🧮 algebra

1. The problem is to find the value of $x$ in the equation $3x + 5 = 20$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. El problema es factorizar el polinomio de tercer grado $x^3+3x^2-x-3$ y resolver la ecuación $x^3+3x^2-x-3=0$. 2. Para factorizar un polinomio de tercer grado, primero buscamos

1. **Stating the problem:** Solve the system of equations using the mixed method (Elimination-Substitution): $$\begin{cases} 3x - 5y = 5 \\ 4x - 3y = 14 \end{cases}$$

1. **State the problem:** Determine the general term and the 10th term ($t_{10}$) of the sequence: 80, 40, 20, 10, ... 2. **Identify the sequence type:** Check if the sequence is a

1. **Problem Statement:** Determine the sum of each arithmetic series given in question 8. 2. **Formula for the sum of an arithmetic series:**

1. **Problem:** Bestimmen Sie die Funktionsgleichung in Normalform $y = mx + b$ für die lineare Funktion mit den Punkten: a. $(1|2)$ und $(3|4)$

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 2x + y = 1 \\ x - 2y = 18 \end{cases}$$

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

1. **State the problem:** Simplify the expression $$\left(\frac{4p^{5}}{p^{-3}}\right)^{-2}$$ and write the answer using only positive exponents. 2. **Recall the rules:**

1. **State the problem:** Factor the expression $$8u^9v^6 - 24u^3v^2x^4$$ by factoring out the greatest common monomial factor. 2. **Identify the greatest common factor (GCF):**

1. **State the problem:** Simplify the expression $7 + 2 + 5y + 3y$. 2. **Identify like terms:** Combine constant terms and terms with $y$ separately.

1. **State the problem:** Simplify the algebraic expression $5m + m + 6$. 2. **Identify like terms:** Like terms are terms that contain the same variable raised to the same power.

1. The problem asks to fill the box with a symbol to form: a) an equation

1. **State the problem:** Simplify the algebraic expression $$4 + 6x - 5x + 4x$$. 2. **Identify like terms:** Like terms are terms that have the same variable raised to the same po

1. **State the problem:** Simplify the expression $$3 + 4 - 1 + 3x - 2x + 4x$$. 2. **Combine like terms:** Group the constant terms and the terms with $x$ separately.

1. **Énoncé du problème** : Soit la matrice $A = \begin{pmatrix} 2 & 1 & 0 \\ 1 & 2 & 0 \\ 1 & 1 & 1 \end{pmatrix}$. Nous devons :

1. **Nêu bài toán:** Anh An bắt đầu với lương tháng đầu là 6 triệu đồng. 2. **Phân tích điều kiện tăng lương:** Sau mỗi 6 tháng, lương tăng 8% so với mức lương trước đó.

1. The problem is to evaluate the expression $n^5$ for a given value of $n$. 2. The formula used is the power rule: $$n^5 = n \times n \times n \times n \times n$$ which means mult

1. **Stating the problem:** Simplify the function $$f(x) = \frac{2x^{2} + 3x - 1}{x + 2}$$ and analyze its behavior. 2. **Formula and rules:** For rational functions, simplify by f

1. **State the problem:** We are given the function $$f(x) = (x+1)^4 (x-2)^5$$ and asked to find its inverse function $$f^{-1}(x)$$. 2. **Understand the problem:** Finding the inve

1. The problem is incomplete as the function definition for $f(x)$ is missing. 2. To proceed, please provide the full expression for $f(x)$ so I can help with evaluation, simplific