🧮 algebra

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

1. I corresponde a $h(x) = -3x^2$. 2. II corresponde a $f(x) = -x^2$.

1. **Stel het probleem vast:** We hebben twee getallen, noem ze $x$ (eerste getal) en $y$ (tweede getal). We weten dat: - Het eerste getal $x$ is 5 meer dan het dubbel van het twee

1. **State the problem:** We are given four quadratic equations and two graphs with their properties. We need to match each graph to the correct equation and find the axis of symme

1. **State the problem:** Given a downward-opening parabola with vertex approximately at $(-3,4)$, axis of symmetry $x=-3$, and zeros at $(-5,0)$ and $(-1,0)$, identify the axis of

1. The problem is to solve the inequality $$\frac{12q}{x} > 43$$ for $x$. 2. We want to isolate $x$ on one side. Since $x$ is in the denominator, we multiply both sides by $x$, but

1. **State the problem:** Simplify the expression $X9 + 1$. 2. **Identify the expression:** The expression appears to be $X9 + 1$. Assuming $X9$ means $9X$ (9 times $X$), the expre

1. **State the problem:** Solve for $x_{1/2}$ using the quadratic formula given by $$x_{1/2} = \frac{-0.7 \pm \sqrt{0.49 + 0.6}}{0.4}$$

1. **State the problem:** Ojo is 3 years older than Pejee. We need to find Ojo's age. 2. **Define variables:** Let Pejee's age be $p$ years.

1. **State the problem:** Determine if the ordered pairs (-1, 0), (-1, 5), and (0, -3) satisfy the system of inequalities: $$y \leq 3x + 4$$

1. The problem is to determine if given ordered pairs are solutions to the inequality derived from the line equation $y = 2 - \frac{3x}{2}$ and to prove algebraically that $(2,1)$