x - 1)) - 1)/(-3((-1x)/(2x - 1)) + 4)) - 2) + 5) + 3| - 2) - 1)/(1(1|(-4(5((-2((-1x)/(2x - 1)) - 1)/(-3((-1x)/(2x - 1)) + 4)) - 2)^... | -4 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (2(1sin(2π(-1(-1((1(-4x - 5) - 2)/(-2(-4x - 5) - 1)) - 2)^2 - 1(-1((1(-4x - 5) - 2)/(-2(-4x - 5) - 1)) - 2) - 4) + 1) - 2) - 3)/(2(1sin(2π(-1(-1((1(-4x - 5) - 2)/(-2(-4x - 5) - 1)) - 2)^2 - 1(-1((1(-4x - 5) - 2)/(-2(-4x -... | -3 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-1((-1(3(-2|((-3(1x^2 + 4x + 3) - 2)/(-2(1x^2 + 4x + 3) + 1)) + 3| - 2) - 1))/(-1(3(-2|((-3(1x^2 + 4x + 3) - 2)/(-2(1x^2 + 4x + 3) + 1)) + 3| - 2) - 1) - 3)) + 2)/(-1((-1(3(-2|((-3(1x^2 + 4x + 3) - 2)/(-2... | 4 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-1(-3(4(5(-1(-3x + 5) + 4) + 4) + 3)^2 + 2(4(5(-1(-3x + 5) + 4) + 4) + 3) + 4) - 3)/(-3(-3(4(5(-1(-3x + 5) + 4) + 4) + 3)^2 + 2(4(5(-1(-3x + 5) + 4) + 4) + 3) + 4) + 4) and g(x) = -2((1(-1((-3((3x)/(3x + 1)) - 1)/(-1((3x... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-1(2((-2(-4(5((-1x - 1)/(3x - 2)) + 3)^2 + 2(5((-1x - 1)/(3x - 2)) + 3) + 4) - 3)/(3(-4(5((-1x - 1)/(3x - 2)) + 3)^2 + 2(5((-1x - 1)/(3x - 2)) + 3) + 4) + 3))^2 - 4((-2(-4(5((-1x - 1)/(3x - 2)) + 3)^2 + 2(5((-1x - 1)/(3x ... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1|(3|(1(3(-5(3x + 5) - 4)^2 + 5(-5(3x + 5) - 4))^2 + 4(3(-5(3x + 5) - 4)^2 + 5(-5(3x + 5) - 4)) + 5) + 1| - 1) + 1| + 3 and g(x) = -4(-1(2|(3cos(1π(2|x - 2| + 1) + 1) - 1) - 2| - 2)^2 + 5(2|(3cos(1π(2|x - 2| + 1) + 1) - ... | -2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -2|(-2|((2(-2sin(1π(-1|(3x - 3) - 1| - 3) + 3) + 3) + 1)/(-1(-2sin(1π(-1|(3x - 3) - 1| - 3) + 3) + 3) - 3)) + 3| - 3) + 3| + 2 and g(x) = (-2(2|(-1|((2(-2x - 3) - 1)/(1(-2x - 3))) + 2| + 1) + 3| + 1) + 2)/(-2(2|(-1|((2(-2x - 3) - 1)/(1... | -3 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1(-2|(-3|(-2|(5(-3x - 3) - 3) + 2| - 3) + 1| + 1)| - 1) - 2 and g(x) = 2|(-1(3e^(-1(-5((-1x + 1)/(-1x - 3))^2 + 1((-1x + 1)/(-1x - 3)) + 2))) - 5) - 1| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Y... | -1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -1((2(-3cos(2π((2(-2|(4x - 5) + 1|) - 2)/(-1(-2|(4x - 5) + 1|) - 2)) - 1)) - 1)/(-3(-3cos(2π((2(-2|(4x - 5) + 1|) - 2)/(-1(-2|(4x - 5) + 1|) - 2)) - 1)) - 1)) + 3 and g(x) = -3(1|(2e^(-1(1(1|x + 1| + 3)^2... | 2 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1e^(1(4(-3((-3(1(4x + 5)) - 3)/(1(1(4x + 5)) - 3))^2)^2 - 5(-3((-3(1(4x + 5)) - 3)/(1(1(4x + 5)) - 3))^2) + 5)) - 3 and g(x) = -1(2|(4(-2((-3x + 2)/(-2x - 2))^2 + 5((-3x + 2)/(-2x - 2)) - 1) - 4) + 3| + 3) - 4 interse... | -3 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3(3(-4(-3(-4(1|x + 1| - 2)) + 4) - 5) + 1))/(3(3(-4(-3(-4(1|x + 1| - 2)) + 4) - 5) + 1) + 2) and g(x) = 3|((3(-3(2|(-2x^2 - 1x - 1)|) + 1) - 2)/(1(-3(2|(-2x^2 - 1x - 1)|) + 1) - 2)) + 1| + 2 meet in the interval [-1... