🧮 algebra

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 $c$

1. **Probleemstelling:** Gegeven is de lijn $k: \frac{x}{250} + \frac{y}{350} = 1$. De vergelijking moet herschreven worden in de vorm $35x + 25y = c$ en $c$ moet worden berekend.

1. **Énoncé du problème :** Nous avons deux modèles pour l'évolution de la concentration en principe actif d'un médicament dans le sang.

1. The problem asks to identify the dependent quantities from the table showing Kenzi's weekly allowance savings. 2. In a table showing a relationship between two quantities, the i

1. **State the problem:** Factor the expression $$147(2x-5)^2 - 48(2y+1)^2$$. 2. **Recognize the formula:** This is a difference of squares, which follows the rule:

1. The problem is to evaluate the expression $0/2$. 2. Division by a nonzero number is defined as splitting the numerator into that many parts.

1. **State the problem:** Solve the quadratic equation $$x^2 + 2x - 35 = 0$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an equation of

1. **State the problem:** Factor the quadratic expression $120x^2 - 52x - 224$. 2. **Formula and rules:** To factor a quadratic $ax^2 + bx + c$, find two numbers that multiply to $

1. **State the problem:** We are given the equation $$x^2 + y^2 - 4y + 4 = 100$$ and need to identify the shape and its properties. 2. **Rewrite the equation:** Notice that the ter

1. **State the problem:** We are given the polynomial function $$f(x) = -6x^5 - 3x^4 + 2x - 1$$ and we want to analyze or solve it depending on the context (e.g., find roots, evalu