🧮 algebra

1. **Problem statement:** We are given the product term $$T = 1,5x \cdot (3x + y - 2)$$ which represents the area of the blue rectangle.

1. The problem is to analyze the set of points $\{(-7, -3), (-7, 2), (-6, 1), (-2, 6), (5, 3)\}$ and understand their properties. 2. Each ordered pair represents a point on the Car

1. The problem is to simplify the expression $1 - \frac{3}{4}$. 2. To subtract a fraction from a whole number, convert the whole number to a fraction with the same denominator: $1

1. **State the problem:** Simplify the expression $\frac{1}{5} \times 3 + \frac{7}{10} - \frac{1}{2}$. 2. **Recall the order of operations:** Multiplication and division come befor

1. Expand and Simplify each expression: 1.a) Expand and simplify $ (3x^2 - 4xy + 5y^2) - (5x^2 - 7xy - 4y^2) $.

1. **State the problem:** We need to add the fractions $\frac{4}{7}$ and $\frac{3}{2}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The formula

1. **Expand and Simplify:** a) Expand and simplify $ (3x^2 - 4xy + 5y^2) - (5x^2 - 7xy - 4y^2) $.

1. The problem is to simplify the expression $10^1 \times 10^{-2}$. 2. We use the rule of exponents that states when multiplying powers with the same base, we add the exponents:

1. **State the problem:** Calculate the value of the expression $$10^4 - 10^3 + 10^0$$. 2. **Recall the powers of 10:**

1. **Stating the problem:** We need to find the value of $n$ in the equation $5.62 \times 10^n = 0.0562$.

1. The problem is to calculate the value of $(-50)^3$. 2. The formula for raising a number to a power is $a^n = a \times a \times \cdots \times a$ (n times).

1. Énoncé du problème : Calculer la valeur de l'expression $$ (4^2 - 2) \times 5 + 4 $$ et donner la réponse sous forme d'un entier relatif. 2. Rappel des règles :

1. **Énoncé du problème** : Calculer la valeur de l'expression $9 - 5 \times 5^2$ et donner la réponse sous forme d'un entier relatif. 2. **Rappel des règles** :

1. The problem is to simplify the expression $10^2 \times 10^5$. 2. We use the rule of exponents that states when multiplying powers with the same base, we add the exponents: $$a^m

1. Énoncé du problème : Calculer la valeur de l'expression $$7 \times 10^{2} + 2 \times 10^{1} + 3 \times 10^{0} + 7 \times 10^{-1}$$ et donner la réponse sous forme d'un entier re

1. **State the problem:** Simplify the expression $7^6 \times 7^4$. 2. **Formula used:** When multiplying powers with the same base, use the rule:

1. Énoncé du problème : Résoudre l'équation $x \times 10^{-2} = 1,1$ pour $x$. 2. Rappel de la règle des puissances : $10^{-2} = \frac{1}{10^2} = \frac{1}{100} = 0,01$.

1. **State the problem:** We are given the equation $\frac{\log x}{\log 2} = -0.515$ and need to find the value of $x$. 2. **Recall the formula:** The expression $\frac{\log x}{\lo

1. Problema: Calculați suma numerelor întregi date. 2. Formula folosită: Pentru adunarea numerelor întregi, dacă semnele sunt aceleași, adunăm valorile absolute și păstrăm semnul c

1. Problema: Calculați expresiile cu radicali. 2. Formula și reguli: Pentru a aduna sau scădea termeni cu radicali, trebuie să avem același radical (radicalul și indicele să fie id

1. The problem is to solve a system of simultaneous linear equations. 2. The general form of simultaneous linear equations is: