messages listlengths 2 2 |
|---|
[
{
"role": "user",
"content": "The two lines $y = 4x - 19$ and $2x+y = X intersect. What is the value of $x$ at the point of intersection?\nIf we know the answer to the above question is 19, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackl... |
[
{
"role": "user",
"content": "If Kim's scores on her first three math exams were 87, 83, and 88, and she scores a 90 on the fourth exam, how much will her average increase?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. Kim has taken four math exams. Her first three scores were... |
[
{
"role": "user",
"content": "In an arithmetic sequence, the sixteenth term is 8 and the seventeenth term is 10. What is the value of the second term?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem again. So, we have an arithmetic sequence where the sixteenth ter... |
[
{
"role": "user",
"content": "Find the value of $a$ so that the lines described by\n\\[\\begin{pmatrix} 2 \\\\ -1 \\\\ 0 \\end{pmatrix} + t \\begin{pmatrix} a \\\\ -2 \\\\ 1 \\end{pmatrix}\\]and\n\\[\\begin{pmatrix} 1 \\\\ -3/2 \\\\ -5 \\end{pmatrix} + u \\begin{pmatrix} 1 \\\\ 3/2 \\\\ X \\end{pmatrix}\\]a... |
[
{
"role": "user",
"content": "What is the value of $\\sqrt{3! \\cdot 3!}$ expressed as a positive integer?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking for the value of the square root of (3! multiplied by 3!), expressed as a positive integer. Alright, s... |
[
{
"role": "user",
"content": "How many complex solutions are there to the equation $\\frac{z^3 - 1}{z^2 + z - 2} = 0$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking how many complex solutions there are to the equation (z³ - 1... |
[
{
"role": "user",
"content": "Let $A$ be the greatest common factor and let $B$ be the least common multiple of 8, 12 and 24. What is the value of $A + B$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. So, the question is asking for the sum of the ... |
[
{
"role": "user",
"content": "What is the value of $2 \\times 2^5 - \\frac{8^{58}}{8^{56}}$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to solve this problem again step by step. The expression given is $2 \\times 2^5 - \\frac{8^{58}}{8^{56}}$. \n\nFirst, I remember that whe... |
[
{
"role": "user",
"content": "An environmental agency needs to hire a number of new employees so that X of the new employees will be able to monitor water pollution, 73 of the new employees will be able to monitor air pollution, and exactly 27 of the new employees will be able to monitor both. (These 27 are... |
[
{
"role": "user",
"content": "If $A$ represents the greatest common factor and $B$ represents the least common multiple of 8, 12, and 24, what is the sum of $A$ and $B$?"
},
{
"role": "assistant",
"content": "<think>\n\n</think>\n\nTo find the greatest common factor (GCF) and least common multip... |
[
{
"role": "user",
"content": "If $x-y=15$ and $xy=4$, what is the value of $x^2+y^2$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that x minus y equals 15 and the product of x and y is 4. We need to find x squared plus y squared. Hmm, how do I approach this?... |
[
{
"role": "user",
"content": "If $(x + y)^2 = 25$ and $xy = 6$, what is the value of $x^2 + y^2$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that (x + y) squared equals 25 and that the product of x and y is 6. They want to find the value of x squared plus y... |
[
{
"role": "user",
"content": "The U.S. produces about 5.5 million tons of apples each year. Of the total, $20\\%$ is mixed with other products, with $50\\%$ of the remainder used for apple juice and the other $50\\%$ sold fresh. How many million tons of apples are used for apple juice? Express your answer a... |
[
{
"role": "user",
"content": "A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out the smallest abundant number. An abundant number is defined as a natur... |
[
{
"role": "user",
"content": "What is the number of distinct prime factors in the factorial of 20, denoted as 20!?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking for the number of distinct prime factors in 20 factorial, which is denoted as 20!. Hmm, so I n... |
[
{
"role": "user",
"content": "What is the value of the expression |2-4i| + |2+4i|?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem again. The question is to find the value of |2 - 4i| + |2 + 4i|. \n\nFirst, I remember that the absolute value of a complex number a ... |
