🧮 algebra

1. **Problem:** A fashion designer buys fabric for 500 and sells a dress made from it for 800. What's the profit percentage? 2. **Formula:** Profit percentage is given by

1. The problem is to find the sum of the integers from 1 to 13. 2. The formula to find the sum of the first $n$ natural numbers is:

1. **Problem:** Calculate the value of $(-a)(+a)$. 2. **Formula:** Multiplying a negative and a positive number results in a negative number. Also, $(-a)(+a) = -a^2$.

1. **Énoncé du problème :** On a une suite définie par $u_0=2$ et $u_{n+1} = \frac{u_n}{u_n+1}$ pour tout $n \in \mathbb{N}$. On pose $v_n = \frac{1}{u_n}$.

1. Planteamos el problema: Dada la ecuación $(x - a)(x - b) = x^2 - 12x + 27$, debemos encontrar el valor de $a + b$. 2. Recordemos que al expandir el producto de dos binomios $(x

1. Let's start with a simple fractions aptitude test problem: Simplify the fraction $\frac{18}{24}$.\n\n2. The formula to simplify a fraction is to divide both the numerator and th

1. The problem is to find the sum of two fractions. 2. The formula to add fractions is $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a$, $b$, $c$, and $d$ are integers

1. مسئله را بیان می‌کنیم: مقدار $$\log_4 \left( \log_3 \left( \log_2 512 \right) \right)$$ را بیابید. 2. ابتدا مقدار داخل‌ترین لگاریتم را محاسبه می‌کنیم: $$\log_2 512$$.

1. **Énoncé du problème :** Compléter les relations d'appartenance entre les nombres et ensembles donnés. 2. **Rappel des symboles :**

1. The problem is to solve the equation, but the equation is not provided. Please provide the equation you want to solve.

1. **Problem statement:** We have a rectangular sheet of metal 20 cm by 12 cm. Squares of side length $x$ cm are cut from each corner, and the sides are bent up to form an open box

1. **Problem Statement:** Calculate the profit or loss when an item is bought for 100 and sold for a certain price. 2. **Formula:**

1. The problem is to understand and solve questions related to matrices, which are rectangular arrays of numbers arranged in rows and columns. 2. A matrix is usually denoted by a c

1. The problem is to find the equation of a straight line graph given certain conditions. 2. The general formula for a straight line is $$y = mx + c$$ where $m$ is the slope and $c

1. **State the problem:** We are given the function $X(t) = 3x\left(1-\frac{t}{2}\right) + 1$. We want to understand or simplify this expression. 2. **Clarify the function:** It se

1. **State the problem:** Solve the exponential equation $$2^{3x - 2} = 8^{\frac{1}{2x}}.$$\n\n2. **Rewrite the bases:** Note that 8 can be written as a power of 2: $$8 = 2^3.$$ So

1. **State the problem:** Calculate the value of $$\left(\frac{30 \times 10^{-3} \text{ m}}{1.2 \times 10^{7} \text{ m/s}}\right)^2$$. 2. **Formula and rules:** We are squaring a f

1. The problem is to understand the inequality $n > 50$. 2. This inequality means that the variable $n$ must be greater than 50.

1. **Problem Statement:** Simplify the expression $$\frac{3^5 \times 3^{-11}}{2^{-1} \times 5^0}$$. 2. **Formula and Rules:** When multiplying powers with the same base, add the ex

1. **Stating the problem:** We need to calculate the value of $$K = \frac{748.200 \times (748.200 \times 735.493 - 2 \times (735.493 \times 748.200) + 748.200 \times 760.607)}{735.

1. **State the problem:** Mokaya bought and sold a cow twice at different prices. We need to find the total profit he made. 2. **Identify the transactions:**