🧮 algebra

1. **State the problem:** Write expressions for given descriptions and describe given expressions in words.

1. مسئله: الگوی شکل‌ها را ادامه دهید و تعداد دایره‌ها را برای شکل‌های داده شده پیدا کنید و رابطه بین شماره شکل و تعداد دایره‌ها را بیابید. 2. مشاهده الگو: تعداد دایره‌ها در شکل‌ها

1. The problem is to find the value of $x$ when $y = -2.18$ for the function $y = -2.18$. 2. Since the function is a constant function $y = -2.18$, it means that for every value of

1. **State the problem:** We need to find the value of $b$ in the equation $$y = \frac{-0.42}{-0.65} \times 2.05 + b$$. 2. **Understand the equation:** The equation is in the form

1. **State the problem:** Solve the system of equations using the Gauss elimination method: $$\begin{cases} 2x + y + 6z = 14 \\ 3x + 5y + 2z = 21 \\ 4x + y - z = 1 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{7}{2} + \frac{3}{4} - \frac{2}{2}$$. 2. **Find a common denominator:** The denominators are 2 and 4. The least common deno

1. **State the problem:** Factorize the expression $2y(x - 1) + 5y(x - 1)^3$ by removing common factors. 2. **Identify common factors:** Both terms contain the factor $y$ and $(x -

1. **State the problem:** Simplify the expression $\frac{2}{4} + \frac{5}{4} + \frac{3}{4}$. 2. **Formula and rules:** When adding fractions with the same denominator, add the nume

1. **Problem Statement:** We need to compute the exact value of $k = \gcd(d, x^2 - 1)$, where $d$ and $x$ are integers. 2. **Understanding the problem:** The greatest common diviso

1. Let's clarify what "each term" means in a math expression. A term is a part of an expression separated by plus (+) or minus (-) signs. 2. For example, in the expression $3x^2 +

1. We are asked to multiply the fractions and variables in the expression $$-\frac{1}{4} \times 3$$. 2. The multiplication of a fraction and a whole number is done by multiplying t

1. **Problem statement:** The sum of two numbers is 50. We need to find the least value of the sum of their squares. 2. **Let the two numbers be** $x$ and $y$. Given:

1. **Problem statement:** 18 boys or 3 girls can complete a piece of work in 4 days. We need to find how many days 1 boy and 2 girls together will take to complete the same work. 2

1. **State the problem:** Solve the equation $$\frac{2X+5}{2} = \frac{3X}{5} + \frac{1}{4}$$ for $X$. 2. **Identify the formula and rules:** To solve for $X$, we need to eliminate

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

1. **State the problem:** Solve the equation $$\frac{3^{z+2}}{9^{z-2}} = 81$$ for $z$. 2. **Rewrite the bases:** Note that $9 = 3^2$ and $81 = 3^4$. Substitute these into the equat

1. **State the problem:** Simplify the expression $3x^2 - x + 6$. 2. **Identify the terms:** The expression consists of three terms: $3x^2$ (quadratic term), $-x$ (linear term), an

1. **State the problem:** Solve the equation $$\frac{3^{z+2}}{9^{z-2}} = 81$$ for $z$. 2. **Rewrite bases to the same base:** Note that $9 = 3^2$ and $81 = 3^4$. So rewrite the equ

1. Problemi: Gjej vlerën e $x$ në ekuacionin $me = e^{thelluat}$. 2. Së pari, duhet të kuptojmë se $me$ dhe $thelluat$ janë fjalë dhe nuk përfaqësojnë shprehje matematikore të njoh

1. Problemi: Të kuptojmë funksionet e fuqisë së tretë dhe funksionin përpjestimor të zhdrejtë. 2. Funksioni i fuqisë së tretë është i formës $$f(x) = x^3$$. Ky funksion merr një nu

1. مسئله: حاصل عبارت $$-(-5) \times (5045-1)$$ را بیابید. فرمول: ضرب اعداد و قوانین علامت‌ها.