[
{
"role": "user",
"content": "How many values of $k$ exist such that $12^{12}$ is the least common multiple of the positive integers $6^6$, $8^8$, and $k$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out how many values of $ k $ exist such that $ 12^{12} $ is the le... |
[
{
"role": "user",
"content": "What is the sum of the digits $a$ and $b$ in the repeating decimal representation $0.ababab\\dots$ for $\\frac{3}{11}$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the sum of the digits 'a' and 'b' in the repeating decimal representation ... |
[
{
"role": "user",
"content": "If $a$ represents the smallest positive two-digit multiple of 3 and $b$ represents the smallest positive three-digit multiple of 4, what is the value of $a+b$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question... |
[
{
"role": "user",
"content": "In the game of Mindmaster, secret codes are created by placing pegs of any of seven different colors into four slots. Colors may be repeated, and no slot may remain empty. How many secret codes are possible?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let'... |
[
{
"role": "user",
"content": "In the diagram, $AB = X \\mbox{ cm},$ $AC = 20 \\mbox{ cm},$ and $\\angle A = 90^\\circ.$ What is the area of triangle $ABC?$\n\n[asy]\ndraw((0,0)--(25,0)--(0,20)--cycle,black+linewidth(1));\ndraw((0,0)--(1,0)--(1,1)--(0,1)--cycle,black+linewidth(1));\nlabel(\"$A$\",(0,0),SW);\... |
[
{
"role": "user",
"content": "Given that $a + 4b = 33$ and $6a + 3b = 51$, what is the value of $a + b$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the value of $a + b$ given the equations $a + 4b = 33$ and $6a + 3b = 51$. Let me start by recalling how to solve syste... |
[
{
"role": "user",
"content": "A square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the square, in inches?\n\n[asy]\ndraw((0,0)--(0,5)--(5,5)--(5,0)--cycle);\ndraw((1,0)--(1,5));\ndraw((2,0)--(2,5));\ndraw((3,0)... |
[
{
"role": "user",
"content": "Find $3 \\cdot 5 \\cdot X + 15 \\div 3.$\nIf we know the answer to the above question is 110, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to solve this problem again. The equation given is 3 multiplied by... |
[
{
"role": "user",
"content": "If the graph of $y = 2x^2 - x + 7$ is shifted four units to the right, it becomes the graph of $y = ax^2 + bx + c$. Find the value of $a + b + c$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out this problem again. The original equation... |
[
{
"role": "user",
"content": "Let $f(x)=2x^4+x^3+x^2-3x+r$. For what value of $r$ is $f(2)=0$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the value of $ r $ such that $ f(2) = 0 $ for the function $ f(x) = 2x^4 + x^3 + x^2 - 3x + r $. Let me start by recalling that w... |
[
{
"role": "user",
"content": "When the value of $y$ is doubled and then this increased value is divided by 5, the result is 10. What is the value of $y$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem again. So the problem says: When the value of y is doubl... |
[
{
"role": "user",
"content": "If $x - 2x + 3x = 100$, what is the value of $x$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem again step by step. The equation given is $ x - 2x + 3x = 100 $. Hmm, combining like terms. Let me recall that when you have multi... |
[
{
"role": "user",
"content": "Find the minimum value of\n\\[2 \\sqrt{x} + \\frac{1}{x}\\]for $x > 0.$"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to find the minimum value of the function $2\\sqrt{x} + \\frac{1}{x}$ for $x > 0$. Alright, so I need to figure ou... |
[
{
"role": "user",
"content": "Given that $\\frac 1n - \\frac{1}{n+1} < \\frac{1}{10}$, what is the least possible positive integer value of $n$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking for the smallest positive integer ... |
[
{
"role": "user",
"content": "When simplified, what is the value of $\\sqrt{3} \\times 3^{\\frac{1}{2}} + X \\div 3 \\times 2 - 4^{\\frac{3}{2}}$?\nIf we know the answer to the above question is 3, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let... |
[
{
"role": "user",
"content": "The shaded region is bounded by two concentric circles with radii of 19 and 29 units. A third circle will be drawn to have the same area as the shaded region. What is the radius of the third circle, expressed in simplest radical form?"
