🧮 algebra

1. **Énoncé du problème :** Écrire sous la forme d'une puissance d'exposant positif les expressions suivantes :

1. **State the problem:** Solve the inequalities and expressions for problems IV to VII as requested.

1. The problem is to simplify the expression after the term $28k + 7$. 2. We start by factoring the expression $28k + 7$.

1. **State the problem:** A number $n$ when divided by 7 leaves a remainder of 3. We need to find the remainder when $4n + 5$ is divided by 7. 2. **Express the given condition math

1. Énoncé du problème : Calculer les valeurs de $a$, $b$ et $c$ donnés par : $$a = \frac{2^{17} \times 2^{-4}}{(2^5)^3}, \quad b = 3^0 + 3^{-1} + 3^{-2}, \quad c = \left(\frac{19}{

1. **State the problem:** Add two fractions, for example, $\frac{a}{b} + \frac{c}{d}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc

1. **Stating the problem:** We are given the formula $C = kabc$ and need to understand or simplify it. 2. **Understanding the formula:** The formula $C = kabc$ suggests that $C$ is

1. The problem states the formula $C = kab$, where $C$ is a variable dependent on $k$, $a$, and $b$. 2. This formula represents a direct variation where $C$ varies directly as the

1. **State the problem:** Find the roots of the cubic equation $$-4x^{3}+12x^{2}-6x+1=0$$. 2. **Rewrite the equation:** Multiply both sides by $$-1$$ to simplify the leading coeffi

1. **State the problem:** We need to find the missing number in the series: 7864, 7839, 7812, ___, 7767, 7740. 2. **Analyze the pattern:** Let's find the differences between consec

1. **State the problem:** Simplify the expression $ (y+2)(y-2) $. 2. **Recall the formula:** This is a difference of squares pattern, which states:

1. **Stating the problem:** We are given a numeric sequence: 01, 7639, 7812, __, 7767, 7740, and we need to find the missing term. 2. **Analyzing the sequence:** Let's look at the

1. **State the problem:** We need to write the inequalities describing the unshaded region on the graph. 2. **Identify the lines:** The solid line passes through (0, -1) and (3, 6)

1. The problem is to simplify the expression $\sqrt[2]{18}$, which is the square root of 18. 2. Recall the property of square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$.

1. **State the problem:** Simplify the expression $$\sqrt[3]{50} - \sqrt{18} + \sqrt{98}$$. 2. **Recall the rules:**

1. **State the problem:** Solve the system of equations: $$2x + 6y = 17$$

1. **State the problem:** Multiply and divide the given integers using the Rules-Based Method. 2. **Rules for multiplication and division of integers:**

1. The problem is to find the $x$-intercept and $y$-intercept of a function or equation. 2. The $x$-intercept is the point where the graph crosses the $x$-axis. At this point, $y=0

1. **State the problem:** Solve the linear inequality $$y \leq 2x - 6$$. 2. **Understand the inequality:** This inequality means that the value of $y$ is less than or equal to the

1. **State the problem:** We need to draw the graph of the quadratic function $$y = x^2 - 4x + 3$$ using a scale of 1 cm = 1 unit on both axes, and then use the graph to solve the

1. **State the problem:** Solve the rational equation $$x + \frac{3}{x} = 4$$ and determine which given options are solutions. 2. **Write the equation:** $$x + \frac{3}{x} = 4$$