🧮 algebra

1. **Problem statement:** Solve the radical equation $\sqrt{2x} = 12$ and determine if the solution is acceptable. 2. **Formula and rules:** To solve equations involving square roo

1. **State the problem:** Simplify the expression $$7\sqrt{18x^2} + \sqrt{48x^4} + \sqrt{x^8}$$. 2. **Recall the square root properties:**

1. Асуудлыг тодорхойлж эхэлье: Та бүх бодолтыг дэлгэрэнгүйгээр хүссэн байна. 2. Бодолтын жишээ авч үзье: Жишээ нь, $2x + 3 = 7$ тэгшитгэлийг бодъё.

1. **State the problem:** Simplify the expression $8n + 12 + (-9) - (-6n)$. 2. **Recall the rules:** When subtracting a negative, it becomes addition: $-(-6n) = +6n$. Also, combine

1. **State the problem:** Simplify and solve for $a$ given the expression: $$a = \ln \left( \left(\sqrt{e+1} - 1\right)^{2025} \right) + \ln \left( \left(\sqrt{e+1} + 1\right)^{202

1. **State the problem:** Simplify the expression $8n + (-6n)$. 2. **Recall the rule:** When adding terms with the same variable, add their coefficients.

1. **State the problem:** We are given the inequality $y \le 2x - 3$ and need to understand its meaning and graph. 2. **Explain the inequality:** This inequality means that the val

1. Problem (g): Simplify $ (3 - 4i) + (6 + i) $. Step 1: Add the real parts: $3 + 6 = 9$.

1. **Problem Statement:** Determine whether the relation in graph (b) is discrete, continuous, discontinuous, or neither. Then state its domain and range.

1. The problem is to analyze and solve the first equation: $2x^3 + y^2 = 1 - 4y$. 2. Start by rewriting the equation to isolate terms and simplify:

1. The problem asks to find the LCM (ল.সা.গু.) and GCD (গ.সা.গু.) of the second and third polynomials: $3x^2 + 7x + 2$ and $6x^2 - x - 1$. 2. First, factorize each polynomial.

1. **প্রশ্ন:** ax^2 + (a^2 + 1)x + a রাশিকে উৎপাদক বিশ্লেষণ কর। 2. **ফর্মুলা:** একটি দ্বিঘাত রাশির উৎপাদক বিশ্লেষণের জন্য আমরা ব্যবহার করি মূল সূত্র $$ax^2 + bx + c = a(x - x_1)(x

1. **Énoncé du problème :** Soient $f(x) = x^2 - x$ et $g(x) = \sqrt{x} + 2$. Déterminer le domaine de définition de $g$, vérifier que $f(2) = g(2)$.

1. The problem is to graph the function $$h(x) = -3|x + 3| - 2$$. 2. This is an absolute value function transformed by a vertical stretch/compression, reflection, and translation.

1. ප්‍රශ්නය: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 යන සංඛ්‍යානුක්‍රමය පිළිබඳව පියවර වශයෙන් විස්තර කරන්න. 2. මෙම සංඛ්‍යානුක්‍රමය යනු සරල ගුණක අනුක්‍රමයක් (Arithmetic sequence) වේ.

1. **State the problem:** Solve the inequality $2x - 1 < 9$. 2. **Recall the rule:** To solve inequalities, we isolate the variable on one side. Adding or subtracting the same numb

1. **State the problem:** Solve the inequality $3x - 8 > 16$. 2. **Use the inequality solving rule:** To isolate $x$, add or subtract terms on both sides and divide or multiply by

1. The problem is to determine if the cryptarithm SEND + MORE = MONEY has only one solution. 2. Cryptarithms like SEND + MORE = MONEY are designed so that each letter represents a

1. The problem is to solve the cryptarithm SEND + MORE = MONEY, where each letter represents a unique digit. 2. The goal is to find digits for S, E, N, D, M, O, R, Y such that the

1. **Énoncé du problème :** Montrer que la fonction $f$ définie sur $]-\infty, -2[$ par $$f(x) = \frac{x^2}{1+x}$$ est injective. 2. **Formule et rappel :** Une fonction est inject

1. The problem is to find the first 10 questions, but since no specific questions are provided, I will assume you want the first 10 questions of a common math topic such as algebra