},
{
"role": "assistant",
"con... |
[
{
"role": "user",
"content": "How many numbers are in the list $ 4, 6, 8, \\ldots, 128, 130 ?$"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking how many numbers are in the list 4, 6, 8, ..., 128, 130. Hmm, so first, I need to figure out the pattern here. The... |
[
{
"role": "user",
"content": "A circle with a radius of 2 units is circumscribed around a regular hexagon. What is the area of the hexagon, in square units, expressed in simplest radical form?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. So the problem says a circle with radi... |
[
{
"role": "user",
"content": "What is the measure, in degrees, of the acute angle formed by the hour hand and the minute hand of a 12-hour clock at 6:48?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the acute angle between the hour and minute hands at 6:48 on a 12-hour... |
[
{
"role": "user",
"content": "What is the solution for $x$ in the equation $5 - x = 8$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem again. The equation given is $5 - x = 8$. I need to solve for $x$. \n\nFirst, I remember that to isolate the variable, I need to... |
[
{
"role": "user",
"content": "Every bag of Dummies (a chocolate candy) contains the same number of pieces.\n\nThe Dummies in one bag can't be divided equally among $9$ kids, because after each kid gets the same (whole) number of pieces, $7$ pieces are left over.\n\nIf the Dummies in three bags are divided e... |
[
{
"role": "user",
"content": "When the value of $y$ is doubled and then this increased value is divided by 5, the result is 10. What is the value of $y$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem again. So, the problem says that when the value of $ y $... |
[
{
"role": "user",
"content": "What is the distance, in units, from the origin to the point $(-15, 8)$ in a rectangular coordinate system?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the distance from the origin to the point (-15, 8) in a rectangular coordinate system.... |
[
{
"role": "user",
"content": "Let $f(x) = 3x^2 - 7$ and $g(f(4)) = 9$. What is $g(f(-4))$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem gives me two functions: f(x) = 3x² - 7 and g(f(4)) = 9. I need to find g(f(-4)). \n\nFirst, I remember that when dealing with f... |
[
{
"role": "user",
"content": "Determine the largest prime factor of $15^4+2\\times15^2+1-14^4$ without using a calculator."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The original expression is $15^4 + 2 \\times 15^2 + 1 - 14^4$. The goal is to f... |
[
{
"role": "user",
"content": "How many different ways can Michael select 3 math classes out of a total of 8 options?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so Michael wants to pick 3 math classes out of 8 total options. Let me think about how to approach this. \n\nFirst, combinati... |
[
{
"role": "user",
"content": "Express $\\sqrt[4]{81} \\cdot \\sqrt[3]{27} \\cdot \\sqrt{9}$ as a positive integer."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to express the product of the fourth root of 81, the cube root of 27, and the square root of 9 as a p... |
[
{
"role": "user",
"content": "Out of the 100 students in the science club, 65 students take mathematics, 43 students take physics, and 10 students take both mathematics and physics. How many students in the science club do not take either mathematics or physics?"
},
{
"role": "assistant",
"conte... |
[
{
"role": "user",
"content": "What is the value of t that satisfies the equation $3 \\cdot 3^t + \\sqrt{9 \\cdot 9^t} = 18$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this equation step by step. The equation given is $3 \\cdot 3^t + \\sqrt{9 \\cdot 9^t} = 18$. \n\n... |
[
{
"role": "user",
"content": "What is the sum of the reciprocals of the natural-number factors of 6?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem again. The question is asking for the sum of the reciprocals of the natural-number factors of 6. \n\nFirst, I... |
[
{
"role": "user",
"content": "Let\n\\[z = \\frac{-\\sqrt{3} + i}{2}.\\]Compute $z^6.$"
},
{
"role": "assistant",
"content": "<think>\n\n</think>\n\nTo compute \\( z^6 \\) where \\( z = \\frac{-\\sqrt{3} + i}{2} \\), we convert \\( z \\) to polar form. The modulus \\( r \\) of \\( z \\) is calcul... |
[
{
"role": "user",
"content": "Brent rolls a fair dodecahedral die with numbers $1,2,3,...,12$ on its faces. What is the expected number of digits in the number he obtains? Express your answer in a decimal."
