🧮 algebra

1. El problema nos pide expresar la función $m$ en términos de $h$ cuando $m$ es una traslación de $h$, y también indicar el dominio de cada función. 2. Observamos que $h(x)$ es un

1. **Problem Statement:** Given functions $f(x) = 2x + 1$ and $g(x) = 3x + 1$, find the following operations: \(\frac{f}{g}(x)\), \((fg)(x)\), \(f \circ g(x)\), and \(g \circ f(x)\

1. Énonçons le problème : Simplifier l'expression $$E = \sqrt{11} + 2\sqrt{10} \times (\sqrt{10} - 1)$$. 2. Rappelons la formule et les règles importantes :

1. **State the problem:** We need to find the sum of the three prime numbers in the list: 12, 27, 23, 47, 51, 61, 75, 93. 2. **Identify prime numbers:** A prime number is a natural

1. **State the problem:** Solve the expression \( \frac{y-2}{2y^2} \). 2. **Understand the expression:** This is a rational expression where the numerator is \( y-2 \) and the deno

1. The problem is to simplify and solve an expression or equation where the variable \(m\) is removed or replaced. 2. Since the user requests to "mark work everything again but wit

1. **State the problem:** We are given two lines, Line P and Line Q, intersecting at the point $(8, -5)$. Line Q is vertical at $x=8$. We need to:

1. **Déterminer le domaine de définition de la fonction** $f(x) = \frac{2x^2 - x - 1}{x+2}$. Le domaine est l'ensemble des $x$ pour lesquels le dénominateur n'est pas nul.

1. The problem is to solve the cubic equation $$x^3 - 9x^2 + 22x + 12 = 0$$. 2. To solve a cubic equation, one common method is to try to find rational roots using the Rational Roo

1. Simplify $\sqrt[3]{80}$. - Step 1: Factor 80 into prime factors: $80 = 2^4 \times 5$.

1. Let's consider a challenging algebra problem involving solving a system of nonlinear equations. 2. Problem: Solve the system of equations:

1. **Problem statement:** We are given that the stay of 12 men for 7 days costs 21200. We need to find the cost for the stay of 10 men for 8 days. 2. **Formula and concept:** The c

1. **State the problem:** Simplify the expression $$\sqrt{\frac{9 + 2\sqrt{20}}{18 - 2\sqrt{32}}}$$. 2. **Recall the formula and rules:** To simplify nested radicals, especially fr

1. El problema es encontrar la resolución o expresión de la función $f(x)$ dada por $f(x) = 5x + 2$. 2. La función es una función lineal, que tiene la forma general $f(x) = mx + b$

1. We are given the quadratic function $f(x) = 2x^2 + 6x - 5$ and asked to analyze it. 2. The general form of a quadratic function is $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c

1. **Problem Statement:** We have five cards, each with two three-digit numbers. Some digits are obscured by ink. We need to find the card where the sum of the digits of both numbe

1. The problem states that a player scores one goal in every match, including the final, in a FIFA World Cup tournament. 2. The tournament structure is: 3 group matches followed by

1. **State the problem:** We have three scales balanced as follows: - Scale 1: 3 circles + 2 triangles = 9 squares

1. **Problem Statement:** Given that A and B together can complete a work in 12 days, and B alone can complete the same work in 30 days, find how many days A alone will take to fin

1. Problem: When $y$ varies directly as $x$, and $y=21$ when $x=16$, find $y$ when $x=8$. 2. Formula: Direct variation means $y=kx$ where $k$ is a constant.

1. **Problem Statement:** (a) Factorize completely: