🧮 algebra

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

1. **State the problem:** We have three types of tickets sold for a concert: adult, child, and student. We know the total tickets sold, total money collected, and the relationship

1. **Problem statement:** Given the system of equations: $$n + h = 12$$

1. **Problem statement:** We need to determine if it is possible to create a mango orchard where the length is twice the width and the area is 800 m². If possible, find the length

1. The problem is to understand and analyze the function $y = x^2$. 2. This is a quadratic function, which generally has the form $y = ax^2 + bx + c$. Here, $a=1$, $b=0$, and $c=0$

1. Let's start with a simple algebra problem: Solve for $x$ in the equation $2x + 3 = 7$. 2. The formula to isolate $x$ is to get $x$ alone on one side of the equation. We do this