},
{
"role": "assistant",
"content": "<think>\nOkay, so Brent is rolling a fair dodecahed... |
[
{
"role": "user",
"content": "The sum of two numbers is $12$ and their difference is X$. What is the smaller number?\nIf we know the answer to the above question is -4, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem ... |
[
{
"role": "user",
"content": "What is the value of the product of the roots in the equation $x^3 - 12x^2 + 48x + 28 = 0$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the value of the product of the roots in the equation $x^3 - 12x^2 + 48x + 28 = 0$. Let me start by re... |
[
{
"role": "user",
"content": "What is the value of $\\log_2\\frac{1}{16}$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the value of the logarithm log base 2 of 1/16. Let me think about how to approach this.\n\nFirst, I remember that a logarithm answers the question: \... |
[
{
"role": "user",
"content": "We are given that $$54+(98\\div14)+(23\\cdot 17)-200-(312\\div 6)=200.$$Now, let's remove the parentheses: $$54+98\\div14+23\\cdot 17-200-312\\div 6.$$What does this expression equal?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is t... |
[
{
"role": "user",
"content": "Let $z$ be a complex number such that $|z| = 13.$ Find $z \\times \\overline{z}.$"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that z is a complex number with |z| = 13. We need to find z multiplied by its conjugate, which is z *... |
[
{
"role": "user",
"content": "The sum of the squares of two positive integers is 90. The product of the two integers is 27. What is the sum of the two integers?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that the sum of the squares of two positive integers ... |
[
{
"role": "user",
"content": "The sum of two consecutive negative integers is asked for when their product is 2550."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by step. The problem is asking for two consecutive negative integers whose product is 255... |
[
{
"role": "user",
"content": "Solve the equation $|y-6| + 2y = 9$ for $y$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve the equation |y - 6| + 2y = 9. Hmm, okay, so I remember that absolute value equations can sometimes be tricky because of the absolute value itself. ... |
[
{
"role": "user",
"content": "Find the cross product of $\\begin{pmatrix} 5 \\\\ X \\\\ -6 \\end{pmatrix}$ and $\\begin{pmatrix} 1 \\\\ 1 \\\\ 3 \\end{pmatrix}.$\nIf we know the answer to the above question is \\begin{pmatrix}12\\-21\\3\\end{pmatrix}, what is the value of unknown variable X?"
},
{
"... |
[
{
"role": "user",
"content": "Find $1273 + 120 \\div 60 - 173$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to calculate 1273 + 120 ÷ 60 - 173. Hmm, so first, I remember the order of operations here. Since there's division, I should do that first. So 120 divid... |
[
{
"role": "user",
"content": "Let $O$ and $H$ be the circumcenter and orthocenter of triangle $ABC$, respectively. Let $a$, $b$, and $c$ denote the side lengths, and let $R$ denote the circumradius. Find $OH^2$ if $R = 7$ and $a^2 + b^2 + c^2 = 29$."
},
{
"role": "assistant",
"content": "<thin... |
[
{
"role": "user",
"content": "What is the second number in the row of Pascal's triangle that has 43 numbers?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out the answer step by step. The problem is asking for the second number in the row of Pascal's triangle that has... |
[
{
"role": "user",
"content": "What is the value of $x$ in the equation $9^4 + 9^4 + 9^4 = 3^x$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to find the value of $ x $ in the equation $ 9^4 + 9^4 + 9^4 = 3^x $. Alright, first, I need to figure out how to simpli... |
[
{
"role": "user",
"content": "After a 30% discount, a store owner further reduces the price of a $10 dollar scarf by 50% of the reduced price. What is the current price of the scarf, in dollars?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure out this problem again. Th... |
[
{
"role": "user",
"content": "What is the value of $n$ in the equation $8^n \\cdot 8^n \\cdot 8^n = 64^3$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to find the value of $ n $ in the equation $ 8^n \\cdot 8^n \\cdot 8^n = 64^3 $. \n\nFirst, I need to simplif... |
[
{
"role": "user",
"content": "If the price of a stamp is 33 cents, what is the maximum number of stamps that could be purchased with $\\$32$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking for the maximum number of stamps that can be bought with $32, wher... |
[
{
"role": "user",
"content": "What percent of the positive integers less than or equal to $100$ have no remainders when divided by X The answer is 20. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem again. The questio... |
[
{
"role": "user",
"content": "What is the smallest possible value of $2 \\sqrt{x} + \\frac{1}{x}$ for $x > 0$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by step. The question is asking for the smallest possible value of the function $2\\sqrt{x} + ... |
[
{
"role": "user",
"content": "In order to fill a cylindrical barrel with a radius of 10 inches and height of 15 inches using a hemisphere-shaped bucket with a radius of 10 inches, Brad needs to make several trips to the well. How many trips does Brad need to make to fill the barrel?"
