🧮 algebra

1. Het probleem: We onderzoeken de eigenschappen van uitdrukkingen met de macht $x^3$. 2. Formule en regels: De macht $x^3$ betekent $x \times x \times x$.

1. **State the problem:** Simplify the expression $ (2x)^2 \times x $. 2. **Recall the formula:** When raising a product to a power, use the rule $ (ab)^n = a^n b^n $. Also, when m

1. Il problema riguarda le frazioni algebriche, cioè espressioni che contengono polinomi al numeratore e al denominatore. 2. La regola principale è che il denominatore non può mai

1. **Problema:** Si vuole costruire un recinto ad angolo formato da due lati maggiori di lunghezza $x$ e due lati minori congruenti, usando 60 m di rete. 2. **Formula per il perime

1. **Problème :** Factoriser l'expression $4x^2 - 28x + x^3 - 32$. 2. **Formule et méthode :** On regroupe les termes pour faciliter la factorisation par regroupement.

1. Das Problem lautet: Löse die Gleichung $$3x + 5 = 20$$ nach $$x$$ auf. 2. Die verwendete Formel ist die lineare Gleichung in der Form $$ax + b = c$$, wobei $$a$$, $$b$$ und $$c$

1. The problem is to plot the graph of the line given by the equation $$y = 4x + 3$$ where the gradient (slope) is positive. 2. The equation of a straight line in slope-intercept f

1. **State the problem:** We need to draw and understand the graph of the line given by the equation $y = 4x - 4$. 2. **Recall the formula:** The equation of a straight line in slo

1. **Problem statement:** Solve the system of equations using the Gleichsetzungsverfahren (equalization method) for part (a): (I) $4x + 5y = 12$

1. **State the problem:** Solve the equation $$\frac{x}{x - 1} = \frac{10}{x + 3}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, cross-multiply to eliminat

1. **Enunciado do problema:** Escreva na forma de polinómio reduzido cada uma das expressões dadas. 2. **Fórmula usada:** Para multiplicar dois polinómios, usamos a distributiva: $

1. **State the problem:** Solve the inequality $$\frac{3x - 2}{4} \leq \frac{4x + 1}{3}$$. 2. **Write the inequality:** $$\frac{3x - 2}{4} \leq \frac{4x + 1}{3}$$.

1. Calculer $A = 9(c + 3)$ pour $c = 11$. 2. Calculer $B = 14y + 9$ pour $y = 2$.

1. **Problemstellung:** Wir sollen für jede der vier Figuren den Term für den Flächeninhalt der gefärbten Fläche angeben. 2. **Wichtige Formel:** Der Flächeninhalt eines Quadrats m

1. The problem asks to identify the domain and range of the function $f(x)$ from the given graph points. 2. The domain of a function is the set of all possible input values ($x$-va

1. The problem asks to find the domain and range of the function $f(x)$ based on the given graph with points at approximately $(-10, 2)$, $(-4, -5)$, $(-1, -9)$, $(6, -2)$, and $(9

1. The problem states that $C(g)$ represents the cost to produce $g$ gallons of chocolate chunk ice cream. 2. The statement $C(727) = 152$ means that when $g = 727$, the cost $C(g)

1. The problem states that $D(t)$ represents the total average credit card debt in a U.S. household (in thousands of dollars) $t$ years after 1995. 2. We are given $D(24) = 20.3$.

1. **State the problem:** We are given a table of values for a function $f(x)$ and asked to evaluate $f(21)$ and find $x$ when $f(x) = 18$. 2. **Given table:**

1. The problem asks to complete the table by matching function notation values with ordered pairs. 2. Function notation $f(input) = output$ means the function $f$ takes an input an

1. **Problem Statement:** Determine the domain and range of the given piecewise line graph with endpoints at approximately $(-5,-5)$ and $(1,2)$, and vertices near $(-4,-2)$ and $(