🧮 algebra

1. Énoncé du problème : Déterminer les variations de la fonction $f$ telle que $u_n = f(n)$ pour la suite $u_n = 3n^2 - 4$ et en déduire les variations de $u$. 2. Formule et règles

1. The problem asks to evaluate $2^{-3}$. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$ and $n$ is a positive integer.

1. **Problem statement:** Löse die Gleichung $$5 \cdot (x + 3) = 2 \cdot x + 12 + 3 \cdot x$$. 2. **Formel und Regeln:** Um lineare Gleichungen zu lösen, verwenden wir die Distribu

1. **State the problem:** We are given the quadratic function $f(x) = -2x^2 - 12x - 7$ and need to analyze its properties. 2. **Formula and rules:** A quadratic function is general

1. The problem is to find linear equations that pass through the points where the stars are located: (2,8), (2,4), (8,7), and (14,4). 2. Recall that a linear equation in two variab

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} x + 1, & x \leq -2 \\ -6, & -2 < x \leq 2 \\ 5, & x > 2 \end{cases}$$

1. **State the problem:** We are given the quadratic function $$h(x) = -\frac{1}{2}x^2 + 4x - 10$$ and need to find its vertex, line of symmetry, x-intercepts, and y-intercept. 2.

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} -x - 4, & x < -3 \\

1. Problem: Given the vector \(\vec{a} = \begin{pmatrix} t \\ 8 \end{pmatrix}\), (a) Find the length \(|\vec{a}|\) when \(t=6\).

1. **Problem a:** Solve the equation $x(x - 4) = 0$. 2. The zero product property states that if $ab=0$, then either $a=0$ or $b=0$.

1. The problem involves understanding and plotting linear equations given in different forms, along with their corresponding points. 2. The general form of a linear equation is $y

1. **State the problem:** Simplify the expression $$\sqrt{\frac{25w^6}{x^2}} \div wx^3$$ leaving the answer with positive exponents. 2. **Rewrite the expression:** The division can

1. **State the problem:** We need to find the value of $y$ when $x=13$ for the function $$y=\frac{3}{2}\sqrt{x+3}.$$\n\n2. **Formula and explanation:** The function involves a squa

1. **Problem (a):** Express $\sqrt{50} - \frac{2}{\sqrt{8}}$ in the form $a\sqrt{b}$, where $a$ and $b$ are rational numbers. 2. **Step 1:** Simplify each term separately.

1. Das Problem lautet: Dividiere die Potenz $3^a$ durch $6 \cdot 2^a \cdot 5$.\n\n2. Die allgemeine Regel für Division von Potenzen mit gleicher Basis ist: $$\frac{x^m}{x^n} = x^{m

1. Planteamos el sistema para \(\lambda = 1\) usando la matriz \(A - \lambda I\): $$A - I = \begin{pmatrix} 1-1 & 2 & 3 \\ 0 & 0-1 & 2 \\ 0 & 1 & 1-1 \end{pmatrix} = \begin{pmatrix

1. **State the problem:** Simplify the expression $$\frac{27}{(-2)^5} \cdot \frac{4^8}{6^4}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{\sqrt{x^2 y z^3}}{\sqrt{x^2 y z^2}}$$ assuming $x, y, z > 0$. 2. **Use the property of square roots:** $$\frac{\sqrt{A}}{\

1. Das Problem ist: "Löse das bitte". Da keine spezifische Gleichung oder Aufgabe gegeben ist, kann ich nur allgemeine Schritte zum Lösen von Gleichungen erklären. 2. Allgemeine Fo

1. The problem is to determine which number or expression is greater between two given values. 2. To compare two numbers or expressions, we can subtract one from the other and anal

1. Problem: Berechne den Wert der Unbekannten in der Gleichung $10 - a = 4$. 2. Formel und Regeln: Um $a$ zu finden, isolieren wir $a$ auf einer Seite der Gleichung. Wir subtrahier