🧮 algebra

1. **Problem statement:** We are asked to perform a Kurvendiskussion (curve discussion) for the function $$f(x) = (x - 1) \cdot (x + 2)^2$$ starting with expanding (Ausklammern) th

1. Il problema chiede di utilizzare il teorema del resto per trovare il resto della divisione di un polinomio per un binomio del tipo $x - a$. 2. Il teorema del resto afferma che i

1. **State the problem:** We are given two functions: $$A(x) = x^3 - 2x^2 - 11$$

1. **Problem statement:** (a) Determine the temperature shown on the thermometer.

1. **State the problem:** Solve the equation $$\frac{2x+3}{4} = \frac{x-1}{2}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by th

1. **State the problem:** Solve the equation $$\frac{2x+3}{4} = \frac{x-1}{2}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by th

1. **Problemstellung:** Zeichne die Graphen der linearen Funktionen $f$, $g$ und $h$ aus Aufgabe 9a) in dasselbe Koordinatensystem. Gegeben sind:

1. **Problemstellung:** Gegeben ist die lineare Funktion $f(x) = 0{,}4x + 1$. Wir sollen den Graphen zeichnen und den Schnittpunkt mit der y-Achse bestimmen. 2. **Formel und wichti

1. **Problem:** Given the parametric form of a plane $E$, find its coordinate form (Cartesian equation). 2. **Formula and rules:**

1. **State the problem:** Find six numbers whose mean is 3 and range is 0. 2. **Recall the formulas:**

1. **State the problem:** Find six numbers whose mean is 3 and range is 6. 2. **Recall the formulas:**

1. Problem: Berechne a) aus Aufgabe 4: $-3 - 1,5 : \frac{5}{6}$. 2. Formel und Regeln: Division durch einen Bruch entspricht Multiplikation mit dem Kehrwert, also $a : \frac{b}{c}

1. **State the problem:** Identify which expressions are equivalent to $\frac{m^5}{n^5}$ and multiply the binomials $(x - 1.2)(-0.2x)$.

1. **State the problem:** Find the equation of line N in the form $y = mx + c$ given it crosses the y-axis at 20 and passes through the point $(1, 35)$. 2. **Recall the formula:**

1. **State the problem:** Solve the logarithmic equation $$\log(5x^2) - \log(8) = 1$$. 2. **Recall the logarithm subtraction rule:** $$\log(a) - \log(b) = \log\left(\frac{a}{b}\rig

1. **State the problem:** Find the unit rate for each table where $x$ and $y$ values are given. 2. **Formula:** The unit rate is found by dividing $x$ by $y$ or $y$ by $x$, dependi

1. **State the problem:** We are given four functions and asked to compare their slopes and y-intercepts. 2. **Identify slopes and y-intercepts:**

1. **State the problem:** We are given four functions and need to compare their y-intercepts and slopes. 2. **Given information:**

1. El problema presenta tres matrices 3x3 y dos operaciones elementales de filas aplicadas entre ellas. Debemos determinar si las operaciones son correctas y qué se puede concluir

1. **State the problem:** We are given gallons per minute (gpm) for sections B, C, D, E, F, and G, and several inequalities involving section A's gpm. We need to determine the poss

1. **State the problem:** Multiply the binomials $ (x + 19)(3x + 1) $. 2. **Formula used:** To multiply two binomials, use the distributive property (also known as FOIL method for