🧮 algebra

1. **State the problem:** We need to divide the polynomial $3x^2 - 18x - 46$ by the binomial $3x + 5$. 2. **Formula and method:** Polynomial division is similar to long division wi

1. **Problem:** Sketch the graph of the function $g(x) = 3x$. 2. **Formula and rules:** This is a linear function of the form $y = mx + b$ where $m=3$ and $b=0$. The graph is a str

1. **State the problem:** Write the expression $\log_5 \left(\frac{1}{2}\right) + \log_5 50$ as a single logarithm and evaluate it. 2. **Recall the logarithm property:** The sum of

1. **بيان المسألة:** لدينا متتالية حسابية $(U_n)$ معرفة على $\mathbb{N}$ حيث $U_4=5$ و $U_8=7$. المطلوب: أ) إيجاد أساس المتتالية $r$ والحد الأول $U_0$.

1. **Enunciado do problema:** Calcular o valor das horas paradas para cada produto (A, B, C, D) considerando o atraso de 2 dias na entrega da matéria-prima, e preencher a tabela co

1. **Problem statement:** Determine the sign of each quotient. 2. **Recall the rule for division of rational numbers:** When dividing two numbers, the sign of the quotient depends

1. **State the problem:** We are given two points on a parabola: the vertex at $(6,7)$ and another point $(4,13)$. The parabola is described by the vertex form equation:

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 $f(x) = mx + b$