🧮 algebra

1. Bonjour! Comme tu es en 4ème et que tu n'as pas encore vu les vecteurs, on va commencer par des notions simples en algebra. 2. Par exemple, résolvons une équation du premier deg

1. **Problem statement:** We consider the function $f(x) = 2x\ln x - 1$ defined on $(0, +\infty)$. We need to analyze limits, derivatives, solve equations involving $f$, and study

1. The problem is to understand why, in certain exercises, the last part is compared to 1. 2. Often in math, comparing a quantity to 1 helps determine if it is greater than, equal

1. State the problem: Solve the system of equations $$\begin{cases} x+y+z=6 \\ 2x-y+2z=14 \\ x+4y-z=2 \end{cases}$$

1. We need to determine whether the function $f(x) = \sin^9 x \cos^5 x$ is even, odd, or neither. 2. Recall the definitions:

1. **Statement of the problem:** Calculate various results for the given sets of numbers and expressions.

1. **State the problem:** Find the number of positive integers less than or equal to 10030 that are not divisible by 3, 4, 7, or 11. 2. **Use the principle of inclusion-exclusion:*

1. The problem is to simplify the expression $5^7 + 5^9$. 2. Notice that both terms have a common base of 5, so we can factor out the smallest power, which is $5^7$.

1. **State the problem:** We are given that the product of $x$ and $y$ is 23, i.e., $xy=23$. 2. **Interpretation:** To find the value of $x$, we need either a value or an expressio

1. We are given the function $$f(x)=\sqrt{x-5}$$ and need to determine whether it is even, odd, or neither. 2. Recall the definitions:

1. The problem is to simplify and rewrite the expression: $$\left(\frac{-2}{5}\right)^{-2} \cdot \left(\frac{-5}{2}\right)^{-3}$$

1. **State the problem:** We need to find how many hours Salma and Mary each take to read a 120-page book. 2. **Find Salma's reading rate:**

1. Given: $\log_2(x) = 3$ and $\log_2(y) = 5$. 2. We need to find $\log_2\left( \frac{4x^2}{y} \right)$.

1. **Exercice 2 - Problème 1** Déterminer la fonction polynôme du second degré $f$ telle que : $f(0)=4$, $f'(0)=3$ et $f(1)=3$.

1. The problem is to determine whether the function $f(x) = 5x^3$ is even, odd, or neither. 2. Recall definitions:

1. The problem is to simplify the expression $$\frac{2x^3}{3x^2} \times \frac{4x^3}{6x}$$ and find the simplified result. 2. Start by rewriting the expression:

1. Énoncé du problème : Développer et simplifier la fonction $f(x) = (2x^2 + 1)(3x - 1)^2$, puis étudier les autres fonctions données. 2. Développons $(3x - 1)^2$ :

1. **Stating the problem:** Marwan's car needs 5 liters of gasoline to cover 50 km. We need to find how much gasoline is required for a 200 km trip.

1. First, state the problem: Ahmed’s mother uses 2 oranges and 4 spoons of sugar to make 1 cup of orange juice. 2. We want to find how many oranges and spoons of sugar are needed t

1. First, identify the function described by the graph in the image. The graph appears to be a parabola, so it likely represents a quadratic function. 2. Use the standard form of a

1. **Statement of the problem:** Given: