🧮 algebra

1. **Énoncé du problème :** Soit $x \in \mathbb{R}$ tel que $-2 < x < 0$, on pose $A = x^2 + x - 2$ et $B = \frac{x}{x-1}$.

1. **State the problem:** Convert the fractions $\frac{2}{5}$, $\frac{7}{12}$, $\frac{3}{4}$, and $\frac{-5}{6}$ to equivalent fractions with a common denominator. 2. **Find the Le

1. **State the problem:** We need to convert the fractions $\frac{3}{4}$, $\frac{9}{22}$, $\frac{7}{8}$, and $-\frac{5}{11}$ to equivalent fractions with a common denominator calle

1. **State the problem:** Solve the equation $-4(p + 2) + 8 = 2(p - 1) - 7p + 15$ for $p$. 2. **Apply the distributive property:**

1. **State the problem:** We need to graph the line given by the equation $$y + 6 = -\frac{1}{2}(x + 10)$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept

1. مسئله: عدد رادیکالی $\sqrt{18}$ را به صورت عدد گویا بین دو عدد 3 و 8 بنویسیم. 2. ابتدا رادیکال را ساده می‌کنیم. چون $18 = 9 \times 2$ و $9$ یک مربع کامل است، داریم:

1. **State the problem:** Find the equation of the line passing through the points $(1,-5)$ and $(9,11)$. 2. **Formula used:** The equation of a line in slope-intercept form is $y

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 2x_1 - 5x_2 - 6x_3 = 5 \\ -3x_1 + 2x_2 + 5x_3 = 1 \\ 2x_1 + 4x_2 - 3x_3 = -16 \end{cases}$$

1. The user message lists multiple lessons and skills related to algebra topics such as solving systems of equations, graphing quadratic functions, complex numbers, and polynomial

1. **Problem Statement:** Draw addition ⊕ and multiplication ⊗ tables for the set {2, 4, 6, 8} modulo 9.

1. Planteamos el problema: Tenemos una maquinaria con valor depreciado linealmente, con valor S/24000 a los 4 años y S/18000 a los 10 años. 2. La fórmula para depreciación lineal e

1. **State the problem:** We need to determine the feasible region and vertices for the system of inequalities: $$4x - 2y < 2$$

1. **State the problem:** We need to find the number that should be added to $\frac{3}{32}$ to get $\frac{53}{96}$. 2. **Set up the equation:** Let the unknown number be $x$. Then,

1. The problem asks which method is used to solve a linear system by multiplying one or both equations by appropriate numbers so that one variable has the same coefficient with opp

1. **State the problem:** Find the y-intercept of the line given by the standard equation $$2x - 3y = 4$$. 2. **Recall the formula for y-intercept:** The y-intercept occurs where $

1. **State the problem:** We need to find the number that should be added to $\frac{3}{32}$ to get $\frac{53}{96}$. 2. **Set up the equation:** Let the number to be added be $x$. T

1. **State the problem:** Solve the system of equations for $x$, $y$, and $z$ given by: $$\begin{cases} y + 2 = 5 \\ 2x - y = 45 \\ 3y - 4z = 12 \end{cases}$$

1. Masalah: Diberi dua titik (5, m) dan (n, 9) yang memuaskan fungsi $$y = \frac{20}{x} + 4$$. Cari nilai $$m - n$$. 2. Formula fungsi yang diberikan adalah $$y = \frac{20}{x} + 4$

1. **Problem Statement:** We are working with a multiplication operation \(\otimes\) modulo 8 on the set \(\{3,5,7\}\).

1. Masalah: Diberi dua titik (5, m) dan (n, 9) yang memuaskan fungsi $$y = \frac{20}{x} + 4$$, cari nilai $$m - n$$. 2. Formula fungsi yang diberikan adalah $$y = \frac{20}{x} + 4$

1. Evaluate $12 - \left(\frac{8}{5} + 3 \div \frac{2}{3}\right)$. - First, calculate $3 \div \frac{2}{3} = 3 \times \frac{3}{2} = \frac{9}{2}$.