🧮 algebra

1. The problem is to find the solution step by step for the given question (not specified, so assuming a general approach). 2. First, identify the type of problem (e.g., algebraic

1. **State the problem:** Grandma made a certain number of tiny apple pies. Josh and his brother ate $\frac{3}{7}$ of all the pies. Then three friends came over and shared the rema

1. **State the problem:** Find the value of the square root of 42 divided by 7, i.e., calculate $$\frac{\sqrt{42}}{7}$$. 2. **Recall the formula:** The square root of a number $x$

1. **State the problem:** We have three health clubs with different payment plans. We need to match each club to its payment table and write equations representing their costs.

1. **Stating the problem:** We have three health clubs with different payment plans: - Club A: Initial fee $150, monthly fee $45

1. **Problem statement:** Three numbers have a sum of 2400. When the largest number is divided by the smallest, the remainder is 6. When the middle number is divided by the smalles

1. Define Group, Semigroup, Monoid, Subgroup, Abelian Group, Cyclic Group, and Lattice with properties. - Group: A set $G$ with a binary operation $\cdot$ is a group if it satisfie

1. **Stating the problem:** Find the smallest real solutions of the equation $$x^2 = g$$ where $$g$$ is a real number. 2. **Formula used:** The solutions to $$x^2 = g$$ are given b

1. **Problem Statement:** Define Group, Semigroup, Monoid, Subgroup, Abelian Group, Cyclic Group, and Lattice along with their properties. 2. **Definitions and Properties:**

1. **State the problem:** Simplify the expression $$\frac{3x^2 - 27x}{2x - 9}$$. 2. **Identify the formula and rules:** To simplify a rational expression, factor both numerator and

1. المشكلة: حل المعادلة $x^2 - 5x + 6 = 0$. 2. الصيغة المستخدمة: لحل المعادلات التربيعية نستخدم صيغة التحليل أو صيغة الجذر التربيعي.

1. Мәселені түсіндіру: Берілген теңсіздік $$a^2 + b^2 \leq a^3 + b^3 \leq a^2 + b^2$$, мұнда $a$ және $b$ нақты сандар. 2. Формуланы қолдану: Кез келген нақты сандар үшін куб пен к

1. Problem: Find the domain and range of $f(x) = x^2 - 4x + 1$. 2. Formula: Quadratic function $f(x) = ax^2 + bx + c$ with $a=1$, $b=-4$, $c=1$.

1. **State the problem:** Kelly gave 1/5 of her picture cards to Holly, which equals 10 cards. We need to find how many picture cards Kelly has left. 2. **Set up the equation:** Le

1. **State the problem:** We are given two numbers whose sum is 36, and one number exceeds the other by 8. We need to find the smaller number. 2. **Set variables:** Let the smaller

1. The problem is to provide examples and solutions for arithmetic, geometric, and Fibonacci sequences. 2. Arithmetic sequence formula: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the fi

1. **State the problem:** Simplify the expression $$23. \left( \frac{a + b}{a^2 + b^2} - \frac{5a + b}{a^2 - b^2} : \frac{5a^3 + a^2b + 5ab^2 + b^3}{2ab(a - b)} \right) \cdot \left

1. **State the problem:** Simplify the expression $$\frac{a + b}{a^2 + b^2} - \frac{5a + b}{a^2 - b^2} : \frac{5a^3 + a^2b + 5ab^2 + b^3}{2ab(a - b)}$$ 2. **Recall important formul

1. **State the problem:** We are given five numbers: 5, 9, x, 17, and 21. Their mean (average) is 13. We need to find the value of $x$. 2. **Formula for mean:** The mean of $n$ num

1. **State the problem:** Solve the equation $$64^{2x-1} = 128^x \cdot 2^{x-1}$$ for $x$. 2. **Rewrite bases as powers of 2:**

1. **Problema:** Multiplicar los polinomios $\left(2x^{4} - 2x^{2}y + xy^{2}\right)$ y $\left(3x^{5} + 3x^{4}y + 4x^{3}y^{2} + 2xy^{4} + xy^{5}\right)$.\n\n2. **Fórmula y reglas:**