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2e^(2((-2(-1((-1((3(5x + 3) - 1)/(2(5x + 3) + 2)) - 1)/(-3((3(5x + 3) - 1)/(2(5x + 3) + 2)) + 4))^2 + 3((-1((3(5x + 3) - 1)/(2(5x + 3) + 2)) - 1)/(-3((3(5x + 3) - 1)/(2(5x + 3) + 2)) + 4)) + 4) + 2)/(2(-1((-1((3(5x ... | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 5(1|((-3(-2|(4(-1e^(1x))^2 + 2(-1e^(1x)) - 3) + 2| + 3) - 3)/(-2(-2|(4(-1e^(1x))^2 + 2(-1e^(1x)) - 3) + 2| + 3) - 1))| + 1) and g(x) = 3((-3((1((-1(-1|x - 1| - 1) - 1)/(-3(-1|x - 1| - 1) + 1)) +... | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -3sin(1π(1((1(-5(-4(-1x^2 + 5x + 3) + 2)) - 3)/(-2(-5(-4(-1x^2 + 5x + 3) + 2)) - 1))^2 + 1((1(-5(-4(-1x^2 + 5x + 3) + 2)) - 3)/(-2(-5(-4(-1x^2 + 5x + 3) + 2)) - 1)) - 3) + 1) and g(x) = -1(5((-1((2(-2x - 1) - 2)/(1(-2x - 1) + 1)) + 1)... | -2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -5(-2(-2|((1(1(-1e^(1x) - 1) + 3))/(-3(1(-1e^(1x) - 1) + 3) - 1)) - 2|)^2 - 3(-2|((1(1(-1e^(1x) - 1) + 3))/(-3(1(-1e^(1x) - 1) + 3) - 1)) - 2|) - 2)^2 - 5(-2(-2|((1(1(-1e^(1x) - 1) + 3))/(-3(1(-1e^(1x) - 1) + 3) - 1)) - 2|)^2 - 3(-2|((... | 2 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -3|(2(-1(-2(-1((-3x + 2)/(1x + 3)) - 1) + 1)^2 - 5(-2(-1((-3x + 2)/(1x + 3)) - 1) + 1) - 3) - 5) + 3| + 3 and g(x) = (-2((1(-2(-1(1x^2 - 3x - 3) - 3)^2 + 2(-1(1x^2 - 3x - 3) - 3) - 3) - 3)/(-1(-2(-1(1x^2 - 3x - 3) - 3)^2 + ... | 9 | MATH |
[
{
"content": "Find the third intersection point (counting from left to right) between the functions f(x) = -4((1(-4(-2|(3e^(2(3x + 4)) - 3)| + 3)^2 - 1(-2|(3e^(2(3x + 4)) - 3)| + 3) + 5) + 3)/(-1(-4(-2|(3e^(2(3x + 4)) - 3)| + 3)^2 - 1(-2|(3e^(2(3x + 4)) - 3)| + 3) + 5)))^2 + 2((1(-4(-2|(3e^(2(3x + 4)) - 3)| + 3... | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (-2(-1e^(2(-3|(-2|(-1|(-4x^2 + 3x - 1) - 1| - 2) + 2| - 1) - 1| + 3))) + 1)/(1(-1e^(2(-3|(-2|(-1|(-4x^2 + 3x - 1) - 1| - 2) + 2| - 1) - 1| + 3))) + 1) and g(x) = (1(-3(-1(-5((2x + 3)/(-3x - 2))^2 - 2((2x + 3)/(-3x - 2)) - 3) - 2) + 4) - 2)/(1... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 1((-3(1(-4(-2e^(2(-2x + 1)) + 1)^2 + 2(-2e^(2(-2x + 1)) + 1) + 2)^2 + 1(-4(-2e^(2(-2x + 1)) + 1)^2 + 2(-2e^(2(-2x + 1)) + 1) + 2) - 3) + 3)/(-1(1(-4(-2e^(2(-2x + 1)) + 1)^2 + 2(-2e^(2(-2x ... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-2(-4(2(-1|((2(-2|x - 2| - 3) - 2)/(1(-2|x - 2| - 3) - 3)) + 1| + 1)^2 - 2(-1|((2(-2|x - 2| - 3) - 2)/(1(-2|x - 2| - 3) - 3)) + 1| + 1) + 2) - 1) + 1)/(-2(-4(2(-1|((2(-2|x - 2| - 3) - 2)/(1(-2|x - 2| - 3) - 3)) + 1| + 1... | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 5(-1(4(3((-2((2x + 1)/(-3x - 3)) + 2)/(-2((2x + 1)/(-3x - 3)))) - 3)^2 + 1(3((-2((2x + 1)/(-3x - 3)) + 2)/(-2((2x + 1)/(-3x - 3)))) - 3) - 2) - 2) + 4 and g(x) = -1(1cos(2π((2((2((1x + 3)/(3x - ... | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (-3(1cos(2π(-1|((-1(-4((-1x - 2)/(3x - 1)) - 5) + 2)/(-3(-4((-1x - 2)/(3x - 1)) - 5) + 2)) + 2|) - 2) + 1))/(-1(1cos(2π(-1|((-1(-4((-1x - 2)/(3x - 1)) - 5) + 2)/(-3(-4((-1x - 2)/(3x - 1)) - 5) + 2)) + 2|) - 2) + 1) + 2) and g(x) = (-3(3e^(-1(... