🧮 algebra

1. Problem: A two-digit positive integer has its digits reversed, and the resulting integer differs from the original by 27. Find the difference between the digits. 2. Let the tens

1. **Problem:** You have saved 135 Taka by purchasing a blanket with a 15% discount. What is the quoted price of the blanket? 2. **Formula:** Discount amount = (Discount % / 100) \

1. المشكلة: شرح مفهوم المعادلات الجبرية وكيفية حلها. 2. المعادلة الجبرية هي تعبير رياضي يحتوي على متغيرات وأعداد وعلامات عمليات حسابية، مثل الجمع والطرح والضرب والقسمة.

1. The problem is to analyze the given quadratic equations and understand their structure. 2. The general form of a quadratic equation is $$ax^2 + bx + c = 0$$ where $a$, $b$, and

1. **State the problem:** Solve for $x$ in the equation $$4(x+2) = 2x + 18$$. 2. **Use the distributive property:** Multiply 4 by each term inside the parentheses:

1. **State the problem:** Solve for $x$ in the equation $5x - 7 = 3x + 9$. 2. **Write down the equation:**

1. **Stating the problem:** We are given a prime number $p$ and asked to find the quadratic equation whose factors are zero. 2. **Understanding the problem:** If the factors of a q

1. Diketahui suku ke-3 ($a_3$) dan suku ke-6 ($a_6$) dari deret geometri adalah 32 dan 2048. 2. Rumus suku ke-n deret geometri adalah $$a_n = a_1 \times r^{n-1}$$ dengan $a_1$ adal

1. مسئله: حل معادله $2x + 3 = 11$ را یاد بگیریم. 2. فرمول و قانون: برای حل معادله، باید $x$ را تنها کنیم. یعنی باید کاری کنیم که $x$ در یک طرف معادله باشد و بقیه اعداد در طرف دیگر.

1. The problem is to understand the meaning and properties of the ceiling function $\lceil x \rceil$. 2. The ceiling function $\lceil x \rceil$ is defined as the smallest integer g

1. Masalani bayon qilamiz: Bir xil 5 ta sonni ko'paytirganda natija 59049 chiqadi. 2. Formulani ko'rib chiqamiz: Agar son $x$ bo'lsa, 5 marta ko'paytirish $$x^5 = 59049$$ shaklida

1. The problem is to draw the graph of the function $y=6$. 2. This is a constant function where the value of $y$ is always 6 regardless of $x$.

1. **Problem Statement:** We are studying the quadratic function in the form $$f(x) = ax^2 + bx + c$$ where $a,b,c \in \mathbb{R}$ and $a \neq 0$.

1. The problem is to understand key properties and rules about polynomial functions and their graphs. 2. A zero of multiplicity $k$ means $(x - c)^k$ divides $f(x)$ but $(x - c)^{k

1. **Problem:** Simplify and solve the equation $$2^{x+1} = 5 \cdot 2^{x-2}$$. 2. **Formula and rules:** Recall the properties of exponents:

1. **Problem Statement:** Solve the equation $$x^7 + x + 1 = 0$$ and find the value of $$5 \cdot x + \frac{1}{5 \cdot x}$$ for the root(s) of the equation. 2. **Understanding the p

1. **State the problem:** Solve the quadratic equation $$x^2 + x + 1 = 0$$ and analyze the expressions $$\frac{5}{x} + \frac{1}{x^5}$$. 2. **Recall the quadratic formula:** For an

1. **Stating the problem:** Given $x > 0$ and $$\frac{x^2}{1 + x^4} = \frac{1}{3},$$ find the value of $$\frac{x^4}{1 + x^8}.$$\n\n2. **Use the given equation:** From $$\frac{x^2}{

1. **State the problem:** We want to find the value of $$\frac{x^2}{x^4 + 1}$$ given that $$\frac{x^2}{x^2 + 1} = \frac{1}{4}$$. 2. **Given equation:** $$\frac{x^2}{x^2 + 1} = \fra

1. مسئله را بیان می‌کنیم: اگر \(\frac{x}{x^2+1} = \frac{1}{4}\) باشد، مقدار \(\frac{x^2}{x^4+1}\) را بیابید. 2. ابتدا معادله داده شده را بررسی می‌کنیم:

1. **State the problem:** Factor the expression $x^2 - 81$. 2. **Recall the formula:** This is a difference of squares, which follows the rule: