🧮 algebra

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:**

1. **Problem Statement:** Suresh's factory production changes over 5 years starting from 2003 with the following pattern:

1. The problem is to write the given equation in the form $$ax + by + c = 0$$. 2. This form is called the standard form of a linear equation in two variables, where $a$, $b$, and $

1. The problem is to write the equation \(-2x + 4y = 7\) in the form \(ax + by + c = 0\). 2. The general form of a linear equation in two variables is \(ax + by + c = 0\), where \(

1. The problem asks for the temperature increase in degrees Fahrenheit equivalent to a 10 degree Celsius increase. 2. The formula relating Fahrenheit ($F$) and Celsius ($C$) is:

1. **State the problem:** Calculate the value of the expression $\frac{2}{5} + \frac{7}{8} \times \frac{17}{19} \div 6 \div 5$ step by step. 2. **Recall the order of operations:**

1. The problem is to understand why the expression is written as $8e^1$. 2. The expression $8e^1$ means $8$ multiplied by $e$ raised to the power of $1$.

1. **State the problem:** Solve the equation $\log_3 \frac{x+25}{x-1} = 3 \log_2 2^2$ for $x$. 2. **Recall logarithm properties:**

1. **Problem statement:** Two points A and B are 1200 km apart. They start moving towards each other at the same time and meet in 24 hours. If A starts 10 hours after B, they meet

1. The problem is to analyze and understand the function $$y = 5 \sin^2\left((x^4 - x + 3)^2\right)$$. 2. The function involves a sine function raised to the power 2, and the argum