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -2(-3(1((-3(3|(-3|x + 2| - 3) + 3| - 2) - 1)/(3(3|(-3|x + 2| - 3) + 3| - 2) + 2)) - 2) - 4) and g(x) = -2e^(-1(-3(1((-1((-3x - 1)/(-3x - 1)) + 2)/(1((-3x - 1)/(-3x - 1)) + 3))^2 - 1((-1((-3x - 1)/(-3x - 1)) + 2)/(1((-3x - 1... | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2e^(-2(1|(-1(-5(-4(2x^2 - 2x + 2) - 5)^2 + 4(-4(2x^2 - 2x + 2) - 5) + 5)^2 - 2(-5(-4(2x^2 - 2x + 2) - 5)^2 + 4(-4(2x^2 - 2x + 2) - 5) + 5) + 3) + 2| + 3)) - 3 and g(x) = (-1((3(2(-1((1x - 1)/(2x))) - 5) - 1)/(-1(2(-... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (2((-1(-1|((2(-1((-1x - 2)/(-3x)) + 5))/(2(-1((-1x - 2)/(-3x)) + 5) - 3)) + 1| + 1) - 2)/(1(-1|((2(-1((-1x - 2)/(-3x)) + 5))/(2(-1((-1x - 2)/(-3x)) + 5) - 3)) + 1| + 1))) - 1)/(3((-1(-1|((2(-1((-1x - 2)/(-3x)) + 5))/... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -5(-3(-2e^(2(-5((2(-4x^2 + 4x + 4) + 3)/(3(-4x^2 + 4x + 4) + 3))^2 - 4))) - 1)^2 - 4(-3(-2e^(2(-5((2(-4x^2 + 4x + 4) + 3)/(3(-4x^2 + 4x + 4) + 3))^2 - 4))) - 1) - 5 and g(x) = (1(-5(-5((-1(1x + 2) + 3)/(3(1x + 2) - 2... | -3 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 5((-2((1(3(1(-4x + 3)^2 + 5(-4x + 3) - 1) + 2) - 2)/(2(3(1(-4x + 3)^2 + 5(-4x + 3) - 1) + 2) + 2)) - 2)/(-3((1(3(1(-4x + 3)^2 + 5(-4x + 3) - 1) + 2) - 2)/(2(3(1(-4x + 3)^2 + 5(-4x + 3) - 1) + 2) + 2)) - 1)) - 1 and g(x... | 3 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -4(1|(1(-2|(3(2x^2 + 1x)^2 - 4(2x^2 + 1x) + 2) - 1| - 3) - 2)| + 1) + 5 and g(x) = (3(-2|(1|((-2(-4x + 3) - 2)/(3(-4x + 3))) + 2| - 3)| + 1))/(1(-2|(1|((-2(-4x + 3) - 2)/(3(-4x + 3))) + 2| - 3)| + 1) + 2) meet in the... | 2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1(3(-2(-2|(2|(3sin(1πx - 3) - 1) - 1| + 1) + 1| + 2)^2 + 3(-2|(2|(3sin(1πx - 3) - 1) - 1| + 1) + 1| + 2) + 2) + 2) and g(x) = -4(-2|(3(-3(2|x + 3|)^2 - 5(2|x + 3|) - 3)^2 - 4(-3(2|x + 3|)^2 - 5... | -3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -3cos(1π((1((-1(-4(1|(-2|x - 2| - 3)| - 1)^2 - 5(1|(-2|x - 2| - 3)| - 1) + 4) - 3)/(-1(-4(1|(-2|x - 2| - 3)| - 1)^2 - 5(1|(-2|x - 2| - 3)| - 1) + 4) + 2)) - 2)/(-1((-1(-4(1|(-2|x - 2| - 3)| - 1)^2 - 5(1|(-2|x - 2| - 3)| - 1... | 4 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -4(-4(-3((-3(-2|((1x + 2)/(2x - 1)) + 3| - 1) + 1)/(2(-2|((1x + 2)/(2x - 1)) + 3| - 1) - 1)) - 3) + 1) - 5 and g(x) = (-2((1(-1(-5(-2x^2 + 5x + 4)^2 + 5)^2 + 4(-5(-2x^2 + 5x + 4)^2 + 5)) - 3)/(2(-1(-5(-2x^... