🧮 algebra

1. Planteamos el problema: dividir el polinomio $x^3 - 1$ entre el binomio $x - 5$. 2. Usamos la división sintética o división larga para polinomios. La fórmula general para dividi

1. The problem is to simplify the expression $\frac{h^{14}}{h^{8}}$. 2. Use the rule of exponents for division: $\frac{a^m}{a^n} = a^{m-n}$.

1. The problem is to express a given value or expression in fractions. 2. To convert decimals or other forms into fractions, we use the fact that any decimal can be written as a fr

1. **State the problem:** We need to write a compound inequality that describes the graph. 2. **Analyze the graph:** There are two filled circles at $-7$ and $-2$.

1. The problem asks to write a compound inequality that describes the graph shown. 2. The graph shows a number line with a highlighted segment between 0 and 3.

1. The problem is to find the value of $-7 + 11$. 2. We use the rule of addition for integers: adding a positive number to a negative number involves subtracting the smaller absolu

1. **Problemstellung:** Gegeben ist die Funktion $f(x) = \frac{a}{x+b} + c$ mit $a,b,c \in \mathbb{Q}$ und $a \neq 0$. Gesucht sind zu den geschätzten Werten der Parameter $b$ und

1. The problem is to simplify the expression $(3)5$. 2. This expression means multiplying 3 by 5.

1. We are asked to find the maximum and minimum values of the functions $\max(-m, 2m^3)$ and $\min(m, -2m^3)$.\n\n2. The problem involves comparing two expressions for each functio

1. **State the problem:** Given the points $(-4,-4), (-2,-1), (0,2), (2,5), (4,8), (6,11)$, find the equation of the line passing through these points. 2. **Formula used:** The equ

1. (a) Evaluate each expression exactly. (i) Evaluate $$\left(\frac{3}{2}\right)^2 - 1 + 6$$.

1. **State the problem:** Given the table of points, find the equation of the line that passes through these points and describe its graph. 2. **Identify the points:** The points g

1. **Stwierdzenie problemu:** Znajdź równanie stycznej do wykresu funkcji $$f(x) = \frac{4x + 2}{x + 1}$$ w punkcie $$x_0 = 1$$. 2. **Wzór na równanie stycznej:** Równanie stycznej

1. Problem: Find the equations of the asymptotes of the function $$f(x) = \frac{3x - 12}{x + 2}$$. 2. To find vertical asymptotes, set the denominator equal to zero and solve for $

1. Stwierdzenie problemu: Znajdź równania asymptot wykresu funkcji $$f(x) = \frac{3x - 12}{x + 2}$$. 2. Przypomnienie: Asymptoty pionowe występują tam, gdzie mianownik jest zerem,

1. **Problem statement:** Given positive numbers $x, y, z, t$ satisfying the equality $$x^2 = y^3 = \sqrt{z} = \frac{1}{t} > 1,$$ determine the correct ordering of $t, y, x, z$. 2.

1. **Stating the problem:** Rozwiąż układ równań liniowych:

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 2x - y + 4z = 8 \\ x - 3y + z = -3 \\ -3x + 2y - z = -1 \end{cases}$$

1. **State the problem:** We need to order the given expressions from greatest to least, including approximate values. 2. **List the expressions:**

1. The problem asks to select all the squares from the given expressions and order them from least to greatest. 2. First, identify which expressions are perfect squares or can be s

1. نبدأ بترتيب الحل لمعادلة أو مسألة معينة. 2. إذا كانت المسألة تتعلق بحل معادلة، نحدد نوع المعادلة أولاً (خطية، تربيعية، إلخ).