🧮 algebra

1. **State the problem:** Find the center of the circle given by the equation $$x^2 + y^2 - 8x + 11y - 2 = 0$$. 2. **Formula and rules:** The general form of a circle's equation is

1. Planteamos el problema: Resolver la inecuación $$-12x - 10 \leq 5$$. 2. Sumamos 10 a ambos lados para aislar el término con $x$:

1. The problem is to determine which of the two given answers satisfies the equation. 2. To check if a value satisfies an equation, substitute the value into the equation and simpl

1. **State the problem:** Solve the equation $$\arctan(3x) + \arctan(2x) = \frac{\pi}{4}$$ for $x$. 2. **Formula used:** The sum of arctangents formula is

1. **State the problem:** We are given the linear equation $$-3x + y = 2$$ and a table of values for $x$: -1, 0, 1. We need to find the corresponding $y$ values and understand the

1. **State the problem:** Solve the equation $$249 \cdot 3^{x+2} = \frac{1}{9}$$ for $x$. 2. **Recall the properties of exponents:**

1. **State the problem:** Simplify the expression $$\frac{w^2 - 10w + 21}{18 - 2w^2}$$. 2. **Factor numerator and denominator:**

1. **State the problem:** Simplify the rational expression $$\frac{2u^2 - 8}{u^2 - u - 6}$$. 2. **Factor numerator and denominator:**

1. **State the problem:** Solve for $n$ in the equation $6.3 = 9n$. 2. **Formula and rules:** To isolate $n$, divide both sides of the equation by 9.

1. **State the problem:** Solve the equation $3m = 39$ for $m$. 2. **Formula and rules:** To solve for $m$, we need to isolate $m$ on one side of the equation. Since $m$ is multipl

1. **State the problem:** Solve for $n$ in the equation $52 = \frac{n}{3}$. 2. **Formula and rules:** To isolate $n$, multiply both sides of the equation by 3 to cancel the denomin

1. **State the problem:** Solve the equation $$832 - n = 365$$ for the variable $$n$$. 2. **Isolate the variable:** To find $$n$$, we need to isolate it on one side of the equation

1. **State the problem:** Solve the equation $$39 = x - 72$$ for $$x$$. 2. **Formula and rules:** To isolate $$x$$, add 72 to both sides of the equation to cancel out the $$-72$$.

1. **State the problem:** Solve the equation $$e^{3+2\ln(x)} = (3x - 2) e^3$$ for $x$. 2. **Recall the properties and formulas:**

1. **Planteamiento del problema:** Se debe cubrir un patio de dimensiones 4,21 m por 5,33 m con losetas que se venden en cajas de dos tipos: una caja cubre 2 m² y cuesta 70, otra c

1. **State the problem:** Solve the equation $ (x^2 - 3) \times \ln(3x) = 0 $. 2. **Formula and rules:** For a product of two factors to be zero, at least one of the factors must b

1. **State the problem:** Simplify the expression $$\frac{\frac{1}{k+2}}{\frac{5}{k^2-4}}$$. 2. **Recall the formula:** Dividing by a fraction is the same as multiplying by its rec

1. **State the problem:** Subtract the two rational expressions: $$\frac{6}{x^2 + 4x - 32} - \frac{x - 5}{x - 4}$$

1. **State the problem:** We have an equilateral triangle with side lengths of $x + 9$ inches. The perimeter is given by the expression $3(x + 9)$. We want to find which expression

1. **Plantejament del problema:** Tenim dues bases A i B de \(\mathbb{R}^3\) i un vector \(v\) expressat en la base A amb coordenades \(\left(\frac{15}{4},1,2\right)\). Calculem le

1. Du fragst nach der Formel, die in Aufgabe 2 verwendet wurde. 2. Ohne den genauen Kontext von Aufgabe 2 zu kennen, erkläre ich eine häufig genutzte Formel in Algebra: die quadrat