},
{
"role": "a... |
[
{
"role": "user",
"content": "If $x$ is a positive multiple of 8 and $x^2>100$, but $x<20$, what is $x$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find a number x that satisfies three conditions: it's a positive multiple of 8, its square is greater than 100, and it's les... |
[
{
"role": "user",
"content": "Add $1_3 + 12_3 + 212_3 + 2121_3.$ Express your answer in base X.\nIf we know the answer to the above question is 10200_3, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to figure out the value of X when the ... |
[
{
"role": "user",
"content": "The sum of three numbers $a, b$ and $c$ is 60. If we decrease $a$ by 7, we get the value $N$. If we increase $b$ by X, we get the value $N$. If we multiply $c$ by 7, we also get the value $N$. The value of $N$ is 28. What is the value of unknown variable X?"
},
{
"role"... |
[
{
"role": "user",
"content": "How many miles can a car travel in 20 minutes if it travels $ \\, \\frac{3}{4} \\, $ as fast as a train going 80 miles per hour?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says a car can travel 3/4 as fast as a train that goes 80 mi... |
[
{
"role": "user",
"content": "The volume of a rectangular box is 108 cubic feet. How many cubic yards are in the volume of this box?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking how many cubic yards are in a rectangular box that has a volume of 108 cubic... |
[
{
"role": "user",
"content": "Evaluate $\\left\\lfloor \\left\\lceil \\left(\\frac{13}{7}\\right)^2\\right\\rceil+\\frac{17}{4}\\right\\rfloor$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to evaluate the expression ⎣ ⎡(13/7)² ⎦ + 17/4 ⎦, where ⎣ denotes the f... |
[
{
"role": "user",
"content": "The areas of three squares are 16, 49 and X. What is the average (mean) of their side lengths?\nIf we know the answer to the above question is 8, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem s... |
[
{
"role": "user",
"content": "The area of a square equals the square of a length of the side of the square. The perimeter of a square equals the sum of the lengths of all four sides. The sum of the areas of two squares is 65, while the difference in their areas is 33. Find the sum of their perimeters."
}... |
[
{
"role": "user",
"content": "12 balls numbered 1 through X are placed in a bin. In how many ways can 3 balls be drawn, in order, from the bin, Each ball remains outside the bin after it is drawn. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let... |
[
{
"role": "user",
"content": "The average age of five children is 6 years old. Each child has a different age and there is a 2-year difference between the ages of any two consecutive children. How old is the oldest child in years?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. ... |
[
{
"role": "user",
"content": "Evaluate the expression $\\frac{x^2 - x - 6}{x - 3}$ when $x = 2$. Simplify your answer."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is to evaluate the expression (x² - x - 6)/(x - 3) when x = 2 and simp... |
[
{
"role": "user",
"content": "Simplify $\\sqrt{8} \\times \\sqrt{50}$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. I need to simplify the product of √8 and √50. Hmm, when you multiply square roots, there's a rule that says you can combine them under a single square root. Let... |
[
{
"role": "user",
"content": "If the perimeter of a rectangle is 24 inches, what is the maximum possible area of the rectangle in square inches?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. So, the question is asking for the maximum possible area ... |
[
{
"role": "user",
"content": "Let $b$ and $c$ be real numbers. If the polynomial $x^2+bx+c$ has exactly one real root and $b=c+1$, find the value of the product of all possible values of $c$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by step. The... |
[
{
"role": "user",
"content": "What is the closest multiple of 15 to 2009?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. I need to find the closest multiple of 15 to 2009. Alright, first, what's a multiple of 15? It's like 15 multiplied by some integer. So the multiples would b... |
[
{
"role": "user",
"content": "Find the number of integers between $\\sqrt[3]{10}$ and $\\sqrt[3]{200}$."
