🧮 algebra

1. **State the problem:** Solve the system of linear equations: $$3x + 9y = 0$$

1. **State the problem:** Solve the system of linear equations: $$3x + 8y = 34$$

1. **State the problem:** Solve the equation $3x + 8y = 34$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by moving o

1. El problema nos pregunta: ¿De qué número su sexta parte es 18? 2. La fórmula para este tipo de problema es: $$\frac{x}{6} = 18$$ donde $x$ es el número que buscamos.

1. Para problemas de partes de un número, usa la fórmula: $$\text{Parte} = \frac{1}{n} \times \text{Número}$$ donde $n$ es la fracción del número. 2. Para encontrar la fracción de

1. **Problem a:** Solve the simultaneous equations using matrix method: $$\begin{cases} 2x + 5y = 13 \\ 2x - 3y = 5 \end{cases}$$

1. Planteamos el problema: calcular $$\sqrt{\left(1 - 2 : \frac{1}{2}\right) \cdot 0,3\overline{3} + 4,9\overline{9}} - \frac{3}{4}$$. 2. Recordemos que dividir por una fracción es

1. **Problem statement:** Solve the system of equations $$\begin{cases}(3x+2)(2y-3)=6xy\\(4x+5)(y-5)=4xy\end{cases}$$

1. **State the problem:** We are given two functions $f(x) = x + 9$ and $g(x) = 2x + 3$. We need to find the value of $f(g(3))$. 2. **Understand the composition:** The expression $

1. **Nêu bài toán:** Tìm tất cả các giá trị của tham số $m$ sao cho đồ thị hàm số $$y = x^3 + 2x^2 + (m - 3)x + m$$ có hai điểm cực trị và điểm $M(9; -5)$ nằm trên đường thẳng đi q

1. **Problem statement:** Solve the equation $x(x + 2) - 2x(x - 3) = 5 - x^2$. 2. **Formula and rules:** Use distributive property and combine like terms.

1. **Problem:** Solve the system of equations from Bài 3: Two cyclists start simultaneously from two cities 38 km apart, moving towards each other. They meet after 2 hours. The fir

1. Giải phương trình $x(x + 2) - 2x(x - 3) = 5 - x^2$. Bước 1: Mở rộng và rút gọn các biểu thức.

1. **Problem:** Solve the equation $x(x + 2) - 2x(x - 3) = 5 - x^2$. 2. **Formula and rules:** Use distributive property and combine like terms.

1. **Problem statement:** We have a roller-coaster track modeled by a cubic function $$y = ax^3 + bx^2 + cx + d$$ for $$0 \leq x < 90$$ meters. The track passes through points:

1. **State the problem:** We are given the expression $$n=\frac{(N-1)E^2+Z^2s^2}{N\cdot Z^2\cdot s^2}$$ with values $$N=4999, E=1, Z=1.7507, s=8.9346$$ and need to evaluate $n$.

1. **Stating the problem:** We are given the mass $y$ (in grams) of an ice cube with side length $x$ (in cm) as follows:

1. The user asked to simplify and show a clear answer, but no specific expression or problem was provided. 2. To help, please provide the exact expression or problem you want simpl

1. **State the problem:** We are given two statues, each made of three parts with given heights as mixed numbers. We need to find which statue is taller and the difference in their

1. **State the problem:** Simplify the expression $$\frac{2}{\sqrt[3]{3} - \sqrt[4]{5}}$$. 2. **Formula and rules:** To simplify expressions with radicals in the denominator, we ra

1. The problem is to find the value of $x$ in the equation $$\frac{2x+3}{4} = 5.$$ 2. The formula used here is to solve for $x$ by isolating it on one side of the equation. We do t