🧮 algebra

1. **State the problem:** Solve the system of linear equations: $$\begin{cases}-4x + y = 6 \\ -5x - y = 21\end{cases}$$

1. **Problem statement:** Factorize the expressions by factoring out the greatest common factor (GCF). 2. **Formula and rules:** To factor out the GCF, find the largest factor comm

1. **State the problem:** Solve the system of equations: $$\frac{1}{2}x + 6y = 12$$

1. **State the problem:** Simplify the expression $x^2 (x^{-1} + y^{-1}) \cdot xy (x+y)^2$. 2. **Recall the rules:**

1. **Problema 11:** $v(r)=\frac{4}{3}\pi r^3$. Fórmula usada: $\frac{d}{dr}(r^n)=nr^{n-1}$.

1. Dada la función $$v(r) = \frac{4}{3} \pi r^3$$ 2. Dada la función $$G(y) = y^{10} + 7y^5 - y^3 + 1$$

1. **State the problem:** Solve the equation $4X - 3 = 2(X + 5)$. 2. **Use the distributive property:** Expand the right side:

1. **State the problem:** Solve the equation $4x - 3 = 2(x + 5)$. 2. **Write the formula and rules:** We use the distributive property and properties of equality to isolate $x$.

1. **Nêu vấn đề:** Chúng ta sẽ tìm hiểu về đơn thức, đa thức và các phép tính đại số cơ bản gồm cộng, trừ, nhân, chia. 2. **Đơn thức:** Là biểu thức đại số gồm một số và một hoặc n

1. El problema es resolver el sistema de ecuaciones por el método de sustitución: $$\begin{cases} x - y = 4 \\ x = 3y \end{cases}$$

1. Planteamos el problema: Comparar la proporción de azúcar respecto al cacao en dos recetas. 2. La fórmula para la proporción es: $$\text{Proporción} = \frac{\text{azúcar}}{\text{

1. **State the problem:** Solve the equation $2x + 5 = 3(x - 2)$. 2. **Write the formula and rules:** We will use the distributive property and properties of equality to isolate $x

1. **State the problem:** Solve the equation $$3(4 - x) = 6(x + 2)$$ for $x$. 2. **Rewrite the equation:** Distribute the constants on both sides:

1. **State the problem:** We are given the function $s(x) = \mu[\sin(2x) - 1]$ defined on the interval $[-\pi, \pi]$ and the inequality $s(x) < \frac{1}{2}$. We need to determine t

1. El problema pide resolver la expresión: $$(-c)^0 \cdot (-c) \cdot (-c)^{11} \cdot (-c)^{10} : (-c)^{22}$$. 2. Recordemos las propiedades de las potencias:

1. **Planteamiento del problema:** Calcular el valor de la expresión $$(-c)^\circ \cdot (-c) \cdot (-c)^{11} \cdot (-c)^{10} : (-c)^{22}$$. 2. **Reglas y fórmulas importantes:**

1. **State the problem:** Solve the system of linear equations: $$y = 0.5x + 4$$

1. **State the problem:** Solve the system of linear equations: $$-6x + y = 3$$

1. **Resuelve la ecuación** $\frac{1}{6} = \frac{x}{5}$ para encontrar $x$. 2. Usamos la propiedad de las proporciones: $$\frac{a}{b} = \frac{c}{d} \implies ad = bc$$

1. **Problem:** Calculate the value of expression a) from Bài 8: $$2^3 - \frac{5^3}{5^2} + 12 \cdot 2^2$$ 2. **Formula and rules:**

1. **Problem:** Calculate the value of expression a) from Bài 8: $$2^3 - \frac{5^3}{5^2} + 12 \cdot 2^2$$ 2. **Formula and rules:**