🧮 algebra

1. نبدأ بتحديد الفترات الزمنية لوصول القطارات إلى كل رصيف: - القطار على الرصيف 1 يصل كل 4 دقائق.

1. نلاحظ الأعداد المعطاة: 3، 8، 18، 38، 78. 2. نحسب الفروق بين الأعداد المتتالية:

1. Let's start by stating the problem: We want to understand and apply common algebraic identities. 2. The most common algebraic identities are:

1. **Énoncé du problème :** Calculer \((\sqrt{6} - \sqrt{5})^{2024} \times (\sqrt{6} - \sqrt{5})^{2024}\) et \(\left( \frac{\sqrt{3}}{\sqrt{3} - 2} \right)^{-2} + \left( \frac{\sqr

1. The laws of exponents are rules that describe how to simplify expressions involving powers of the same base. 2. **Product rule:** When multiplying powers with the same base, add

1. Problem a) Simplify $$(\sqrt{a} - 1 - \sqrt{a} + 1)(\sqrt{a} + 1 + \sqrt{a} - 1)$$ Step 1: Simplify inside each parenthesis:

1. **State the problem:** We need to simplify the expression $$\frac{x^3+6x^2+11x+6}{x+1}$$ by performing polynomial division. 2. **Set up the division:** Divide the cubic polynomi

1. The problem states that a farmer bought material for 325000 after a 35% discount. 2. Let the marketed price be $x$.

1. Problem: Setze für ■ eine passende Zahl bzw. einen passenden Term ein, sodass unter der Wurzel eine binomische Formel entsteht, und ziehe dann die Wurzel. 2. a) Gegeben: $$\sqrt

1. **State the problem:** Solve the quadratic equation $x^2 - 7x + 5 = 0$. 2. **Identify coefficients:** Here, $a = 1$, $b = -7$, and $c = 5$.

1. **State the problem:** We need to find the cost of linoleum to cover a dining room described by the region bounded by the y-axis ($x=0$), x-axis ($y=0$), the line $y=25-5x$, and

1. State the problem: Simplify the expression $$32 - [36 - 2\{5 \times 2 + 7 - 6\}]$$. 2. Simplify inside the curly braces first: Calculate $$5 \times 2 + 7 - 6$$.

1. **State the problem:** We sell an article for 216 resulting in a loss. If sold for 300, the gain is 2.5 times the loss. We need to find the cost price (CP).

1. The problem asks to find the product of 2 and the square root of 3. 2. We write this mathematically as $2 \times \sqrt{3}$.

1. **Problem statement:** We consider the lattice formed by the divisors of 105, denoted as 105D, with the partial order defined by divisibility. We need to (i) draw the Hasse diag

1. The problem is to simplify the expression $-2\sqrt{x}27 - 3\sqrt{x}45$. 2. First, rewrite the terms by separating the constants and the square roots:

1. To help you simplify further, please provide the specific expression or equation you want to simplify. 2. Simplification depends on the form and terms of the expression.

1. The problem is to analyze the function $z8(x) = -4x$ and $y = -4x$, which are linear functions. 2. Both functions have the form $y = mx + b$ where $m$ is the slope and $b$ is th

1. The problem involves understanding and manipulating the function $f(x) = 5x^2 - 10$. 2. Given $y = 5x^2 - 10$, we want to express $x$ in terms of $y$.

1. **State the problem:** Solve the quadratic equation $x^2 - 6x - 3 = 0$. 2. **Identify coefficients:** Here, $a = 1$, $b = -6$, and $c = -3$.

1. **State the problem:** Solve the system of equations using Gauss-Elimination Method: $$\begin{cases} x + y + z = 6 \\ 2x + 3y + z = 14 \\ x - y + 2z = 7 \end{cases}$$