🧮 algebra

1. **Problemstellung:** Gegeben ist die Funktion $f(x) = -5x^2 + 20$. (a) Berechne $f(1)$.

1. **Stating the problem:** Convert the given fractions and mixed numbers to decimals and percentages. 2. **Formula and rules:**

1. O problema pede para resolver o "2", que interpretamos como o número 2, mas para dar um exemplo matemático, vamos considerar a equação simples $x = 2$. 2. A equação $x = 2$ sign

1. **Problem:** Solve the first-degree equation analytically and graphically: $$3 \cdot \left( \frac{2x - 1}{3} - \frac{1 - 2x}{2} \right) = \frac{2 - x}{3} - 1 + x$$

1. **State the problem:** We need to find the solution point $S$ where the two lines given by the system of equations intersect: $$\begin{cases} y = -4x + 2 \\ y = 3x - 5 \end{case

1. The problem asks to classify each equation as linear or nonlinear. 2. A linear equation in two variables $x$ and $y$ has the form $$Ax + By = C$$ where $A$, $B$, and $C$ are con

1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$

1. We start by solving the first logarithmic equation: $$^2\log(16) + ^2\log(x) = 6$$ 2. Recall the logarithm property: $$\log_b(a) + \log_b(c) = \log_b(ac)$$. Here, the base is 2,

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$

1. مسئله: اگر رابطه \{(x-1,2),(5,x-2),(3,y+3),(3,5),(5,3)\} تابع باشد، مقادیر x و y را بیابید. 2. تعریف تابع: در یک تابع، هر عنصر از دامنه دقیقاً به یک عنصر از برد نگاشت می‌شود. یع

1. **Problema 72:** Simplificare $$\left(\frac{6 - \frac{1}{2}}{\frac{11}{2}} - \frac{21}{36} - \frac{5}{12}\right) : \left[\left(\frac{\frac{9}{2} - \frac{3}{4}}{\frac{1}{4}} + \f

1. **State the problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation.

1. **Problem statement:** Solve the quadratic equation $$x^2 + 8x - 100 = -x^2 - 40 + 10x$$. 2. **Step 1: Bring all terms to one side to set the equation to zero.**

1. Das Problem lautet: Löse die Gleichung $$20 - 3x^2 - 7x = -4x^2 + 3x + 4$$ nach $x$ auf. 2. Wir bringen alle Terme auf eine Seite, um die Gleichung zu vereinfachen. Dazu addiere

1. **State the problem:** Divide the polynomial $4x^3 + x + 1$ by the binomial $2x + 3$. 2. **Formula and rules:** Polynomial division is similar to long division with numbers. We

1. **Énoncé du problème :** Déterminer l'ensemble de définition $D_f$ de la fonction $f$ définie par $$f(x) = \frac{2x - 5}{2 - x}.$$ 2. **Formule et règle importante :** Pour une

1. Enunciato del problema: Tracciare i grafici delle funzioni $f(x) = \sqrt{|x|} - 1$ e $g(x) = \frac{|x|}{|x|} - 3$. 2. Analizziamo $f(x)$: la funzione è $f(x) = \sqrt{|x|} - 1$.

1. Enunciato del problema: Consideriamo le funzioni $$f(x) = \sqrt{|x|} - 1$$ e $$g(x) = \frac{|x|}{|x|} - 3$$. 2. Analizziamo la funzione $$f(x)$$: essa è definita come la radice

1. Il problema chiede di risolvere l'equazione IL 196, ma non è chiaro cosa significhi "IL 196". 2. Se si tratta di un'equazione o di un'espressione matematica, per favore fornire

1. **Stating the problem:** Determine the greatest common divisor (MCD) of the polynomials:

1. **Stel het probleem vast:** We hebben de lijn $k$ gegeven door de vergelijking $\frac{x}{250} + \frac{y}{350} = 1$. We willen deze herschrijven in de vorm $35x + 25y = c$ en $c$