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(2(-1(-1(-2((-1x + 3)/(-2x - 1)) - 3)^2 - 1(-2((-1x + 3)/(-2x - 1)) - 3) + 2) - 4)^2 + 4) + 5 and g(x) = 1|(-2|((3((-2(-3x^2 + 3x + 4) + 2)/(1(-3x^2 + 3x + 4) + 2)) + 2)/(3((-2(-3x^2 + 3x + 4) + 2)/(1(-3x^2 + 3x + 4) ... | 3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 4(1|((-1((1((1(2x + 5) - 3)/(-2(2x + 5) + 3)) - 3)/(2((1(2x + 5) - 3)/(-2(2x + 5) + 3)) + 3)) + 1)/(-2((1((1(2x + 5) - 3)/(-2(2x + 5) + 3)) - 3)/(2((1(2x + 5) - 3)/(-2(2x + 5) + 3)) + 3)) - 2)) + 2| - 1) + 3 and g(x) = -3((... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -1|((1(1|((2(-5(1sin(2πx) + 3)^2 - 1(1sin(2πx) + 3) + 3))/(-2(-5(1sin(2πx) + 3)^2 - 1(1sin(2πx) + 3) + 3))) + 2|) + 3)/(-3(1|((2(-5(1sin(2πx) + 3)^2 - 1(1sin(2πx) + 3) + 3))/(-2(-5(1sin(2πx) + 3)^2 - 1(1sin(2πx) + 3) + 3))) + 2|) - 3))... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -1(1|(1|(-3((3(-2x^2 + 1x - 3) - 2)/(1(-2x^2 + 1x - 3) + 2)))| + 2) - 3|)^2 - 2(1|(1|(-3((3(-2x^2 + 1x - 3) - 2)/(1(-2x^2 + 1x - 3) + 2)))| + 2) - 3|) - 1 and g(x) = -3|((2(-1((3(-1|x - 2| - 1) + 2)/(-1(-1|x - 2| - 1)))^2 +... | 2 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (2(2(-1(-1|(5(-4x - 1) + 3) + 1| - 2))^2 + 3(-1(-1|(5(-4x - 1) + 3) + 1| - 2)) + 2) - 3)/(2(2(-1(-1|(5(-4x - 1) + 3) + 1| - 2))^2 + 3(-1(-1|(5(-4x - 1) + 3) + 1| - 2)) + 2) + 3) and g(x) = (-1(-3(-4((-2((-... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -2(1(2(1(-4(-5x^2 + 5x) - 1) - 5) - 1)) - 1 and g(x) = 2(3|(1(3(-3x^2 - 2x + 3)^2 + 5(-3x^2 - 2x + 3))) - 3| - 2) - 4 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex form... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2e^(-1((2(-4(4((1((1x - 3)/(-3x - 1)) - 3)/(3((1x - 3)/(-3x - 1)) + 1)))^2 - 3(4((1((1x - 3)/(-3x - 1)) - 3)/(3((1x - 3)/(-3x - 1)) + 1))) - 2) + 1)/(-1(-4(4((1((1x - 3)/(-3x - 1)) - 3)/(3((1x - 3)/(-3x - 1)) + 1)))... | 2 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -4(1|(2|(-2(-3(-2cos(2πx - 2)) - 5) + 5) + 2| + 1) - 2| - 2) - 1 and g(x) = -1(-2((-3((3(-1x^2 + 5x + 3) - 1)/(2(-1x^2 + 5x + 3))) - 3)/(1((3(-1x^2 + 5x + 3) - 1)/(2(-1x^2 + 5x + 3))) - 3)) - 1) - 2 in the... | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 3|(-2cos(2π(-5(1|(-2(-3|x - 1| - 1)^2 - 2(-3|x - 1| - 1) + 1)| - 1) + 4) - 2) - 2) - 2| - 2 and g(x) = 3(-1(-1e^(-2((-1(2x - 1) - 1)/(-2(2x - 1) - 3))) + 2) - 3) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: ... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -5((3(3|(-2e^(-1(-1|(3|x + 2| + 3)| + 1)) + 1) - 3| - 1) + 1)/(-1(3|(-2e^(-1(-1|(3|x + 2| + 3)| + 1)) + 1) - 3| - 1) + 2))^2 - 5((3(3|(-2e^(-1(-1|(3|x + 2| + 3)| + 1)) + 1) - 3| - 1) + 1)/(-1(3|(-2e^(-1(-1|(3|x + 2| + 3)|... