🧮 algebra

1. Énoncé du problème : Calculer et simplifier les expressions suivantes : $$A = \frac{1}{7} \times \left(\frac{4}{7} - \frac{3}{7}\right), \quad B = \left(-\frac{5}{-3}\right) \ti

1. **Calculer les expressions données :** A = \sqrt{2} + \sqrt{49} = \sqrt{2} + 7

1. **Problem Statement:** Given a line with intercepts $a$ and $b$ on the x-axis and y-axis respectively, and $p$ as the length of the perpendicular from the origin to this line, s

1. The problem is to understand and work with matrices, which are rectangular arrays of numbers arranged in rows and columns. 2. A matrix is usually denoted by a capital letter, fo

1. **Énoncé du problème :** Calculer les puissances suivantes : $(-1)^{2022}$, $1^{3099}$, $0^{1990}$, $\left(-\frac{1}{3}\right)^1$, $10^{-6}$, $(-4)^2$, $\left(\frac{3}{2}\right)

1. The problem is to find an alternative solution to a previously solved problem that yields the same answer. 2. Since the original problem is not specified, let's consider a commo

1. **State the problem:** We need to find the ratio of the lengths of the purple, green, and orange sections of the pole. 2. **Given lengths:**

1. **State the problem:** We need to find the ratio of glass to cardboard in a recycling bin, where the glass weighs 2 kg and the cardboard weighs 500 g. 2. **Convert units to be c

1. **Problem Statement:** Given a line with intercepts $a$ and $b$ on the coordinate axes, and $p$ as the length of the perpendicular from the origin to this line, show that $$\fra

1. **State the problem:** We have 50 fish in total. Among them, 15 are tench. Of the remaining fish, 1/5 are minnows and the rest are goldfish. We need to find the ratio of tench t

1. **State the problem:** A motorist takes 2 hours to travel from one town to another and 1 hour 40 minutes to travel back. We need to calculate the percentage change in the speed

1. The problem is to understand the logarithm function and how to work with it. 2. The logarithm function is defined as the inverse of the exponential function. For a base $b > 0$,

1. The user asked to "show examples," which is a general request without a specific math problem. 2. Since no specific math problem is given, I will provide a simple example of sol

1. **Problem statement:** A diamond necklace's selling price increases by 5% each year. The price in 2000 was 36000.

1. The problem is to express the equation $6x + 7y = ?$ in a meaningful way. 2. This is a linear expression with two variables $x$ and $y$. Without additional information, such as

1. The problem asks which expression is equivalent to $5x^2 - 8$. 2. To check equivalence, we simplify each given expression and compare it to $5x^2 - 8$.

1. **State the problem:** Simplify the expression $$\frac{2}{3}y + 14 - \frac{1}{6}y - 8$$. 2. **Combine like terms:** The terms involving $y$ are $$\frac{2}{3}y$$ and $$-\frac{1}{

1. **State the problem:** Simplify the expression $$\frac{3}{5}x + 19 - \frac{3}{20}x - 7$$. 2. **Combine like terms:** Group the terms with $x$ and the constant terms separately.

1. Let's start by stating the problem: understanding logarithmic and exponential equations. 2. Exponential equations have the form $y = a^x$, where $a$ is a positive constant not e

1. Let's state the problem: We want to solve an algebraic problem using a simple method. 2. The simple method often involves isolating the variable on one side of the equation. For

1. **State the problem:** We want to find the least number of copies sold so that the publishing company makes a positive profit.