🧮 algebra

1. **State the problem:** We need to find an expression for the area of a rectangle with height $\frac{3}{n+2}$ and width $\frac{5(n+2)}{13n}$. 2. **Formula for area of a rectangle

1. **State the problem:** Find the equation in point-slope form of the line perpendicular to the line passing through points (1, -1) and (4, 2), and passing through the point (2, 5

1. **State the problem:** Find the equation of the line perpendicular to the given line passing through the point $(3,4)$. 2. **Identify the slope of the given line:** The line pas

1. The problem states: If $\cosh(x) = 2$, find the value of $x$. 2. Recall the definition of hyperbolic cosine:

1. **State the problem:** Solve the equation $$30 - \frac{d}{3} = 18$$ for $d$. 2. **Isolate the term with $d$:** Subtract 30 from both sides to get

1. **State the problem:** We need to solve the equation or expression you have, but since you didn't specify it, let's assume you want a simple example solved in an easy way. 2. **

1. The problem asks to graph the numbers 3 and 4 on a number line. 2. Graphing a number means placing a point at its position on the number line.

1. **State the problem:** Simplify the expression $$A= \sqrt{52 a^2 + 14 a \sqrt{3} a^2}$$. 2. **Rewrite the expression inside the square root:**

1. **State the problem:** Solve the equation $$\frac{1}{x} + \frac{1}{4} = \frac{7}{12}$$ for $x$. 2. **Identify the formula and rules:** To solve for $x$, we need to isolate $x$ b

1. **Problem Statement:** Calculate the product of the two matrices: $$

1. The problem is to simplify the expression A. 2. Since the expression A is not provided, I cannot perform any simplification.

1. **State the problem:** Simplify the expression $4x(5x-20)$. 2. **Use the distributive property:** Multiply $4x$ by each term inside the parentheses. The distributive property st

1. Problem: You want to solve the fractions by "utvide brølene på 3" which means to multiply numerator and denominator by 3. 2. Formula: To extend a fraction by 3, use the rule:

1. **State the problem:** We have a banquet room that can seat a maximum of 69 people. The coach, principal, and vice principal are attending along with the 22 girls on the tennis

1. **State the problem:** Simplify or analyze the expression $2x(x - i)^2(x - \sqrt{3i})^2$ where $i$ is the imaginary unit. 2. **Recall important rules:**

1. **Problem:** Determine whether \(\alpha\) is a mapping in each case. (a) \(\alpha: \mathbb{N} \to \mathbb{N}\) defined by \(\alpha(x) = -x\) for all \(x \in \mathbb{N}\).

1. **Énoncé du problème :** Résoudre dans $\mathbb{R}$ l'équation quadratique $$x^2 - 5x + 6 = 0.$$ 2. **Formule utilisée :** Pour résoudre une équation quadratique $ax^2 + bx + c

1. **State the problem:** Simplify and expand the expression $\left(2\sqrt{x} + \frac{1}{\sqrt{x}}\right) x^5$ using algebraic manipulation and the binomial theorem if applicable.

1. The problem asks to express the quadratic expression $x^2 + 6x + 5$ in the form $(x + a)^2 + b$, where $a$ and $b$ are constants. 2. We use the method of completing the square.

1. The problem is to solve an exponential equation, which generally has the form $a^x = b$ where $a$ and $b$ are constants and $x$ is the variable. 2. The key formula to solve such

1. **State the problem:** Solve the equation $$52x - 120(5x) - 625 = 0$$ and understand how to factor the numbers easily. 2. **Rewrite the equation:** First, simplify the term $$-1