🧮 algebra

1. **Stating the problem:** Calcolare il valore dell'espressione $$\left(\frac{1}{\sqrt[3]{3}} + \frac{1}{\sqrt[3]{9}}\right) \cdot \frac{6}{\sqrt[3]{3} + \sqrt[3]{9}}$$.

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Rewrite division as multiplication by the reciprocal:**

1. **Problem:** Find a function for the sinusoidal graph with amplitude 3, midline $y=0$, x-intercepts at $-\frac{2\pi}{3}$, $0$, and $\frac{2\pi}{3}$, and a negative slope at $x=0

1. **State the problem:** Simplify the expression $$(2u^{-2}v^{2})^{2} \cdot 2v^{-5}$$. 2. **Apply the power of a product rule:** $$(ab)^n = a^n b^n$$, so

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Recall the division rule for fractions:** Dividing by a

1. **State the problem:** Solve the linear equation $16 - 2t = 5t + 9$ for $t$. 2. **Write the formula and rules:** To solve for $t$, we want to isolate $t$ on one side of the equa

1. Il problema chiede di risolvere l'espressione $y^3 + \frac{7}{4}y + 1 : \left(y + \frac{1}{2}\right)$ usando il metodo di Ruffini. 2. Il metodo di Ruffini si usa per dividere un

1. **Stating the problem:** Simplify the expression $$\frac{y(alla 3)+\frac{7}{4}y+1}{y+\frac{1}{2}}$$. It seems "alla 3" means $y^3$, so the expression is $$\frac{y^3 + \frac{7}{4

1. **Resuelve el sistema de ecuaciones:** \[\begin{cases} 3 \log x - 2 \log y = 4 \\ \log(xy) = 3 \end{cases}\]

1. **Planteamiento del problema:** Resolver el sistema de ecuaciones: $$\begin{cases} 3 \log x - 2 \log y = 4 \\ \log(x \cdot y) = 3 \end{cases}$$

1. **Problem statement:** Tina drives 150 km from Cork to Kilkenny, leaving at 7:45 a.m. She stops for 15 minutes to charge her car. The average speed for the whole journey is 60 k

1. **State the problem:** We need to calculate the income tax Artem pays on his gross earnings with a tiered tax rate and an annual tax credit.

1. **State the problem:** Solve the quadratic equation $$x^2 + 8x = 13$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the equation $2x - 2 = \sqrt{3x^2 + 13}$ for $x$. 2. **Formula and rules:** To solve equations involving square roots, we isolate the square root te

1. We beginnen met het probleem: vereenvoudig de breuk $$\frac{v^2}{188v}$$. 2. De formule die we gebruiken is het vereenvoudigen van breuken door gemeenschappelijke factoren te sc

1. Vamos resolver a equação quadrática dada: $$2x^2 - 5x = 0$$. 2. Para resolver, usamos a propriedade distributiva para fatorar a equação:

1. **Énoncé du problème** : Trouver les fonctions dérivées des fonctions données. 2. **Rappel des règles** :

1. The question asks about the location of the exponent 2 in step 6 of a problem. 2. Typically, an exponent 2 means squaring a quantity, which applies to the entire expression or t

1. **Problemstellung:** Gegeben ist die Funktion $f(x) = -4x + 3$. Wir sollen den Achsenabschnitt, die Nullstelle, den Fixpunkt, die Umkehrfunktion berechnen und eine Zeichnung anf