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -5(-2|(2|(-1e^(2(-2(-5x^2 - 3x + 3) + 4)) - 2) - 3| - 2) - 2| - 2)^2 - 1(-2|(2|(-1e^(2(-2(-5x^2 - 3x + 3) + 4)) - 2) - 3| - 2) - 2| - 2) - 4 and g(x) = -5(4(-4(1|((2x - 2)/(2x + 3)) - 2| - 3)^2 + 1(1|((2x - 2)/(2x + ... | -1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -1(1(1|(-1((-2(-1cos(1πx + 3) + 2) + 2)/(2(-1cos(1πx + 3) + 2) + 1))^2 - 2((-2(-1cos(1πx + 3) + 2) + 2)/(2(-1cos(1πx + 3) + 2) + 1)) - 4) + 3| + 2)) - 2 and g(x) = 1(-1|(-1e^(-2((-2(-3|x + 2| - 3) - 3)/(1(-3|x + 2| - 3) - 3))) + 3)| + ... | -4 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -1|(1|(2|(-3|((-2(-3x^2 + 4x - 1) - 2)/(3(-3x^2 + 4x - 1) + 2)) - 2| + 2) + 1| - 3) + 2| - 3) + 2| + 3 and g(x) = -1(-1(-1(3(-3|x + 2| - 2) + 4)^2 + 1(3(-3|x + 2| - 2) + 4) + 1) + 2) - 2 intersect in the range -10 ≤ x ≤ 10.\n\nPresent... | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (3(3|(1(1((-2(2|x - 3| + 2) + 2)/(2(2|x - 3| + 2) - 1)) + 3)^2 - 3(1((-2(2|x - 3| + 2) + 2)/(2(2|x - 3| + 2) - 1)) + 3) + 4) + 1| + 1) - 3)/(-2(3|(1(1((-2(2|x - 3| + 2) + 2)/(2(2|x - 3| + 2) - 1... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-1(3(-2|(-3|((-3(3|x - 1| + 1) - 1)/(-1(3|x - 1| + 1) - 1)) - 3| + 1) - 2| + 2)^2 + 1(-2|(-3|((-3(3|x - 1| + 1) - 1)/(-1(3|x - 1| + 1) - 1)) - 3| + 1) - 2| + 2) - 5) - 2)/(-3(3(-2|(-3|((-... | -1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1|((-1(1(1((1(1x - 3) + 1)/(1(1x - 3))) + 5) - 1) - 3)/(1(1(1((1(1x - 3) + 1)/(1(1x - 3))) + 5) - 1) + 1)) - 1| + 3 and g(x) = 2e^(-2(-1(-2(1|(2x - 2) + 3| + 1) + 5) - 4)) + 1 in the interval [-10, 10], r... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2|(-3|(3|(3(1|(-2x^2 + 1x - 5) + 3| + 2)) - 1| + 3) - 3| + 1) + 3| - 3 and g(x) = 1(2(-4(-2(-2x + 2) + 1)^2 + 3)^2 - 2(-4(-2(-2x + 2) + 1)^2 + 3) + 1)^2 - 3(2(-4(-2(-2x + 2) + 1)^2 + 3)^2 - 2(-4(-2(-2x + 2) + 1)^2 + 3) + ... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3(2((3((-1((1((-1x - 2)/(-1x + 3)) - 3)/(-3((-1x - 2)/(-1x + 3)) + 4)) + 1)/(-2((1((-1x - 2)/(-1x + 3)) - 3)/(-3((-1x - 2)/(-1x + 3)) + 4)) - 2)) + 3)/(-3((-1((1((-1x - 2)/(-1x + 3)) - 3)/(-3((-1x - 2)/(-1x + 3)) + ... | 5 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2((-2(-1|(4(-3|((1x)/(-2x - 3)) + 3| + 1) + 3) - 2| - 2))/(-3(-1|(4(-3|((1x)/(-2x - 3)) + 3| + 1) + 3) - 2| - 2) - 3))^2 + 2((-2(-1|(4(-3|((1x)/(-2x - 3)) + 3| + 1) + 3) - 2| - 2))/(-3(-1|(4(-3|((1x)/(-2x - 3)) + 3| +... | 3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -5(-3|(-5(-1|(-1|(-3x + 2) - 3| + 2)| + 3)^2 - 4(-1|(-1|(-3x + 2) - 3| + 2)| + 3) + 4) + 1| - 2)^2 + 2 and g(x) = 2(-1(1e^(-1(-4((-2x - 1)/(1x))^2 + 2((-2x - 1)/(1x)) + 1)) - 2)^2 + 5(1e^(-1(-4((-2x - 1)/(1x))^2 + 2((-2x - ... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(1cos(3π((-1(-3|(-5(1x^2 - 4x + 1)^2 + 3(1x^2 - 4x + 1) + 3) - 3| + 1) - 2)/(-2(-3|(-5(1x^2 - 4x + 1)^2 + 3(1x^2 - 4x + 1) + 3) - 3| + 1) + 3)) + 2))^2 + 2(1cos(3π((-1(-3|(-5(1x^2 - 4x + 1)^2 + 3(1x^2 - 4x + 1) + 3) - 3... | 0 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3|(-3(-1(3e^(2(1((3x - 2)/(-1x + 2))^2 - 3((3x - 2)/(-1x + 2)) - 5)) - 3) - 4)^2 - 1(-1(3e^(2(1((3x - 2)/(-1x + 2))^2 - 3((3x - 2)/(-1x + 2)) - 5)) - 3) - 4) - 1) + 2| + 1 and g(x) = (-3((-1(2(2cos(1π((-3x - 3)/(-2x -... