🧮 algebra

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

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + y + z = 2 \\ 3x - 4y - 4z = -1 \\ 2x - 5y + 2z = -17 \end{cases}$$

1. **State the problem:** Convert the recurring decimal $0.26\dot{6}$ (where 6 repeats indefinitely) into a fraction in simplest form. 2. **Understand the notation:** The decimal $

1. Let's create a challenging algebra problem involving quadratic equations and systems. 2. Problem: Solve the system of equations:

1. Let's start by stating the problem: We want to understand the next phase of surds, which involves simplifying expressions containing roots (square roots, cube roots, etc.). 2. T

1. Let's continue with surds, which are expressions containing roots, such as square roots, cube roots, etc. 2. The main rules for surds are:

1. **Problem Statement:** Determine the nature of the system of linear equations: $$\begin{cases} x + y + z = 6 \\ x + 2y + 3z = 14 \\ x + 4y + 7z = 30 \end{cases}$$

1. **State the problem:** We need to find a polynomial expression for the perimeter of the given L-shaped polygon with sides labeled $x$, $3y$, $y$, $2y$, and $3x$. 2. **Recall the

1. **State the problem:** Simplify the expression $$\frac{5}{6} - \frac{2}{3} \times \frac{3}{8}$$. 2. **Recall the order of operations:** Multiplication must be done before subtra

1. **State the problem:** We have two sauces being mixed: one is 5 ounces with 50% tangy mustard, and the other has an unknown amount $x$ ounces with 75% tangy mustard. The resulti

1. Let's start by understanding what surds are. A surd is an irrational root, usually a square root, that cannot be simplified to remove the root sign. For example, $\sqrt{2}$ is a

1. **State the problem:** Simplify the algebraic expression $3r^2 - rs + 5s + r^2 - 2rs - 4s$. 2. **Combine like terms:** Group terms with $r^2$, terms with $rs$, and terms with $s

1. **State the problem:** Simplify the algebraic expression $pq - 1 - p^2 + 5p - 5pq - 2p$. 2. **Group like terms:** Group terms involving $pq$, $p$, and constants separately:

1. **State the problem:** Calculate the value of $1.5 \times 10^{-3}$ divided by $311 \times 10$.

1. Let's start by stating the problem: A quadratic equation is any equation that can be written in the form $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are constants and $a \neq

1. The problem is to simplify the expression $$(4 - \sqrt{5})(4 + \sqrt{5})$$ and find which of the given options (A. 9, B. 11, C. 21, D. -1) is correct. 2. This expression is a pr

1. The problem is to simplify the expression $(5\sqrt{3})(3\sqrt{6})$. 2. Recall the multiplication rule for radicals: $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$.