🧮 algebra

1. Problemstellung: Zeigen Sie, dass die in Definition 11.1.2 von Reiss und Schmieder erklärten Rechenoperationen assoziativ und kommutativ sind, um die Behauptung von Satz 11.1.3

1. **State the problem:** Simplify the expression $T=4+n(3-1)$. 2. **Apply the order of operations:** First, evaluate the expression inside the parentheses.

1. **State the problem:** Simplify the expression $$\frac{6x}{x^2 - 5x + 6} - \frac{3x}{x^2 + x - 12}$$ and state any restrictions on the variables. 2. **Factor the denominators:**

1. **Problem:** Find the slope between the points (-2, -3) and (6, 5). 2. **Formula:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

1. **Problem:** Find the slope between points $(-2, 3)$ and $(6, 5)$. 2. **Formula:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

1. **State the problem:** We have the system of equations: $$\begin{cases} x + y = 6 \\ x^2 - y^2 = 2 \times 3! \end{cases}$$

1. **Problem:** Factor the expression $$12y^2 + 3y - 9$$. 2. **Step 1: Identify common factors.**

1. **State the problem:** We are given the equation $Y = 2.5x$ and a graph showing the relationship between cups of lemonade mix (x-axis) and cups of water (y-axis). 2. **Understan

1. The problem is to understand the relationship between cups of lemonade mix and cups of water. 2. Given the table:

1. **State the problem:** Factor completely the expression $$-3x^6yz^2 + 2x^2y$$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in each term.

1. The problem is to find a Pythagorean triple, which is a set of three positive integers $a$, $b$, and $c$ such that they satisfy the Pythagorean theorem: $$a^2 + b^2 = c^2$$ 2. T

1. **State the problem:** We are given a point $(1,4)$ on the graph of $y=f(x)$ and need to find the coordinates of its image on the graph of $y=3f[-4(x+1)]-2$. 2. **Understand the

1. **Problema:** Calcula la suma o resta de fracciones y simplifica el resultado. 2. **Ejercicio 10 a):** $\frac{3}{5} + \frac{6}{5} = \frac{3+6}{5} = \frac{9}{5}$ (ya simplificado

1. The problem is to simplify the expression $14a$. 2. Since $14a$ is already in its simplest form, it represents the product of the number 14 and the variable $a$.

1. Let's clarify the origin of the expression $2x - 1$ in the final answer. 2. Typically, $2x - 1$ arises from simplifying or factoring an algebraic expression or solving an equati

1. **Planteamiento del problema:** Simplificar la expresión $$(x+2)^2 - 3(x^2 - 2x + 4)$$ 2. **Expansión de los términos:**

1. **State the problem:** Solve the linear equation $12x + 72 = 10x + 78$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the quadratic equation $9n^2 + 79 = -18n$ by completing the square. 2. **Rewrite the equation:** Move all terms to one side to set the equation to z

1. **State the problem:** We need to divide the polynomial $2x^{3}+3x^{2}+5x-8$ by $x^{2}+2x+3$. 2. **Recall the formula:** Polynomial division is similar to long division with num

1. **State the problem:** We are asked to find how many solutions the system of linear equations has: $$y = -\frac{3}{4}x - 6$$

1. The problem asks for the number of solutions to the system of linear equations: $$y = -5x + 3$$