🧮 algebra

1. The problem is to convert a recurring decimal into a fraction. 2. Let's consider the recurring decimal $x = 0.\overline{3}$, which means the digit 3 repeats indefinitely.

1. المشكلة: حل المعادلة. 2. أولاً، يجب تحديد نوع المعادلة (خطية، تربيعية، إلخ) لمعرفة الطريقة المناسبة للحل.

1. **Problem Statement:** Given the equation $\left(x + \frac{1}{x}\right)^2 = 5^2$, find the values of expressions involving powers of $x$ and $\frac{1}{x}$. 2. **Step 1: Expand t

1. **Stating the problem:** We are given the algebraic expression $4 + n$ and asked to evaluate it when $n = 2$. 2. **Understanding the expression:** The expression $4 + n$ means t

1. The problem is to understand the difference between an algebraic expression and an algebraic equation, and solve the equation given. 2. An algebraic expression is a combination

1. **State the problem:** Solve the linear equation $3x - 6 = 12x + 9$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performi

1. **Stating the problem:** Nanjala and Cherono start from Mwanzo towards Mwisho, which are 17 km apart. Nanjala walks at 9 km/h and starts 45 minutes before Cherono, who cycles at

1. **Тооцоолох асуудлыг тодорхойлно:** Тооцоолох илэрхийлэл нь $$8.4 \div \left(-\frac{2}{5} + 0.2\right)$$ байна.

1. **State the problem:** Solve the inequality $x - 8 > 1$ for $x$. 2. **Recall the rule:** To solve inequalities, you can add or subtract the same number on both sides without cha

1. **State the problem:** We have a rectangular parking lot enclosed by a fence of length 110 meters. The length of the parking lot is 5 meters more than its width. We need to find

1. **State the problem:** Rationalise the denominator of the expression $\frac{6}{\sqrt{10}}$ and simplify the result. 2. **Formula and rule:** To rationalise a denominator contain

1. **State the problem:** Expand and simplify the expression $$(2 - \sqrt{5})(1 - 3\sqrt{5})$$. 2. **Formula used:** Use the distributive property (FOIL method) to expand the produ

1. The previous question involved solving a quadratic equation or analyzing a function (assuming from context). 2. To join this with the previous question, we need to clarify the e

1. **State the problem:** Simplify the expression $$\frac{2}{f(x)} - \frac{5}{g(x)}$$ as a single fraction in terms of $x$. 2. **Formula and rules:** To subtract fractions, find a

1. **State the problem:** We are given two functions $f(x) = 3x - 4$ and $g(x) = 4x + 1$. We need to find: (a) $f(-2)$

1. The problem involves understanding and performing operations with fractions and decimals arranged in a matrix-like format. 2. We start by interpreting each value: fractions like

1. সমস্যাটি হলো: $x^3 + \frac{1}{x^3} = 18\sqrt{3}$ এবং $p = 10^3 + 2\sqrt{42}$, এবং $a^4 - 4a + 3$ উপাদানকে বিশ্লেষণ করতে হবে, সাথে $p^4 - \frac{1}{p^4}$ এর মান নির্ণয় করতে হবে।

1. The problem is to convert the fraction $\frac{1}{8}$ into a decimal. 2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator.

1. **Problem statement:** Find the value of $x$ for the parallelogram where one side is $5x + 10$ and the opposite side is $130$. 2. **Formula and rule:** Opposite sides of a paral

1. **State the problem:** We are given the linear equation $4x + 5y = 20$ and its slope-intercept form $y = -\frac{4}{5}x + 1$. We need to understand the graph of this line and sol

1. The problem is to graph the linear equation $4x + 5y = 20$ and understand its slope-intercept form. 2. The slope-intercept form of a line is given by $y = mx + b$, where $m$ is