🧮 algebra

1. Problem: Vervollständigen Sie die Tabelle mit quadratischen Funktionen in Scheitelpunktform und allgemeiner Form sowie den Scheitelpunkten. 2. Formel: Die Scheitelpunktform eine

1. **State the problem:** Simplify the expression $$\frac{(2h - 3k)^2}{(10h - 15k)} \div hk$$. 2. **Rewrite the division as multiplication by the reciprocal:**

1. **State the problem:** Solve the equation $$\frac{1}{2}n = 4^{n+1}$$ for $n$. 2. **Rewrite the equation:** The equation is $$\frac{1}{2}n = 4^{n+1}$$.

1. **Problem statement:** Paul is currently 1.86 m tall and shrinks 1 mm (0.001 m) per year. Marrit is 1.75 m tall and grows 1 cm (0.01 m) per year. We want to find after how many

1. **State the problem:** We are given two expressions:

1. Stating the problem: Calculate the value of the expression $$(3-3) \cdot 5 - [2 - 4 \cdot (4 + 3) + 2] \cdot 3$$. 2. Apply the order of operations (parentheses, multiplication,

1. **Problemstellung:** Schreibe jede Exponentialgleichung in logarithmischer Form. 2. **Formel:** Die allgemeine Umwandlung von Exponential- zu Logarithmusform lautet:

1. **Problemstellung:** Berechnen Sie die Nullstellen der ganzrationalen Funktionen mittels Polynomdivision für die Aufgaben c) und e): c) $$f(x) = -x^4 + 4x^3 - 16x + 16$$

1. The problem is to simplify or analyze the expression or polynomial given: $3x^3 + 2x^2 + 1$ and compare or relate it to other expressions like $2x^2$ and $2x + 5$. 2. Since no e

1. **State the problem:** Determine which expression is a monomial upon simplification between $\frac{x^4}{x^5}$ and $\frac{x^3}{x^2}$. A monomial is a polynomial with only one ter

1. Énoncé du problème : On considère une suite arithmétique $(u_n)$ telle que $u_3=12$ et la raison $r=-2$. Il faut calculer $u_0$, donner l'expression générale de $u_n$ en fonctio

1. **Stating the problem:** Factorise the given expression (not specified, so assuming a general approach). 2. **Formula and rules:** To factorise an expression, we look for common

1. **Problem:** Expand and simplify $ (x + 3)(x + 5) + 4(x - 2) $. 2. **Formula and rules:**

1. **State the problem:** Solve the system of equations: $$x + 2y = 5$$

1. **State the problem:** Solve the linear equation $x + 2y = 5$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by per

1. Vamos resolver a inequação $$x^2 e^x + x e^{x+1} \geq 0$$. 2. Primeiro, fatoramos a expressão para simplificar:

1. The problem is to analyze the behavior of the function $$f(x) = -0.5x^4 + 1.2x^2 - 0.9x - 1$$ as $$x \to \infty$$ and $$x \to -\infty$$ and understand the shape of its graph. 2.

1. **State the problem:** We are given a point $(4, -6)$ on the graph of $y = f(x)$ and need to find the corresponding coordinates on the graph of $$y = \frac{2}{\sqrt{x + 3}} - 4.

1. Vamos resolver a inequação $$e^x + 1 > 6e^{-x}$$. 2. Primeiro, multiplicamos ambos os lados da inequação por $$e^x$$ para eliminar o termo $$e^{-x}$$, lembrando que $$e^x > 0$$

1. **State the problem:** Reduce the fraction $\frac{10}{16}$ to its simplest form. 2. **Formula and rules:** To simplify a fraction, divide the numerator and denominator by their

1. Problemet: Vi skal finne den deriverte av funksjonen $f(x) = x^n$, hvor $n$ er en konstant. 2. Formel: Den generelle regelen for derivasjon av potensfunksjoner er: