🧮 algebra

1. **State the problem:** Solve the first system of linear equations:

Let's expand and simplify step by step! 🎉 **Step 1:** Imagine you have two groups:

1. **State the problem:** We need to find the value of the sum $$\sum_{n=2}^{43} 900(0.85)^{n-1}$$ and round it to the nearest integer. 2. **Identify the type of sum:** This is a g

1. **State the problem:** We need to find the value of the sum $$\sum_{n=2}^{25} 200(0.85)^{n-1}$$ and round it to the nearest integer. 2. **Identify the type of sum:** This is a g

1. **State the problem:** Simplify the expression $$\frac{1}{3\sqrt[3]{4} + \sqrt{2}}$$. 2. **Recall the formula and rules:** To simplify expressions with roots in the denominator,

1. **State the problem:** Simplify the expression $$\frac{1}{3\sqrt{9 + \sqrt{2}}}$$. 2. **Recall the formula and rules:** To simplify expressions with radicals in the denominator,

1. **State the problem:** Solve the inequality $x + 2 > 2$. 2. **Understand the inequality:** We want to find all values of $x$ such that when we add 2 to $x$, the result is greate

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)$