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (2((3(2|(4(3(2sin(3πx - 1) + 2) - 4) - 3) + 3| - 1) + 1)/(2(2|(4(3(2sin(3πx - 1) + 2) - 4) - 3) + 3| - 1) - 3)) + 2)/(-1((3(2|(4(3(2sin(3πx - 1) + 2) - 4) - 3) + 3| - 1) + 1)/(2(2|(4(3(2s... | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 2|(-2(-3(2cos(1π(2|(-3x - 5) - 1| - 1) + 2) + 1)^2 - 1)^2 + 5(-3(2cos(1π(2|(-3x - 5) - 1| - 1) + 2) + 1)^2 - 1)) + 1| - 3 and g(x) = (-2(3|(1(3(-1x - 4) - 3) - 3) + 1|) + 1)/(-1(3|(1(3(-1x - 4) - 3) - 3) + 1|) + 2) intersect in the interval [... | -6 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (1(3|(-2|(-3|(-1|((-1x + 3)/(-1x + 2)) + 2| + 1) - 3| - 1)| - 1) + 1| - 3) + 1)/(-2(3|(-2|(-3|(-1|((-1x + 3)/(-1x + 2)) + 2| + 1) - 3| - 1)| - 1) + 1| - 3) - 3) and g(x) = (-3((-1(-2(-3(-3x - 5)^2 - 1(-3x - 5) + 3) + 2) - 1)/(3(-2(-3(-... | -3 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-2(5((2(-3((2(-5x + 5) - 1)/(1(-5x + 5) - 2)) - 4))/(-3(-3((2(-5x + 5) - 1)/(1(-5x + 5) - 2)) - 4) - 1)) + 3) + 1)/(3(5((2(-3((2(-5x + 5) - 1)/(1(-5x + 5) - 2)) - 4))/(-3(-3((2(-5x + 5) - 1)/(1(-5x + 5) - 2)) - 4) -... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-1((2(3sin(3π(-1|((-1((2x + 3)/(3x - 2)) + 2)/(-1((2x + 3)/(3x - 2)) - 1)) + 2| - 1)) + 2) - 2)/(2(3sin(3π(-1|((-1((2x + 3)/(3x - 2)) + 2)/(-1((2x + 3)/(3x - 2)) - 1)) + 2| - 1)) + 2) - 1)) + 1)/(2((2(3sin(3π(-1|((-1((2x +... | 3 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -1((-3((1(-1(-3(3e^(1x) - 1)^2 + 5(3e^(1x) - 1) - 3)^2 - 5(-3(3e^(1x) - 1)^2 + 5(3e^(1x) - 1) - 3)) + 2)/(2(-1(-3(3e^(1x) - 1)^2 + 5(3e^(1x) - 1) - 3)^2 - 5(-3(3e^(1x) - 1)^2 + 5(3e^(1x) - 1) - 3)) - 1)) + 1)/(-2((1(-1(-3(3e^(1x) - 1)... | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (3(2(2|(2|(2(-2x + 4)^2 + 5(-2x + 4) - 5) + 1| - 1) + 1| - 1) - 5) + 1)/(2(2(2|(2|(2(-2x + 4)^2 + 5(-2x + 4) - 5) + 1| - 1) + 1| - 1) - 5) + 2) and g(x) = (2(1e^(1((1((2(-1x + 1) - 3)/(3(-1x + 1) + 1)) - 1)/(2((2(-... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2|(2((-2(-1(-4(-2|x - 3|)^2 + 1(-2|x - 3|) - 3) + 3))/(-3(-1(-4(-2|x - 3|)^2 + 1(-2|x - 3|) - 3) + 3) - 1)) + 5) - 3| and g(x) = -2|(-3|(-1((1(-4x) - 1)/(-3(-4x) - 3)) + 5) + 3|) - 2| + 2 meet in the interval [-10, ... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 2(3e^(-1((3(-2|(-2(-1x - 2) + 5) + 2| + 3))/(2(-2|(-2(-1x - 2) + 5) + 2| + 3) + 2))) - 2)^2 + 2(3e^(-1((3(-2|(-2(-1x - 2) + 5) + 2| + 3))/(2(-2|(-2(-1x - 2) + 5) + 2| + 3) + 2))) - 2) + 2 and g(x) = 1|((-3(-1(1(3x - 5) + 1)... | 3 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (-1(-2(-3((2((-1(-2x) + 2)/(-2(-2x) + 3)) - 2)/(2((-1(-2x) + 2)/(-2(-2x) + 3)) - 3)) + 5) - 4) - 1)/(-1(-2(-3((2((-1(-2x) + 2)/(-2(-2x) + 3)) - 2)/(2((-1(-2x) + 2)/(-2(-2x) + 3)) - 3)) + 5) - 4) + 2) and g(x) = (1(2|(4(-3e^(2(-1x + 5))) + 4) ... