🧮 algebra

1. **State the problem:** Simplify the expression $ (x+3-3)^2 $. 2. **Understand the expression:** Inside the parentheses, we have $ x + 3 - 3 $. According to the order of operatio

1. The problem is to prove a mathematical statement or formula. Since the user did not specify which proof, I will demonstrate a classic proof: the sum of the first $n$ natural num

1. **Stating the problem:** We are investigating how the slope $m$ of a line affects the graph of the line as $m$ changes. 2. **Formula used:** The equation of a line in slope-inte

1. The problem is to understand how changing the value of $b$ in the linear equation $y = x + b$ affects the graph of the line. 2. The equation $y = x + b$ represents a straight li

1. Let's start by stating the problem: factoring an equation means rewriting it as a product of simpler expressions. 2. The most common form to factor is a quadratic equation $ax^2

1. **State the problem:** We are given the function $f(x) = -x(x+2)^2$ and want to understand its behavior and possibly simplify or analyze it. 2. **Recall the formula and rules:**

1. The problem is to simplify the expression $^{(x-4)2}$. 2. This expression appears to be ambiguous or incorrectly formatted. If you meant $(x-4)^2$, it represents the square of t

1. **State the problem:** Solve the system of linear equations: $$x + 2 + y = -2$$

1. **State the problem:** Solve the system of linear equations: $$5a + 2 + b = 15$$

1. **State the problem:** Solve the system of linear equations: $$3x + 9y = 0$$

1. **State the problem:** Solve the system of linear equations: $$3x + 8y = 34$$

1. **State the problem:** Solve the equation $3x + 8y = 34$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by moving o

1. El problema nos pregunta: ¿De qué número su sexta parte es 18? 2. La fórmula para este tipo de problema es: $$\frac{x}{6} = 18$$ donde $x$ es el número que buscamos.

1. Para problemas de partes de un número, usa la fórmula: $$\text{Parte} = \frac{1}{n} \times \text{Número}$$ donde $n$ es la fracción del número. 2. Para encontrar la fracción de

1. **Problem a:** Solve the simultaneous equations using matrix method: $$\begin{cases} 2x + 5y = 13 \\ 2x - 3y = 5 \end{cases}$$

1. Planteamos el problema: calcular $$\sqrt{\left(1 - 2 : \frac{1}{2}\right) \cdot 0,3\overline{3} + 4,9\overline{9}} - \frac{3}{4}$$. 2. Recordemos que dividir por una fracción es

1. **Problem statement:** Solve the system of equations $$\begin{cases}(3x+2)(2y-3)=6xy\\(4x+5)(y-5)=4xy\end{cases}$$

1. **State the problem:** We are given two functions $f(x) = x + 9$ and $g(x) = 2x + 3$. We need to find the value of $f(g(3))$. 2. **Understand the composition:** The expression $

1. **Nêu bài toán:** Tìm tất cả các giá trị của tham số $m$ sao cho đồ thị hàm số $$y = x^3 + 2x^2 + (m - 3)x + m$$ có hai điểm cực trị và điểm $M(9; -5)$ nằm trên đường thẳng đi q

1. **Problem statement:** Solve the equation $x(x + 2) - 2x(x - 3) = 5 - x^2$. 2. **Formula and rules:** Use distributive property and combine like terms.

1. **Problem:** Solve the system of equations from Bài 3: Two cyclists start simultaneously from two cities 38 km apart, moving towards each other. They meet after 2 hours. The fir