🧮 algebra

1. The problem asks to find the three inequalities that define the shaded triangular region bounded by the lines shown on the graph. 2. From the graph description, the boundaries a

1. The problem is to evaluate the expression $9 + e$ where $e$ is the mathematical constant approximately equal to 2.718. 2. The constant $e$ is the base of the natural logarithm a

1. **State the problem:** Divide the mixed number $1 \frac{4}{9}$ by the fraction $\frac{5}{9}$. 2. **Convert the mixed number to an improper fraction:**

1. The problem is to divide the mixed number $1 \frac{1}{2}$ by the fraction $\frac{3}{4}$. 2. First, convert the mixed number to an improper fraction.

1. **State the problem:** We need to solve the division of the mixed number $2 \frac{1}{7}$ by the fraction $\frac{5}{6}$. 2. **Convert the mixed number to an improper fraction:**

1. Let's start by stating the problem: We want to understand the concepts of domain and range in functions. 2. The **domain** of a function is the set of all possible input values

1. **State the problem:** Divide the mixed number $1 \frac{1}{9}$ by the fraction $\frac{5}{6}$. 2. **Convert the mixed number to an improper fraction:**

1. **State the problem:** Simplify the expression $$\frac{2y - 2x \times \frac{2x}{y}}{y}$$. 2. **Recall the order of operations:** Multiplication and division are performed before

1. **State the problem:** We need to find which ordered pairs satisfy the system of inequalities represented by the two lines and their shading. 2. **Identify the lines and inequal

1. The problem asks us to find which ordered pairs satisfy the system of inequalities defined by the lines $y=2x$ and $y=-2x$ with the shaded region being the left half-plane $x \l

1. Énoncé du problème : Trouver l'ordonnée du point de la courbe $C$ associée à la fonction $f(x) = 2x - 3$ pour l'abscisse $x = 4$. 2. Formule utilisée : Pour une fonction linéair

1. Énoncé du problème : Trouver l'image de $-4$ par la fonction $f$ définie par $f(x) = 5x - 3$. 2. Formule utilisée : Pour une fonction linéaire $f(x) = ax + b$, l'image de $x$ es

1. **Problem 33:** A line from the point $(2,3)$ is perpendicular to the line $y=\frac{1}{3}x+1$. Find the coordinates of the intersection point $P$. 2. **Formula and rules:**

1. The problem is to divide the fraction $\frac{8}{3}$ by the whole number 4. 2. The formula for dividing a fraction by a whole number is:

1. The problem is to determine whether a given number is rational or irrational. 2. A rational number is any number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and

1. The problem is to simplify the expression $5\sqrt{16}$.\n\n2. Recall that $\sqrt{16}$ means the square root of 16, which is the number that when squared gives 16.\n\n3. Since $4

1. **State the problem:** Solve the quadratic equation $x^2 - 7x + 6 = 0$. 2. **Formula and rules:** To solve a quadratic equation of the form $ax^2 + bx + c = 0$, we can use facto

1. **Problem Statement:** Find the asymptotes, intercepts, and graph of the function

1. Let's solve the first problem: Calculate $9^{-3/2}$. 2. Recall the exponent rule: $a^{m/n} = \sqrt[n]{a^m}$ and $a^{-b} = \frac{1}{a^b}$.

1. **Stating the problem:** Simplify the expression $$\frac{25^n - 1 \cdot 6^n}{10^{n-1} \cdot 5^n}$$. 2. **Recall the rules:**

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.