🧮 algebra

1. **Énoncé du problème :** Calculez la valeur de l'expression $$B = \frac{-2 \times 10}{5 \times (-4)}$$.

1. **State the problem:** We need to solve the system of linear equations: $$\begin{cases} 2x + y = 7 \\ x - y = 2 \end{cases}$$

1. **State the problem:** We are given a function $f(x) = 2x + 3$ and asked to find the value of $f(4)$. 2. **Recall the formula:** The function $f(x)$ means for any input $x$, the

1. **State the problem:** We need to sketch the graph of the linear equation $$y = -2x - 2$$. 2. **Formula and rules:** This is a linear equation in slope-intercept form $$y = mx +

1. **State the problem:** We need to check which of the points $$(0,2), (0,3), (3,4), (3,9)$$ lie on the graph of the linear equation $$y = 2x + 3$$. 2. **Formula used:** The equat

1. **State the problem:** Simplify the expression $$(-x - 4) - (3x - 1)$$ by subtracting the second parentheses from the first. 2. **Recall the rule:** Subtracting an expression me

1. **State the problem:** We need to add the polynomials $4x^2 - 3x + 9$ and $2x^2 - x - 7$. 2. **Formula and rules:** When adding polynomials, combine like terms. Like terms have

1. **State the problem:** We are given the polynomial $$x^3y^2 - 3xy^3$$ and need to name it by its degree, number of terms, and leading coefficient. 2. **Identify the number of te

1. **State the problem:** We are given the polynomial $$2x^2y^2 + 3xy - 4y^3$$ and need to identify its degree, number of terms, name, and leading coefficient. 2. **Number of terms

1. The problem asks to find how many terms are in the polynomial $$-10x^6 - 2x^5 + 4x^4 + 7x^3 - 9x^2 + 5.5x - 1$$. 2. A term in a polynomial is each part separated by a plus or mi

1. **State the problem:** Simplify the expression $$(2x^2 + 7x^3 - 5x^4) - (4x^4 + 2x^2 - 5x^3)$$ by adding or subtracting like terms. 2. **Write the expression clearly:**

1. **State the problem:** We need to sketch the graph of the inequality $$y \geq -2x + 4$$. 2. **Understand the inequality:** This inequality represents all points $$ (x,y) $$ wher

1. **Problem Statement:** Solve a system of linear equations. 2. **General Formula:** A linear system can be written as:

1. **Problem:** Expand and simplify $\sqrt{3}(6\sqrt{3} + 2)$. 2. **Formula:** Use distributive property: $a(b+c) = ab + ac$.

1. **State the problem:** We have a quadratic function defined as $$f(x) = c + 8x - x^2$$ and we know the range is $$f(x) \leq 19$$. We need to find the value of the constant $$c$$

1. **State the problem:** We are given two curves $y = e^x - 1$ and $y = 6e^{-x}$ and asked to (a) sketch them, (b) show the intersection satisfies $e^{2x} - e^x - 6 = 0$, and (c)

1. **State the problem:** We need to determine the symmetry of the function given by the equation $$x + y = -4$$. 2. **Recall symmetry tests:**

1. **State the problem:** Determine whether the function $$y = 2x^3$$ has symmetry about the x-axis, y-axis, origin, or none. 2. **Recall symmetry rules:**

1. **Problem:** Solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where the equation is in the

1. **State the problem:** Solve the equation $$\frac{2}{3}(x-6)=\frac{1}{2}x+1$$ for $x$. 2. **Write down the equation:** $$\frac{2}{3}(x-6)=\frac{1}{2}x+1$$

1. **State the problem:** We are given a polynomial function with roots $1$ and $3 + i$. We need to find the root that must also be included according to the complex conjugates the