🧮 algebra

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.

1. The problem involves interpreting a table of values with columns labeled $r$, $t^r$, $T$, $t$, and $1$. 2. Each column likely represents a variable or parameter in a mathematica

1. **State the problem:** Evaluate the expression $$\left[\left(\frac{2}{3} + \frac{3}{4}\right)^2 \div \left(\frac{5}{6} - \frac{1}{3}\right)\right] + \sqrt{81} - 2^3$$. 2. **Reca

1. The problem is to find the product of the matrix \(\begin{bmatrix}a & b \\ c & d\end{bmatrix}\) with itself, i.e., compute \(\begin{bmatrix}a & b \\ c & d\end{bmatrix} \times \b

1. مسئله: تابع پارامتریک $f$ تعریف شده روی بازه $[0,3]$ به صورت $$f(x) = 2x^3 + a$$ است. الف) مقدار $a$ را طوری بیابید که $f(1) = 3$ باشد.

1. Muammo: $x=\frac{\sqrt{a+2b}+\sqrt{a-2b}}{\sqrt{a+2b}-\sqrt{a-2b}}$ bo'lsa, $bx^2-ax+b$ ifodasini soddalashtiring. 2. Avvalo, $x$ ni soddalashtirish uchun kasrni quyidagi tarzda