🧮 algebra

1. مسئله: حل معادله $2x + 3 = 7$. 2. فرمول: برای حل معادله خطی، هدف این است که $x$ را تنها کنیم.

1. **Problem statement:** Find the equation of line L perpendicular to the line $2y + x = 1$ and passing through point $(2, -1)$.

1. The problem is to understand what an improper divisor is. 2. In mathematics, a divisor (or factor) of a number is a number that divides it exactly without leaving a remainder.

1. مسئله: جملات داده شده به صورت کسرهایی با صورت و مخرج مشخص هستند: $$\frac{3}{1}, \frac{6}{1}, \frac{6}{1}, \frac{7}{1}, \frac{15}{2}, \frac{39}{5}, \frac{8}{1}, \frac{57}{8}$$

1. **Énoncé du problème :** Trouver la fonction $f(x) = \frac{x^2}{\ln(x) - 1}$. 2. **Domaine de définition :** La fonction est définie pour $x > 0$ car $\ln(x)$ est défini uniquem

1. The problem is to understand why $q^2$ can divide the expression $3p(p-1)$. 2. To say that $q^2$ divides $3p(p-1)$ means that when you divide $3p(p-1)$ by $q^2$, the result is a

1. The problem is to understand how to order terms by their exponents from biggest to smallest. 2. When dealing with expressions involving exponents, the exponent indicates the pow

1. The problem is to understand how to write a polynomial in standard form. 2. A polynomial is an expression consisting of variables and coefficients, combined using addition, subt

1. **State the problem:** Expand the expression $$(2a - 1)^6$$ using the binomial theorem. 2. **Formula used:** The binomial theorem states that

1. **State the problem:** Expand the expression $$(4a - b)^3$$. 2. **Formula used:** The cube of a binomial $$(x - y)^3$$ expands as $$x^3 - 3x^2y + 3xy^2 - y^3$$.

1. **State the problem:** Simplify or expand the expression $$(4^a - b)^3$$. 2. **Formula used:** We use the binomial expansion formula for cubes: $$(x - y)^3 = x^3 - 3x^2y + 3xy^2

1. **State the problem:** An ice cream shop creates 25 new flavors and discards the 13 least popular ones. They produce 80 cartons of each remaining flavor. Each 2 cartons make 1 l

1. **State the problem:** Solve the quadratic equation $63x^2 = 175$ for $x$. 2. **Rewrite the equation:** To isolate $x^2$, divide both sides by 63:

1. The problem is to evaluate the expression $10 \div 2 (4 + 4)$. 2. According to the order of operations (PEMDAS/BODMAS), first solve the parentheses.

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 -