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2((-2(3(-1(5(-3x - 3) - 2)^2 + 4(5(-3x - 3) - 2) + 4)^2 - 5(-1(5(-3x - 3) - 2)^2 + 4(5(-3x - 3) - 2) + 4) - 4) + 2)/(2(3(-1(5(-3x - 3) - 2)^2 + 4(5(-3x - 3) - 2) + 4)^2 - 5(-1(5(-3x - 3) - 2)^2 + 4(5(-3x - 3) - 2) + 4) ... | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2|(3(2(3(5(-2x^2 - 1x - 1) - 1) + 1)^2 - 3(3(5(-2x^2 - 1x - 1) - 1) + 1) - 3) + 3) - 1| - 3 and g(x) = -1((1(2(-2|(-1|x + 1| - 1) + 1| + 2) - 1) + 3)/(-2(2(-2|(-1|x + 1| - 1) + 1| + 2) - 1) - 2))^2 - 4((1(2(-2|(-1|x... | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-2(2|((-1(-5(2|((-2x - 3)/(-2x + 3)) + 3| - 1)^2 + 4(2|((-2x - 3)/(-2x + 3)) + 3| - 1)) - 2)/(2(-5(2|((-2x - 3)/(-2x + 3)) + 3| - 1)^2 + 4(2|((-2x - 3)/(-2x + 3)) + 3| - 1)) + 2)) + 3| + 1) - 3... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-1(4(2((3(1(1x - 1) - 2) - 2)/(1(1(1x - 1) - 2) - 3)) - 3)^2 + 4(2((3(1(1x - 1) - 2) - 2)/(1(1(1x - 1) - 2) - 3)) - 3) + 5) - 3)/(-2(4(2((3(1(1x - 1) - 2) - 2)/(1(1(1x - 1) - 2) - 3)) - 3)^2 + 4(2((3(1(1x - 1) - 2) ... | 1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (3((2((3((2(1sin(3π(2|x + 2|) + 3) - 3) - 2)/(-3(1sin(3π(2|x + 2|) + 3) - 3) - 2)) + 2)/(1((2(1sin(3π(2|x + 2|) + 3) - 3) - 2)/(-3(1sin(3π(2|x + 2|) + 3) - 3) - 2)) + 2)))/(-1((3((2(1sin(3π(2|x + 2|) + 3) - 3) - 2)/(-3(1sin(3π(2|x + 2|... | 5 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1(-3(-4(1e^(1((1(-4x - 5))/(-1(-4x - 5) - 2))) - 3)^2 + 1(1e^(1((1(-4x - 5))/(-1(-4x - 5) - 2))) - 3)) + 2)^2 - 4(-3(-4(1e^(1((1(-4x - 5))/(-1(-4x - 5) - 2))) - 3)^2 + 1(1e^(1((1(-4x - 5))/(-1(-... | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(-1((3((-1(3(3x + 2)^2 - 1(3x + 2) + 4) - 2)/(-1(3(3x + 2)^2 - 1(3x + 2) + 4) + 3)) + 1)/(-1((-1(3(3x + 2)^2 - 1(3x + 2) + 4) - 2)/(-1(3(3x + 2)^2 - 1(3x + 2) + 4) + 3)) + 2)) - 5)| + 2 and g(x) = -1cos(2π((3((-... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4(-1((-3(2sin(3π(-2(-1|x - 3| - 2) + 2) - 2) + 2) + 1)/(2(2sin(3π(-2(-1|x - 3| - 2) + 2) - 2) + 2) + 2))) + 1 and g(x) = -4(1(-3(-2(-2|x| + 2) + 5) + 3)^2 - 2(-3(-2(-2|x| + 2) + 5) + 3) - 5) - 4 intersect in the interva... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (-2(-1|(-3cos(1π(-5((-1(1|x| - 1) + 1)/(-3(1|x| - 1) - 2))^2 + 4((-1(1|x| - 1) + 1)/(-3(1|x| - 1) - 2)) + 5)) + 1)| - 1))/(3(-1|(-3cos(1π(-5((-1(1|x| - 1) + 1)/(-3(1|x| - 1) - 2))^2 + 4((-1(1|x| - 1) + 1)/(-3(1|x| - 1) - 2)... | 2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (2(2(-4(1|((1(-3|x - 2| - 3) - 3)/(1(-3|x - 2| - 3) + 3)) - 1| - 2) + 3)^2 + 3(-4(1|((1(-3|x - 2| - 3) - 3)/(1(-3|x - 2| - 3) + 3)) - 1| - 2) + 3) - 4) - 