🧮 algebra

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

1. **Énoncé du problème :** Soit la fonction linéaire $f$ définie par $f(x) = -\frac{5}{2}x$.

1. **State the problem:** Expand and simplify the expression $$(4x - 3)(2x - 5)$$. 2. **Recall the distributive property (FOIL method):** To multiply two binomials, multiply each t

1. **State the problem:** Expand and simplify the expression $$5m (2m - 5n) - 3n (m + 2n)$$. 2. **Use the distributive property:** Multiply each term inside the brackets by the ter

1. **State the problem:** We have a sequence where the first term is $5x$ and each subsequent term is found by adding $2x + 3$ to the previous term. 2. **Formula and rule:** The te

1. **State the problem:** Solve the inequality $$\frac{2x - 3}{x + 5} \leq 0$$. 2. **Recall the rule for rational inequalities:** A rational expression $$\frac{A}{B} \leq 0$$ is le

1. The problem is to simplify or understand the expression $\frac{5\pi}{4} + 6m$. 2. This expression is a sum of two terms: a constant term $\frac{5\pi}{4}$ and a variable term $6m

1. **Problem statement:** A jar starts with 1000 g of sugar. Each day, half of the sugar present is removed. We want to find how much sugar remains after 5 days. 2. **Formula:** Th

1. The problem is to solve the equation or expression labeled as "B" (since the user specified "the B one, not the A"). 2. Since the user did not provide the explicit problem state

1. Planteamos el problema: Resolver la ecuación cuadrática $$3x^2 + 3x - 1 = 0$$ usando la fórmula general. 2. Recordemos la fórmula general para ecuaciones cuadráticas $$ax^2 + bx

1. Énoncé du problème : Résoudre dans $\mathbb{R}$ l'inéquation $$y(x) < -2x + 5.$$ 2. Pour résoudre une inéquation de la forme $$y(x) < f(x),$$ il faut trouver les valeurs de $x$