🧮 algebra

1. The problem is to factorize the expression $x^2 - 5x + 6$. 2. The formula used for factorization of a quadratic expression $ax^2 + bx + c$ is to find two numbers that multiply t

1. **Énoncé du problème :** On considère la suite $(u_n)$ définie par $u_0=1$ et $u_{n+1} = \frac{u_n}{5 + 8u_n}$ pour tout $n \in \mathbb{N}$.

1. **State the problem:** Solve the exponential equation $25^{2x-1} = 125^{3x+4}$ for $x$. 2. **Recall the formula and rules:** Both 25 and 125 can be expressed as powers of 5 sinc

1. **State the problem:** Solve the exponential equation $25^{2x-1} = 125^{3x+4}$ for $x$. 2. **Recall the formula and rules:** Both 25 and 125 can be expressed as powers of 5 sinc

1. **State the problem:** Simplify the expression $$\frac{5}{4} - 3\left[ \left( 1 - \frac{1}{4} \right)^{-1} + \frac{2}{3} \left( \frac{1}{2} - \frac{5}{4} \right) - \frac{3}{4} :

1. **State the problem:** Simplify the expression $$\frac{8}{5} - 2 \left( \frac{3}{4} + 4^{-2} \right) + 2$$. 2. **Recall the rules:**

1. مسئله: دنباله $a_n$ به صورت $a_n = \frac{1}{\sin n}$ تعریف شده است و می‌خواهیم مقدار $a_{4506}$ را بیابیم. 2. فرمول: $a_n = \frac{1}{\sin n}$ که در آن $n$ عدد صحیح است.

1. The problem asks to solve the equation $2x^2 - 5x + 3 = 0$. 2. We use the quadratic formula to solve equations of the form $ax^2 + bx + c = 0$:

1. **Problem 1:** Solve $8x^2 - 2x - 15 = 0$ by factorization. - Multiply $a \times c = 8 \times (-15) = -120$.

1. **State the problem:** We are given the equation \((x + 2)(x - 5) = x^2 - 2x - 15\) and need to verify if both sides are equal by expanding and simplifying. 2. **Recall the form

1. نبدأ ببيان المسألة: نريد إيجاد قيمة هـ بحيث يكون المستقيم المار بالنقطتين أ(-1، 2) وب(5، هـ) موازياً للمستقيم المعطى بمعادلته $$2x = y + 1$$. 2. نعيد كتابة معادلة المستقيم المعط

1. The problem asks to determine if the statements about polynomial functions and zeros are true or false. 2. Statement 1: "Every quadratic function is a polynomial function." This

1. The problem is to create a 100-choice question on logarithms. 2. A logarithm answers the question: to what exponent must we raise a base number to get another number? The formul

1. نبدأ بكتابة المعطيات: \( ق(س) = 2س - 5 \) و \( هـ(س) = 3س \). 2. المطلوب هو إيجاد \( ق \circ هـ (س) \) أي تركيب الدالتين، حيث \( ق \circ هـ (س) = ق(هـ(س)) \).

1. نبدأ بكتابة المعطيات: لدينا نقطتان هما $\left(3^{x-1},16\right)$ و $\left(\frac{1}{17},(y+7)^2\right)$.\n2. نفترض أن النقطتين متساويتين، أي أن الإحداثيات المقابلة متساوية.\n3. م

1. مسئله: بررسی یک عبارت یا معادله ریاضی به زبان فارسی. 2. ابتدا باید مسئله دقیق را مشخص کنید تا بتوانیم فرمول‌ها و قوانین مربوطه را به کار ببریم.

1. **Problem statement:** Find the inverse function of $ق(s) = 3s + 2$. 2. **Formula and rules:** To find the inverse function $ق^{-1}(y)$, swap $s$ and $y$ and solve for $s$.

1. **State the problem:** Solve the inequality $$x^3 + 4x^2 - 36 \ge 0$$. 2. **Formula and approach:** To solve polynomial inequalities, first find the roots by setting the polynom

1. დავალება: დავწეროთ მაგალითი, რომელიც მოიცავს ალგებრის ძირითად ოპერაციებს და მისი ამოხსნა. 2. მაგალითი: ამოიღეთ $x$-ის მნიშვნელობა განტოლებიდან $$2x + 3 = 11$$.

1. Problem: Find the HCF (Highest Common Factor) of 12, 14, 19, 25, and 36. 2. The HCF of a set of numbers is the greatest number that divides all of them exactly.

1. The problem is to graph the piecewise function $$f(x) = \begin{cases} 1 - x & \text{if } x < 0 \\ 1 & \text{if } x = 0 \\ x + 1 & \text{if } x > 0 \end{cases}$$. 2. This functio