🧮 algebra

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).

1. The problem asks to find the value of the expression $s + t$ given $s = 3$ and $t = 5$. 2. The formula to use is simple addition: $$s + t$$

1. **State the problem:** We need to find the value of the expression $j \times k \times 2 \times 2$ given $j=2$ and $k=2$. 2. **Write the expression with given values:** Substitut

1. We are asked to solve the division problem $\frac{8}{9} \div \frac{4}{15}$. 2. The formula for dividing fractions is:

1. Rozwiążmy pierwsze zadanie: $\frac{3\sqrt{75} - 2\sqrt{12}}{11\sqrt{3}}$. 2. Najpierw uprośćmy pierwiastki:

1. **State the problem:** Simplify the expression $$\frac{0.1^{0.4} \cdot 0.2^{0.3} \cdot 0.3^{0.2} \cdot 0.4^{0.1}}{0.5^{0.5} \cdot 0.3^{0.8}}$$. 2. **Rewrite the expression:** Gr

1. Problem: If ‘p’ and ‘q’ are natural numbers and ‘p’ is a multiple of ‘q’, find the HCF of ‘p’ and ‘q’. 2. Since p is a multiple of q, we can write $p = kq$ for some natural numb

1. **State the problem:** Simplify the expression $30 - \frac{5}{15} + 3$. 2. **Recall the order of operations:** Perform division before addition and subtraction.

1. **State the problem:** Simplify the expression $\frac{60}{30} + 5 + 2$. 2. **Apply the order of operations:** Division comes before addition.

1. Resolver la ecuación: $x - (2x + 1) = 8 - (3x + 3)$. 2. Primero, eliminamos los paréntesis aplicando la propiedad distributiva:

1. The problem is to simplify the expression $\frac{30}{5} \div 2$. 2. Recall that division of fractions or numbers can be rewritten as multiplication by the reciprocal: $a \div b

1. **State the problem:** Simplify the expression $30/6-(3+2)$.\n\n2. **Apply the order of operations (PEMDAS/BODMAS):** Parentheses first, then division, then subtraction.\n\n3. *

1. **State the problem:** Simplify the expression $30 - \frac{5}{15} + 3$. 2. **Recall the order of operations:** Perform division before addition and subtraction.

1. **State the problem:** Simplify the expression $\frac{30}{5 + \frac{15}{3}}$. 2. **Recall the order of operations:** Always perform operations inside parentheses first, then div