messages listlengths 1 1 | ground_truth stringlengths 0 159 | dataset stringclasses 1
value | constraint_type stringclasses 0
values | constraint stringclasses 0
values |
|---|---|---|---|---|
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 320 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 7 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 22 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | x^3 - 3x^2 + 3x - 3 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{\pi}{6} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 18 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 3\sqrt{5} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{2}{3} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 8 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 2400 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 153 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 6 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | [5.8,6) | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 217 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 1210 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 2019 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \left( \frac{9}{34}, \frac{15}{34} \right) | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 22 \sqrt{11} - 57 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{\sqrt{3}}{12} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 18 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 3 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 98 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 318 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 1 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 60 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | y = 2x - 13 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 8 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 2329 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 50 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 375 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | -1 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 9 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 6\sqrt{3} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 2 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 3 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 1 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 22 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 30 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 1008 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 30 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | (2,1) | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{4}{5} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 392 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \text{odd} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 100 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{25}{6} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 1 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 71 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 2 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 45 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{1}{2} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 0,-3 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 24 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 3 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 36 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | -37 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | [-6,\infty) | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 0 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 210 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{3}{10} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 15 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 0.088 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 25 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{168}{295} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 7465 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 237.5\% | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 10 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 1 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 6 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{60}{37} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 8820 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 24 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{2}{3} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 6 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 36 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 4 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 24 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 1 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{10}{3} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 75 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 81 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{9}{4} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 72 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 4\sqrt{65} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 6 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{1}{2} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 36 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | \frac{9}{2} | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 30 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 0.7 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 15 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 4\pi | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 1 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 168 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 17 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 24 \pi | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 52 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 502 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 597 | MATH | null | null |
[
{
"content": "Question: Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.}\nAnswer:The expressions inside each square root must be non-negative.\nTherefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$.\nAlso, the denominator cannot be equal to zero, so $5-x>0$, which gives $... | 4 | MATH | null | null |
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