3)/(3(2(-4(1|((1(-3|x - 2| - 3) - 3)/(1(... | 1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (2(-2(1|((2(1(-2sin(3πx - 2) - 2) + 1) + 1)/(3(1(-2sin(3πx - 2) - 2) + 1) + 2)) + 3| + 1) + 2))/(-3(-2(1|((2(1(-2sin(3πx - 2) - 2) + 1) + 1)/(3(1(-2sin(3πx - 2) - 2) + 1) + 2)) + 3| + 1) + 2)) a... | 1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-2(3e^(-1((-2(-2(-1((2x - 2)/(1x - 3))^2 - 2((2x - 2)/(1x - 3))) - 4))/(1(-2(-1((2x - 2)/(1x - 3))^2 - 2((2x - 2)/(1x - 3))) - 4)))) + 3) + 3)/(1(3e^(-1((-2(-2(-1((2x - 2)/(1x - 3))^2 - 2((2x -... | 8 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -4(4(-1(1((-2(-1x^2 - 3x - 4) - 3)/(-1(-1x^2 - 3x - 4) + 2))^2 + 1) + 3)^2 + 3(-1(1((-2(-1x^2 - 3x - 4) - 3)/(-1(-1x^2 - 3x - 4) + 2))^2 + 1) + 3) + 5) - 5 and g(x) = -3|(-3(1((-3((-1x - 3)/(-1x + 3)) - 2)/(1((-1x - 3)/(-1x + 3)))) + 2... | -12 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(1|(1|((3(2e^(-1(-4x - 3))) - 3)/(-3(2e^(-1(-4x - 3))) + 2))| - 2) - 1| - 1) - 4 and g(x) = 1|(3|(-2(-2e^(-2(-3|x + 1|)) + 1) - 5) - 3|)| + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format:... | -2 | 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(1(-3x^2 + 1x - 2)^2 + 2(-3x^2 + 1x - 2) + 3) + 3) + 1)/(1(-1(1(-3x^2 + 1x - 2)^2 + 2(-3x^2 + 1x - 2) + 3) + 3))))/(-1((1(-1(1(-3x^2 + 1x - 2)^2 + 2(-3x^2 + 1x - 2) + 3) + 3) + 1)/(1(... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3|(-4(-5(-5(3|(-3cos(3πx + 2) + 2) + 3| + 3)^2 - 1(3|(-3cos(3πx + 2) + 2) + 3| + 3) + 2) + 4) - 4) - 2| - 2 and g(x) = -4(1(1|(2|(-4x + 4) - 3| + 1) - 1| + 1)^2 - 4) + 3 meet in the interval [-10, 10].\n\nPresent the answ... | -10 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1(-2e^(1(5(5(5(-5x) + 3)^2 - 5(5(-5x) + 3) - 3) + 3)) - 3) + 3 and g(x) = (-3(2|(-1sin(2π(-1(3|x + 1| + 3) + 2) + 3)) - 1| - 1) + 2)/(1(2|(-1sin(2π(-1(3|x + 1| + 3) + 2) + 3)) - 1| - 1) - 3) intersect in the interval ... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(-1(-1(4(-3|(-1x + 5) - 3| + 1)^2 + 2(-3|(-1x + 5) - 3| + 1) + 1)^2 - 2)^2 + 4(-1(4(-3|(-1x + 5) - 3| + 1)^2 + 2(-3|(-1x + 5) - 3| + 1) + 1)^2 - 2) + 1) + 3)/(-1(-1(-1(4(-3|(-1x + 5) - 3| + 1)^2 + 2(-3|(-1x + 5) - 3| + 1) + 1)^2 - ... | -1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (2((-3(-2e^(1(1(4(1x + 4)^2 - 5(1x + 4) - 2)^2 - 4(4(1x + 4)^2 - 5(1x + 4) - 2) + 2)) + 2) - 2)/(-3(-2e^(1(1(4(1x + 4)^2 - 5(1x + 4) - 2)^2 - 4(4(1x + 4)^2 - 5(1x + 4) - 2) + 2)) + 2) - 1)) - 3)/(1((-3(-2e^(1(1(4(1x + 4)^2... | -4 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -4(5((2(2|(-1|(1|x + 2| - 1) - 2| + 3) - 1| + 3))/(2(2|(-1|(1|x + 2| - 1) - 2| + 3) - 1| + 3) + 2)) - 2) + 5 and g(x) = (-1((3(2((3(-2|x + 1| + 1))/(2(-2|x + 1| + 1) + 3))))/(-1(2((3(-2|x + 1| + 1))/(2(-2|x + 1| + 1) + 3))) + 3)) - 3)/... | -2 | MATH |
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