🧮 algebra

1. **State the problem:** Solve the system of equations: $$\begin{aligned} 5x - 2y - 4 &= 0 \\ 3x + 16y - 54 &= 0 \end{aligned}$$

1. Énoncé du problème : Trouver la dérivée de la fonction $f_1(x) = - \frac{2}{3} x^5$. 2. Rappel de la règle de dérivation : La dérivée de $x^n$ est $nx^{n-1}$.

1. **State the problem:** Find the equation of the line passing through the points $(3,-8)$ and $(6,-4)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ an

1. Énonçons le problème : vous souhaitez comprendre comment simplifier une expression mathématique. 2. La simplification consiste à réduire une expression à sa forme la plus simple

1. **Énoncé du problème :** On a la suite définie par $u_{n+1} = u_n + 0,05(20 - u_n)$ pour tout entier naturel $n$.

1. We are asked to solve the inequality $$\frac{x^2 + 3}{2x - 8} > 0$$. 2. Important points to consider are where the numerator and denominator are zero because these points divide

1. **Problem Statement:** (a) Determine the price of a tray of eggs and a kilo of sugar.

1. **State the problem:** Divide the polynomial $2x^2 + 11x + 5$ by the binomial $2x + 1$. 2. **Formula and rules:** Polynomial division is similar to long division with numbers. W

1. **State the problem:** We are given a custom operation defined as $x \triangle y = 2x + 3y$. 2. **Given:** $A \triangle 3 = 21$. We need to find the value of $A$.

1. **State the problem:** We are given a custom operation defined as $a \triangledown b = 2a - b$. We need to find the value of $\frac{1}{4} \triangledown \left( \frac{3}{4} \trian

1. **State the problem:** Find the positive square root of 22.09. 2. **Recall the formula:** The square root of a number $x$ is a value $y$ such that $$y^2 = x$$.

1. المشكلة: حل الباقي عند قسمة عدد ما على عدد آخر. 2. القاعدة: الباقي هو الجزء المتبقي بعد قسمة عدد صحيح على عدد صحيح آخر.

1. **Problem:** Find the X- and Y-intercepts of the equation $$\frac{x}{2} + \frac{y}{3} = 1$$. 2. **Formula and rules:**

1. **State the problem:** Solve the quadratic equation $$10 - 9x^2 + 4x = -6x^2$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** We have a two-digit number with tens digit $t$ and units digit $u$. When this number and its reverse are added, the sum is 143. 2. **Define variables:** L

1. **Problem statement:** We are given the line of action of a force with equation $y=2x$ and a point $B(-3,2)$. We need to find the length of the perpendicular dropped from point

1. المشكلة: لدينا دالة د(س) تمثل دالة أُسّية متزايدة، ونريد تحديد أي من الرسوم البيانية المعطاة تمثل هذه الدالة. 2. القاعدة: الدالة الأُسّية المتزايدة تأخذ الشكل العام $$ د(س) = a^

1. **Stating the problem:** Solve the equation $$\frac{2x+3}{x-1} = 4$$ for $x$.

1. نبدأ ببيان المسألة: لدينا الدالة $$d(x) = x^2 - 4$$ ونريد تحديد الفترة التي تزداد فيها الدالة. 2. نستخدم قاعدة زيادة الدالة التربيعية: الدالة $$x^2$$ تزداد عندما يكون $$x > 0$$

1. **State the problem:** Solve the quadratic equation $x^2 + x - 12 = 0$ and analyze its graph. 2. **Recall the quadratic formula:** For $ax^2 + bx + c = 0$, the solutions are giv

1. The problem is to understand the function notation $f(x)$ and what it represents. 2. The notation $f(x)$ means a function named $f$ with input variable $x$. It represents a rule