🧮 algebra

1. **State the problem:** Simplify the expression $\frac{n \times n + n}{n} = 10$ and solve for $n$. 2. **Write the expression clearly:** The numerator is $n \times n + n$, which i

1. **State the problem:** Simplify the expression $$\sqrt{45} - \frac{1}{\sqrt{5}}$$. 2. **Recall the formulas and rules:**

1. **State the problem:** Factor the quadratic expression $x^2 - 4$. 2. **Recall the formula:** This expression is a difference of squares, which follows the rule:

1. The problem is to analyze the function $f(x) = x^2 - 4$. 2. This is a quadratic function in the form $ax^2 + bx + c$ where $a=1$, $b=0$, and $c=-4$.

1. Let's start by stating the problem: factoring is the process of breaking down an expression into simpler expressions (factors) that, when multiplied together, give the original

1. Énoncé du problème : Les billets pour un concert coûtent 12 dollars chacun.

1. **State the problem:** Factor the quadratic expression $x^2 - 4$. 2. **Recall the formula:** This expression is a difference of squares, which follows the rule:

1. **State the problem:** Factor the expression $4x^2 - 16$ and draw its graph. 2. **Formula and rules:** To factor expressions like $a^2 - b^2$, use the difference of squares form

1. Énoncé du problème : Un marchand de fruits génère un revenu $R$ en vendant $n$ boîtes de prunes à 3 dollars chacune. Nous devons identifier la variable indépendante. 2. Formule

1. The problem is to understand why $4$ is not written as $2^2$ in a certain context. 2. The number $4$ can indeed be expressed as $2^2$ because $2$ multiplied by itself equals $4$

1. **State the problem:** We are given the equation $y = ax$ and the value $y = 30$ when $c = 50$. We need to find the relation between $y$ and $x$. 2. **Analyze the given informat

1. **State the problem:** Factor the expression $4x^2 - 16$. 2. **Formula and rules:** To factor expressions like this, look for the greatest common factor (GCF) and recognize spec

1. **State the problem:** Factor the quadratic expression $x^2 - 4$. 2. **Recall the formula:** This expression is a difference of squares, which follows the rule:

1. The problem asks to graph piecewise functions and determine a piecewise formula from a graph. 2. For each piecewise function, the formula is given with domain restrictions. We w

1. **State the problem:** Simplify the expression $$\sqrt{12} - \sqrt{75} + \sqrt{147}$$. 2. **Recall the rule:** The square root of a product can be written as the product of squa

1. **State the problem:** Factor the quadratic expression $x^2 - 4$. 2. **Recall the formula:** This expression is a difference of squares, which follows the rule:

1. **State the problem:** Simplify the expression $$\sqrt{12x} - \sqrt{75x} + \sqrt{147x}$$. 2. **Recall the rule:** The square root of a product can be written as the product of s

1. The problem asks to write the ratio $8w^2 : 6tw$ in the form $1 : n$ and express $n$ in terms of $t$ and $w$ in simplest form. 2. Recall that a ratio $a : b$ can be written as $

1. **Problem statement:** Solve the equation: Seven more than a number is 18.

1. The problem is to identify where the term $8x$ was applied in the previous question. 2. Typically, $8x$ would be a term in an algebraic expression or equation.

1. The question asks where to apply the term $8x$ in an expression or equation. 2. Typically, $8x$ is a term in an algebraic expression or equation and should be combined with like