🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{-125} \times (1 - 0.8)^2 + 0.3}{(\frac{1}{5})^{-1} - \sqrt{2.25}}$$

1. El problema pide expresar cada operación como una sola potencia. 2. La regla importante es que para potencias con el mismo exponente $n$, se puede usar la propiedad:

1. **State the problem:** We need to find the total amount of money given to the three children as pocket money by their father. 2. **Analyze the problem:** The problem does not pr

1. Planteamos resolver la ecuación $$\frac{x^2}{5} - \frac{x}{2} = \frac{3}{10}$$ usando la forma general de la ecuación cuadrática. 2. Multiplicamos toda la ecuación por 10 para e

1. Planteamos la ecuación: $$\frac{x^2}{5} - \frac{x}{2} = \frac{3}{10}$$ 2. Multiplicamos toda la ecuación por 10 (mínimo común múltiplo de 5, 2 y 10) para eliminar denominadores:

1. **State the problem:** Simplify the expression $10 - 10 \times 10 + 10$. 2. **Recall the order of operations:** According to PEMDAS/BODMAS, multiplication is performed before ad

1. **Planteamiento del problema:** Dada la transformación lineal $T : \mathbb{R}^3 \to \mathbb{R}^3$ definida por

1. **Stating the problem:** Calculate the value of the expression:

1. Problema 2: Resolver la ecuación $2x + 3 = 11$. - Fórmula: Para resolver ecuaciones lineales, aislamos la variable $x$.

1. **State the problem:** Calculate 15,000 multiplied by 2.5%. 2. **Formula and rules:** To find a percentage of a number, convert the percentage to a decimal by dividing by 100, t

1. **State the problem:** Calculate 15000 multiplied by 5%. 2. **Formula:** To find a percentage of a number, use the formula $$\text{Percentage value} = \text{Total} \times \frac{

1. The problem is to calculate the value of $\frac{297,973}{890,960} \times 100$. 2. The formula used here is to find the percentage of one number relative to another: $$\text{Perc

1. **State the problem:** Solve the equation $2x + 3x = 15$ by collecting like terms and isolating the variable. 2. **Formula and rules:** When adding terms with the same variable,

1. The problem asks to find 1% of 109,153. 2. The formula to find a percentage of a number is: $$\text{Percentage value} = \frac{\text{percentage}}{100} \times \text{total number}$

1. **State the problem:** We need to find a number based on place value clues: - 1 ten thousand

1. **Problem statement:** Solve the system of equations: $$x^2 - y^2 = \frac{15\sqrt{x} - 17\sqrt{y}}{4\sqrt{xy}}$$

1. Du hast mich gebeten, nur die Scheitelpunkte jeder Aufgabe anzugeben. 2. Der Scheitelpunkt einer Parabel in der Form $y = ax^2 + bx + c$ wird mit der Formel $\left(-\frac{b}{2a}

1. Das Problem verlangt nur die Scheitelpunkte einer Funktion. 2. Der Scheitelpunkt einer Parabel $y = ax^2 + bx + c$ wird mit der Formel $x = -\frac{b}{2a}$ berechnet.

1. Problem: Berechne die Schnittpunkte der Funktionen f(x) und g(x) für jede Aufgabe. 2. Allgemeine Methode: Schnittpunkte zweier Funktionen erhält man, indem man f(x) = g(x) setzt

1. **Problem statement:** Find the intersection points of the functions \(f(x) = -3x\) and \(g(x) = x^2\). 2. **Set the functions equal to find intersection points:**

1. The problem is to find the correct premium subscription price using the revenue function, which is linear. 2. The revenue function is given by $$R(p) = p \times q(p)$$ where $p$