🧮 algebra

1. **State the problem:** We need to find the value of the expression $$x^3 - 3x$$ where $$x = \sqrt[3]{2 - \sqrt{3}} - \sqrt[3]{2 + \sqrt{3}}$$. 2. **Recall the formula:** For any

1. **Énoncé du problème :** Répondre par vrai ou faux aux affirmations suivantes concernant les polynômes.

1. **State the problem:** Solve the quadratic equation $2x^2 - x + 2 = 0$. 2. **Formula used:** The quadratic formula is used to solve equations of the form $ax^2 + bx + c = 0$:

Let's factor the expression step by step! 🎉 **Step 1:** Look at the expression: $x^2 - 3^3$

Let's factor $x^2 - 9$ step by step! 🎉 1️⃣ Imagine you have $x^2$ which is $x$ times $x$:

1. **State the problem:** Find the equation of the line passing through point $(2, -5)$ and perpendicular to the line given by $3x - 6y = 24$. 2. **Rewrite the given line in slope-

1. **State the problem:** We are given two lines defined by points and need to find their slopes and determine their relationship (parallel, perpendicular, or neither). 2. **Formul

1. **State the problem:** Find the equation of the line passing through the point $(5, 10)$ and perpendicular to the line $x = -3$. 2. **Understand the given line:** The line $x =

1. **State the problem:** Solve for $x$ in the equation $$\frac{x + 2}{7} = \frac{2x - 4}{6}.$$\n\n2. **Formula and rules:** To solve equations with fractions, cross-multiply to el

1. Stating the problem: Solve for $x$ in the equation $$\frac{8}{x-6} = \frac{5}{x+6}$$. 2. To solve equations with fractions, we use cross-multiplication: multiply both sides by t

1. The problem states that there is no $p$ in the function, which means the function does not contain the variable $p$. 2. This implies the function is independent of $p$ and does

1. **State the problem:** We need to analyze the function $$f(x) = p|x + 2| - |2x - 4|$$ where $p$ is a constant. 2. **Recall the absolute value definition:** For any real number $

Let's find the equation of the line perpendicular to $y=\frac{2}{3}x - 1$ that goes through the point $(3,4)$! 🎉 1️⃣ First, look at the slope of the given line. It is $\frac{2}{3}$

1. **State the problem:** We are given the line equation $$y=\frac{2}{3}x - 1$$ and need to find the equation of the line perpendicular to it that passes through the point $$(3,4)$

1. **State the problem:** We are given the line equation $y=\frac{3}{2}x-1$ and need to find the equation of the line perpendicular to it that passes through the point $(3,4)$. 2.

1. **State the problem:** We need to graph the quadratic function $$f(x) = -4x^2$$ on a Cartesian coordinate plane. 2. **Recall the formula and properties:** The function is a quad

1. The problem is incomplete as no specific expression or equation is provided to find the value for. 2. To solve any algebraic or arithmetic problem, we first need the exact expre

1. **State the problem:** Solve for $x$ in the equation $\frac{x}{13} = \frac{7}{91}$.\n\n2. **Formula and rule:** To solve for $x$ in a proportion $\frac{a}{b} = \frac{c}{d}$, cro

1. **State the problem:** Graph the inequality $3x - 4y > 12$ using intercepts. 2. **Rewrite the inequality as an equation to find intercepts:**

1. **State the problem:** Simplify the expression $$\frac{c^{-3} d^{5}}{c^{2} d^{-1}}$$. 2. **Recall the laws of exponents:**

1. **State the problem:** Simplify the expression $\frac{b^{-2}}{b^{6}}$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same base, su