🧮 algebra

1. **Stating the problem:** Solve the equation $$2x + 4 = 2x + 4$$ for $$x$$. 2. **Formula and rules:** When solving equations, if after simplifying both sides are identical, it me

1. Problema: Duota sekos $a_n = -n^2 + 26n - 91$ formulė. Reikia nustatyti, kiek teigiamų narių turi ši seka. 2. Formulė ir taisyklės: Sekos narys yra teigiamas, jei $a_n > 0$. Tod

1. Planteamos el problema: Factorizar la expresión $$9x^2 - 6xy + y^2$$. 2. Recordemos que para factorizar un trinomio cuadrado perfecto de la forma $$a^2 - 2ab + b^2$$, el resulta

1. **Problem Statement:** Solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. **Formula and Rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. We can

1. **State the problem:** Simplify the expression $$2\sqrt{5} + \sqrt{5} + \sqrt{20}$$. 2. **Recall the rules:**

1. El problema es graficar la función $$f(x) = \log_{\frac{1}{2}}(x)$$. 2. Esta es una función logarítmica con base $$\frac{1}{2}$$, que está entre 0 y 1, por lo que la función es

1. **State the problem:** A company donates 7.20 each time a social media post is shared. The post is shared 2731 times, and the total donation is divided evenly among 4 charities.

1. **Problem:** Determine if the pairs of lines are parallel, perpendicular, or neither. 2. **Recall:**

1. **State the problem:** Solve the system of equations: $$3x - 5x = 11 - 5$$

1. **State the problem:** Solve the equation $3(x - 2) = 12$ for $x$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses.

1. **State the problem:** Simplify the expression $$\frac{3x - 2}{x^2 - 2x} - \frac{2}{x - 2}$$. 2. **Factor the denominators:**

1. **Problem:** Simplify the expression $$\frac{a - b}{ab} + \frac{b - c}{bc} + \frac{c - a}{ca}$$ 2. **Formula and rules:** To add fractions, find a common denominator. Here, the

1. **State the problem:** Calculate the value of the complex number expression $ (2 + 3i)^2 $. 2. **Formula and rules:** To square a complex number $ (a + bi) $, use the formula:

1. **State the problem:** We are given two functions $f(x) = -2x^2$ and $g(x) = -4x^2$ and the domain $-4 \leq x \leq -2$. We want to analyze these functions over this interval. 2.

1. The problem involves simplifying and evaluating the expression given in the first question, which is a combination of logarithms, powers, and arithmetic operations. 2. Recall th

1. **State the problem:** Mrs Lim starts with 35 liters of water. She uses $\frac{3}{7}$ of it to wash dishes, then uses $\frac{1}{4}$ of the remaining water to water flowers. We n

1. **State the problem:** Divide 560 among 3 people such that the second person gets twice as much as the first, and the third gets twice as much as the second. 2. **Set variables:

1. **State the problem:** We have 1 litre of fruit drink made by mixing cordial and water in the ratio 1:7. 2. **Initial quantities:** Since the total is 1 litre and the ratio is 1

1. **State the problem:** Simplify the expression $$\frac{\sin x \cdot x^{2}}{|\theta x m x|} + \frac{\sin x}{|\theta x m x|^{2}}.$$\n\n2. **Identify the components:** The expressi

1. El problema es factorizar la expresión $6x^2 + 3x$. 2. Para factorizar, buscamos el factor común entre los términos. Recordemos que la factorización por factor común usa la prop

1. **State the problem:** Find the midpoint of the segment connecting the complex numbers $z_1 = 0 + 4i$ and $z_2 = 0 - 5i$ in the complex plane. 2. **Formula for midpoint:** The m