🧮 algebra

1. The problem is to square a given number or expression, which means multiplying it by itself. 2. The formula for squaring a number $x$ is $x^2 = x \times x$.

1. Stating the problem: Simplify the expression \( \frac{\sqrt{3x-2}}{\sqrt{x}} \). 2. Formula and rules: Recall that \( \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \) for \( a,

1. **Stating the problem:** Simplify and expand the expression $\left(3x - \frac{2}{\sqrt{x}}\right)^2$. 2. **Formula used:** The square of a binomial $(a - b)^2 = a^2 - 2ab + b^2$

1. সমস্যাটি হলো: যদি $x - \frac{1}{x} = 4$ হয়, তাহলে প্রমাণ করতে হবে যে $x^4 + \frac{1}{x^4} = 322$। 2. প্রথমে আমরা $x - \frac{1}{x} = 4$ থেকে শুরু করব। এখানে লক্ষ্য করুন, আমরা $x

1. נתחיל בהבנת הבעיה: יש לנו שני טבלאות עם נתונים של מספר הסבוכים ומספר הקרמים עבור שתי קבוצות (א' וב'). 2. נבחן את הנתונים:

1. The problem is to express a matrix in a format that is not a single sentence, meaning we want to write it clearly with line breaks and proper formatting. 2. A matrix is a rectan

1. مسئله: معادله $$7 = \sqrt{x^3 - x - 1} + \sqrt{x^3 - x + 6}$$ را حل کنیم و حاصل ضرب جواب‌ها را بیابیم. 2. ابتدا متغیر کمکی تعریف می‌کنیم: $$y = x^3 - x$$. پس معادله به شکل $$7 =

1. مسئله: باید حاصل ضرب جواب‌های معادله $$7 = \sqrt{x^2 - x - 1} + \sqrt{x^2 - x + 6}$$ را پیدا کنیم. 2. ابتدا توجه کنیم که عبارت‌های زیر رادیکالی باید تعریف شده باشند:

1. **State the problem:** We need to find the quantities of four drugs (A, B, C, D) to distribute to four clinics so that their treatment capacities are met. 2. **Define variables:

1. **State the problem:** Make $x$ the subject of the equation $$y = \frac{3x + 2}{x - 1}$$. 2. **Understand the formula:** We want to isolate $x$ on one side of the equation.

1. The problem is not specified, so I will provide a general example of solving a quadratic equation. 2. Consider the quadratic equation $$ax^2 + bx + c = 0$$ where $a \neq 0$.

1. The problem asks to find the percentage for 1b and 1c. 2. To find a percentage, use the formula: $$\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100$$

1. **Problem Statement:** Use synthetic division to divide a polynomial by a binomial of the form $x - c$. Since the user did not specify the polynomial or divisor, let's assume a

1. **State the problem:** We need to analyze and understand the cubic polynomial $$z^3 + 2z^2 - 23z - 60$$ including its roots and graph behavior. 2. **Formula and rules:** For cub

1. **State the problem:** We are given that $T$ varies inversely with $y$, and that $T=2$ when $S=60$. We need to find the relationship between $T$ and $y$ and possibly find $T$ fo

1. **Stating the problem:** We are given that $T$ varies inversely with $y$, and that $T=2$ when $S=60$. We need to find the relationship between $T$ and $y$ and determine the cons

1. **State the problem:** Simplify and factor the quadratic expression $x^2 + 10x + 21$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbe

1. Diketahui suku banyak $f(x)$ dan $g(x)$ dengan informasi sisa pembagian sebagai berikut: - $f(x)$ dibagi $(x-2)$ bersisa $p+3$

1. **State the problem:** We want to find the time $t$ it takes for a population to grow from 500 to 1200 at an annual growth rate of 12%. 2. **Formula used:** The population growt

1. Énonçons le problème : Il s'agit de comprendre comment déterminer une fraction, c'est-à-dire comment identifier et manipuler ses différentes parties. 2. Une fraction est une exp

1. Muammo: 765 sonini $\frac{2}{3}$, 4, va $\frac{1}{2}$ sonlariga teskari proporsional uchta qismga ajratish. 2. Teskari proporsional bo'lganda, qismlar $x$, $y$, $z$ quyidagicha