🧮 algebra

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: $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$.

1. The problem is to simplify the expression $\sqrt{2} (7 + \sqrt{3})$. 2. We use the distributive property: $a(b+c) = ab + ac$.

1. সমস্যাটি হলো: শতকরা বার্ষিক সরল সুদের হার কত হলে 10 বছরে সুদ, মূলধনের \frac{2}{5} অংশ হবে। 2. সরল সুদের সূত্র হলো: $$S = P \times r \times t$$ যেখানে \(S\) হলো সুদ, \(P\) হলো মূ

1. **State the problem:** We are given the equation $32\sqrt{2} = 2x^a$ and need to find the value of $a$. 2. **Rewrite the equation:** Note that $32 = 2^5$ and $\sqrt{2} = 2^{\fra

1. **State the problem:** We need to estimate $\sqrt{0.05}$ to the nearest hundredth using a number line, then calculate it to the nearest thousandth. 2. **Recall the formula:** Th

1. **State the problem:** Solve the quadratic equation $h^2 + 5h + 4 = 0$ for $h$. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the solution