},
{
"role": "assistant",
"content": "<think>\nOkay, so the problem is to find the number of integers between the cube root of 10 and the cube root of 200. Let me start by recalling that cube... |
[
{
"role": "user",
"content": "Find $x$, where $x$ is a square number which is divisible by four, and between 39 and 80."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The goal is to find a square number x that is divisible by four and lies between 3... |
[
{
"role": "user",
"content": "What is the maximum number of different digits that can be the units digit of a perfect square?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to figure out the maximum number of different digits that can be the units digit of a perfect square. Let ... |
[
{
"role": "user",
"content": "What is the product of the coordinates of the midpoint of a line segment with endpoints at $(2,3)$ and $(-6,5)$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking for the product of the coordinates o... |
[
{
"role": "user",
"content": "The polynomial equation \\[x^3 + bx + c = 0,\\]where $b$ and $c$ are rational numbers, has $5-\\sqrt{2}$ as a root. It also has an integer root. What is it?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by step. So, we ha... |
[
{
"role": "user",
"content": "If a 21-foot tree casts a 24-foot shadow, and Jack's house casts a 56-foot shadow at the same time, what is the height of Jack's house in feet, rounded to the nearest whole number?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem again... |
[
{
"role": "user",
"content": "What is the largest multiple of 19 that is a three-digit number?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking for the largest three-digit number that is a multiple of 19. Hmm, so first, I need to remember that a multiple of ... |
[
{
"role": "user",
"content": "One interior angle of a convex polygon is 160 degrees. The rest of the interior angles of the polygon are each 112 degrees. How many sides does the polygon have?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is about finding the number... |
[
{
"role": "user",
"content": "Compute $\\begin{pmatrix} X & 3 \\\\ 7 & -1 \\end{pmatrix} \\begin{pmatrix} 1 & -5 \\\\ 0 & 4 \\end{pmatrix}.$\nIf we know the answer to the above question is \\begin{pmatrix}2&2\\7&-39\\end{pmatrix}, what is the value of unknown variable X?"
},
{
"role": "assistant",
... |
[
{
"role": "user",
"content": "Find the matrix $\\mathbf{M}$ if it satisfies $\\mathbf{M} \\mathbf{i} = \\begin{pmatrix} 2 \\\\ X \\\\ -8 \\end{pmatrix},$ $\\mathbf{M} \\mathbf{j} = \\begin{pmatrix} 0 \\\\ 5 \\\\ -2 \\end{pmatrix},$ and $\\mathbf{M} \\mathbf{k} = \\begin{pmatrix} 7 \\\\ -1 \\\\ 4 \\end{pmatr... |
[
{
"role": "user",
"content": "Compute: X \\times 102$. The answer is 9996. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to solve for X in the equation X multiplied by 102 equals 9996. The answer is supposed to be 98, but let me go throu... |
[
{
"role": "user",
"content": "To calculate $31^2$, Emily mentally figures the value $30^2$ and adds 61. Emily subtracts a number from $30^2$ to calculate $29^2$. What number does she subtract?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. So Emily wants to calculate 29 squared... |
[
{
"role": "user",
"content": "Let $A,$ $B,$ $C$ be the angles of a non-right triangle. Compute\n\\[\\begin{vmatrix} \\tan A & 1 & 1 \\\\ 1 & \\tan B & X \\\\ 1 & 1 & \\tan C \\end{vmatrix}.\\]\nIf we know the answer to the above question is 2, what is the value of unknown variable X?"
},
{
"role":... |
[
{
"role": "user",
"content": "Evaluate $\\log_2 (4^2)$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is to evaluate $\\log_2 (4^2)$. \n\nFirst, I remember that logarithms can be simplified by converting the expression into exponents. ... |
[
{
"role": "user",
"content": "If there are an infinite number of values of $y$ that satisfy the equation $2(4+cy) = 12y+8$, what is the value of $c$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to solve this problem again. The problem says there are an infinite number of val... |
[
{
"role": "user",
"content": "How many ounces of pure water must be added to $30$ ounces of a $30\\%$ solution of acid to yield a solution that is $20\\%$ acid?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is about diluting a 30% acid solution with water to get a ... |
[
{
"role": "user",
"content": "Each of the ten volumes of the collected works of Theodore Sturgeon is available in paperback for $\\$$15 or in hardcover for X. Theresa buys a copy of each of the ten volumes for a total of $\\$$220. She bought 7 hardcover volumes. What is the value of unknown variable X?"
}... |
[
{
"role": "user",
"content": "The roots of the equation $2x^2 - 5x - 4 = 0$ can be written in the form $x = \\frac{m \\pm \\sqrt{n}}{p}$, where $m$, $n$, and $p$ are positive integers with a greatest common divisor of X. What is the value of $n$?\nIf we know the answer to the above question is 57, what is t... |
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