🧮 algebra

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

1. **State the problem:** We are given two lines, l and k, and need to draw them on a coordinate diagram, find their intersection point R, and then find the area of triangle RST fo

1. **Problem statement:** (a)(i) Find the slope of the line $l$ passing through points $P(-3,6)$ and $Q(9,-2)$.

1. **Problema:** Calcolare il quadrato dei seguenti binomi algebrici: (2x^2 + 7y)^2, (x - 4y^2)^2, (3x^2 + 5xy)^2.

1. **Stating the problem:** Calculate the product of the binomials $$\left(\frac{3}{5} ab^{2} + 6\right)\left(\frac{3}{5} ab^{2} - 6\right)$$ using algebraic identities. 2. **Formu

1. **Problem statement:** Solve the equation $12x - 3 = 8x + 1$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable $x$ by performing the same ope

1. Il problema richiede di moltiplicare due prodotti notevoli: \(\left(\frac{3}{5} ab^{2} + 6\right)\left(\frac{3}{5} ab^{2} - 6\right)\) e \(\left(\frac{1}{4} x + \frac{3}{5} x^{2

1. **Stating the problem:** Simplify the expression $3a - 2b + a - 5b$. 2. **Formula and rules:** To simplify algebraic expressions, combine like terms. Like terms have the same va

1. **Problem statement:** Simplify each algebraic expression by combining like terms. 2. **Formula and rules:** Like terms have the same variable raised to the same power. To simpl

1. **State the problem:** We need to determine which number is larger: $$0.2^{2^{15}}$$ or $$0.05^{2^{10}}$$. 2. **Recall the properties of exponents:** For positive numbers less t

1. **Stating the problem:** Simplify the expression $$\left( \frac{a+b}{ab^2} - \frac{a-b}{a^2b} \right)^2 \cdot \frac{a^5b^6}{a^5b^2 - ab^6} - \frac{2ab}{a^2 - b^2}$$

1. **Stating the problem:** We are given the quadratic polynomial $$f(x) = 2x^2 - 4x - 5$$ and asked to check if $$x = 3$$ is a root (nulpunkt) of $$f(x)$$. 2. **Formula used:** To

1. **State the problem:** Simplify the expression $$\frac{5}{x^2 - 5x - 14} \div \frac{5x + 25}{x^2 - 2x - 35}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. **Problemstellung:** Wir sollen untersuchen, ob die Funktion $f$ einen direkt proportionalen Zusammenhang beschreibt anhand der Wertetabelle mit den Punkten $(4,9)$ und $(5,11)$

1. **Problemstellung:** Gegeben ist die Funktion $f$ mit den Werten $f(2)=4$ und $f(3)=6$. Es soll untersucht werden, ob $f$ einen direkt proportionalen Zusammenhang beschreibt. 2.