🧮 algebra

1. The problem is to find the expression for $v_{n+1} - v_n$. 2. This represents the difference between the term at position $n+1$ and the term at position $n$ in a sequence $\{v_n

1. **Énoncé du problème :** Nous devons préciser le sens de variation de la suite $(v_n)$ définie par $v_n = \frac{u_n - 1}{u_n + 3}$.

1. **State the problem:** Simplify the algebraic expression $$\frac{5}{8}x + \frac{3}{4}y + \frac{1}{2}x - \frac{1}{4}y$$. 2. **Identify like terms:** Terms with $x$ are $$\frac{5}

1. **State the problem:** Solve the equation $3n - 4 = 11$ for $n$. 2. **Formula and rules:** To solve for $n$, we need to isolate $n$ on one side of the equation by performing inv

1. **State the problem:** Solve the equation $2n + 5 = 13$ for $n$. 2. **Use the formula:** To solve linear equations, isolate the variable by performing inverse operations.

1. **State the problem:** Hannah needs to drive 312 miles home and wants to know how much it will cost to fill up her gas tank based on the regression equation derived from her gas

1. **Problemstellung:** Vereinfache den Ausdruck $$\sqrt{2x^3 \sqrt{8x^2 \cdot (x\sqrt{2})^2}}$$. 2. **Formeln und Regeln:**

1. **State the problem:** Simplify the expression $5a(a-3)-2a(a+4)$. 2. **Write the expression:** $5a(a-3)-2a(a+4)$.

1. **Problem:** Simplify the expression $2x(2x - 6) - 3x(x + 5)$. 2. **Formula and rules:** Use the distributive property $a(b + c) = ab + ac$ to expand each term.

1. **State the problem:** Simplify or understand the expression $$\frac{5+x}{12+x}$$. 2. **Formula and rules:** This is a rational expression, a fraction where numerator and denomi

1. **Planteamiento del problema:** Tenemos dos depósitos, A y B, donde A se vacía y B se llena simultáneamente. Se nos dan dos gráficas lineales: una decreciente (azul) y otra crec

1. **State the problem:** Simplify the expression $$\frac{85-7x}{5}$$. 2. **Formula and rules:** When dividing a subtraction by a number, you can split the division over each term:

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations.

1. **Problem statement:** We are given three functions: - $f_b(x) = (x-b)^2$

1. **Énoncé du problème :** Trouver la solution de l'équation $$x^2 + 3x - 2 = 2x + 4$$ parmi les choix proposés : A. 4, B. -2, C. 1, D. -3. 2. **Formule et règles importantes :**

1. **Solve by graphing: $x^2 - 7x + 12 = 0$** - The equation is quadratic and can be written as $y = x^2 - 7x + 12$.

1. **Énoncé du problème :** On modélise une façade du Parthénon par un rectangle GREC avec les longueurs :

1. Il problema chiede di risolvere il sistema di equazioni: $$\begin{cases} 2x + 3y - 3 = 0 \\ 3x - 2y + 2 = 0 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{x}{\sqrt[3]{xy^{2}}}$$. 2. **Recall the formula and rules:** The cube root of a product can be written as the product of c

1. **State the problem:** Simplify the expression $$\frac{x}{\sqrt[3]{xy^{2}}}$$. 2. **Recall the formula and rules:** The cube root of a product can be written as the product of c

1. **Énoncé du problème :** On considère la suite $(u_n)$ définie par $u_0=0$ et la relation de récurrence $$u_{n+1} = \frac{2u_n + 3}{u_n + 4}$$ pour tout entier naturel $n$.