🧮 algebra

1) نُعطى: $$a = \frac{4\sqrt{3} - 2\sqrt{5}}{7}, \quad b = \frac{2\sqrt{3} + \sqrt{5}}{9}$$

1. **Stating the problem:** Solve the equation $$x - 37.1 = 0$$ for $x$. 2. **Formula and rule:** To solve for $x$, we isolate $x$ by adding $37.1$ to both sides of the equation.

1. Stating the problem: Solve the equation $$\frac{x + 92}{x + 8} = 0$$. 2. Important rule: A fraction equals zero only when its numerator is zero and its denominator is not zero.

1. **State the problem:** Solve the system of equations: $$9x + 11y = -9$$

1. Planteamos el problema: Simplificar la expresión $5x + 2y - 3x$. 2. Recordemos que para simplificar expresiones algebraicas, debemos combinar términos semejantes. Los términos s

1. The problem states that the value is equal to 2. 2. Since the problem is a simple equality, no further calculation is needed.

1. **State the problem:** Simplify the expression $$\frac{2 - \sqrt{3}}{-\sqrt{3} \cdot 2 + 1}$$. 2. **Rewrite the denominator:** The denominator is $$-\sqrt{3} \cdot 2 + 1 = -2\sq

1. Let's start by understanding what "it" means in math. Usually, "it" could refer to a concept like solving equations, understanding functions, or working with algebraic expressio

1. **State the problem:** Solve the inequality $x^2 - 5x + 6 < 0$. 2. **Identify the type of inequality:** This is a quadratic inequality of the form $ax^2 + bx + c < 0$.

1. **Problem Statement:** On Odd Street, house numbers are consecutive odd numbers. The sum of two neighbor house numbers is 5056. Find the two house numbers. 2. **Understanding th

1. **State the problem:** Katie burns 150 calories in 25 minutes. We want to find how many calories she burns in 40 minutes. 2. **Set up the proportion:** Since calories burned is

1. Stwierdźmy problem: mamy cztery równania mnożenia ułamków, gdzie jedna z wartości jest nieznana i chcemy ją znaleźć. 2. Wzór do rozwiązania: jeśli $\frac{a}{b} \times x = \frac{

1. **State the problem:** Simplify the expression $$\sqrt{\frac{7x}{10y^3}}$$. 2. **Recall the property of square roots:** $$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$$ for po

1. Stating the problem: We are given sequences of multiplied fractions and their results, and we need to find the missing results without performing full calculations. 2. Observing

1. **Énoncé du problème :** Résoudre le système d'équations linéaires suivant :

1. **Problem statement:** A shopkeeper buys a bicycle for 8000 and spends 500 on repairs. He sells it for 9200. Find his profit or loss. 2. **Formula:** Profit or Loss = Selling Pr

1. **State the problem:** Simplify and evaluate the expression $$\left( \frac{1}{1+i} - \frac{1}{1-i} \right)^{100} = \left( \frac{2+3w}{2w^{2}+3} + \frac{4w^{2}+1}{4+w} \right)^{2

1. The problem asks to simplify the expression and classify the result as a real or imaginary number. If imaginary, specify if it is pure imaginary. 2. To simplify expressions with

1. **State the problem:** We need to find the pattern rule in each series and complete the missing terms. 2. **Series (a):** 32.4, 32.8, 33.2, 33.6, 34, 34.4

1. The problem involves simplifying the fraction $\frac{8}{24}$ and comparing it to other fractions and numbers given. 2. Simplify $\frac{8}{24}$ by dividing numerator and denomina

1. **State the problem:** Ruth bought a canoe originally priced at $141, but it was marked down to $87. We need to find the discount as a percentage. 2. **Formula for discount perc