🧮 algebra

1. Le problème demande de déterminer le domaine de définition des fonctions $f(x) = \frac{2x + 3}{x - 5}$ et $g(x) = \frac{x^2 - 4}{x^2 - 9}$. 2. Pour trouver le domaine d'une fonc

1. Solve the equation: $$\frac{m}{2} + \frac{m}{3} + 3 = 2 + \frac{m}{6}$$ Step 1: Find a common denominator for the fractions on the left side. The denominators are 2, 3, and 6. T

1. We are given two vectors \( \mathbf{a} = 2\mathbf{i} - 3\mathbf{j} + 4\mathbf{k} \) and \( \mathbf{b} = \mathbf{i} + 2\mathbf{j} + 2\mathbf{k} \), and we need to find \( \cos\th

1. The expression you provided is $5N^2 + 3N + 2$. This is a quadratic expression where $N$ is a variable, and $5$, $3$, and $2$ are constants called coefficients. 2. The term $5N^

1. Stated problem: Find the value of the expression $31 - 28 \div 7 \times 4$. 2. According to the order of operations (PEMDAS), we first perform division and multiplication from l

1. **State the problem:** Solve the system of equations for $x$ and $y$: $$\begin{cases} x^2 + xy - y^2 + 3x = -4 \\ 2x^2 + 2xy - 2y^2 + 5x - y = -6 \end{cases}$$

1. The problem is to solve the simultaneous equations: $$3x + 2y = 7$$

1. Given the system: $$x \cos A + y \sin A = m$$

1. **State the problem:** We want to evaluate the expression $$31 - 28 \div 7 \times 4\n\n2. **Apply the order of operations (PEMDAS/BODMAS):** First, perform the division and mult

1. **Understanding the problem:** We need to find missing numerators or denominators in equivalent fractions. 2. **Recall the rule:** Two fractions are equivalent if their cross pr

1. The problem provided is unclear as it contains ambiguous notation: F(2;5) and yV(2;3). 2. Typically, notation like F(2;5) or V(2;3) might represent points or function values but

1. Let's understand the problem: We have a Plan A which has a fixed monthly fee of 50 plus a cost of 0.70 per minute used, where $m$ is the number of minutes. 2. The total cost $C$

1. The user input is incomplete since the value of $z$ is not provided. 2. To proceed with any calculations or explanations, please provide the full expression or value for $z$.

1. The problem states a geometric pattern where a figure's number of sides increases linearly, starting with a triangle (3 sides) and adding 2 sides for each consecutive figure. 2.

1. We are given the equation $a - b = c^2$. 2. This equation states that the difference between $a$ and $b$ equals the square of $c$.

1. The problem involves analyzing a Grade 4 learner's interpretation of the number sentence $$12 + 5 = \square + 8$$ and their incorrect working: $$12 + 5 = 17 + 8 = 25$$. 2. The l

1. We are asked to express the expression $$\frac{y^2}{y^2 - x^2} - \frac{y}{y - x}$$ as a single simplified fraction. 2. Start by recognizing that the denominator $$y^2 - x^2$$ is

1. Let's solve the system by adding the equations to eliminate one variable. 2. Consider the system:

1. Stating the problem: Solve the system of equations $$5x - 4y = 11$$

1. The problem is to solve the quadratic equation $$x^2 - 2x = 0$$. 2. Start by factoring the equation. Factor out the common factor $$x$$:

1. נתון: $f(x)=4x+12$ ו- $g(x)=\frac{1}{f(x)}=\frac{1}{4x+12}$.\n\n(א) תחום ההגדרה של $g(x)$ הוא כל הערכים שבהם המכנה שונה מאפס, כלומר: $$4x+12 \neq 0 \Rightarrow x \neq -3.$$\nלכן