🧮 algebra

1. **Problem:** Simplify $\sqrt{12x^{2}y}$. 2. **Formula and rules:** The square root of a product is the product of the square roots: $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$. Also,

1. 문제 0224: $A=3^{x+1}$일 때, $81^x$를 $A$를 사용하여 나타내시오. 2. 문제 0225: $2^3=A$일 때, $\frac{1}{32^3}$을 $A$를 사용하여 나타내시오.

1. 문제를 이해합니다: 첫 번째 문제는 $2^3 = A$, $3^2 = B$일 때 $7^2$를 $A$, $B$로 나타내는 것입니다.

1. 문제: $2^{20} + 2^{20} + 2^{20} + 2^{20}$ 을 간단히 하시오. 2. 같은 수의 덧셈식은 곱셈식으로 바꿀 수 있습니다. 즉, $a + a + a + a = 4a$ 입니다.

1. **Énoncé du problème :** Soit la fonction $f$ définie par $$f(x) = \frac{x^3 - 3x + 2}{x^2}.$$ Nous devons déterminer le domaine de définition $D_f$.

1. **Énoncé du problème :** On considère la suite $(U_n)_{n\in \mathbb{N}}$ définie par $U_0=2$ et $U_{n+1} = \frac{1}{4} U_n - \frac{1}{4}$. On définit aussi $V_n = 3U_n + 1$.

1. The problem is to express $y$ in terms of $x$ from a given expression or equation involving $y$ and $x$. 2. To do this, we need the original equation or expression that relates

1. **State the problem:** Solve the system of equations: $$x^{2}+y^{2}-5x+2y+1=0$$

1. **State the problem:** We need to complete the missing values in the sales table for different instruments, given some numbers sold and percentages of sales, with a total of 150

1. **State the problem:** We need to determine which statements about Tayona's earnings percentages from different animals are correct based on the given table. 2. **Calculate tota

1. **Stating the problem:** We want to understand the properties of the fraction $\frac{1}{2}$.\n\n2. **Definition:** $\frac{1}{2}$ is a rational number representing one part out o

1. The problem is to find a number that can be used once and has four stars on each side, with the stars being equal in number on both sides. 2. Let's denote the number as $x$ and

1. The problem is to solve the quadratic equation $3x^2 + 48x + 117 = 0$ by completing the square. 2. First, divide the entire equation by 3 to simplify it:

1. We are given the quadratic equation $3x^2 + 48x + 117 = 0$ and asked to solve it by completing the square. 2. First, divide the entire equation by 3 to simplify the coefficients

1. **State the problem:** We need to find the equation of the blue line shown on the graph. 2. **Identify points on the line:** From the description, the line passes through points

1. The problem is to find what percentage the fraction $\frac{35}{50}$ represents. 2. To convert a fraction to a percentage, use the formula:

1. The problem asks to find the three inequalities that define the shaded triangular region bounded by the lines shown on the graph. 2. From the graph description, the boundaries a

1. The problem is to evaluate the expression $9 + e$ where $e$ is the mathematical constant approximately equal to 2.718. 2. The constant $e$ is the base of the natural logarithm a

1. **State the problem:** Divide the mixed number $1 \frac{4}{9}$ by the fraction $\frac{5}{9}$. 2. **Convert the mixed number to an improper fraction:**

1. The problem is to divide the mixed number $1 \frac{1}{2}$ by the fraction $\frac{3}{4}$. 2. First, convert the mixed number to an improper fraction.

1. **State the problem:** We need to solve the division of the mixed number $2 \frac{1}{7}$ by the fraction $\frac{5}{6}$. 2. **Convert the mixed number to an improper fraction:**