🧮 algebra

1. **State the problem:** Convert the repeating decimal $0.2\overline{9}$ into a fraction in its simplest form. 2. **Understand the repeating decimal:** The notation $0.2\overline{

1. **State the problem:** Simplify the expression $-2 - \frac{i}{4} + 10i$. 2. **Recall the rules:**

1. The problem is to expand the expression $ (y - 2)(y - 4) $ and simplify it. 2. We use the distributive property (also called FOIL for binomials):

1. **State the problem:** Simplify the expression $-3x + 4x$. 2. **Recall the rule:** When adding or subtracting like terms (terms with the same variable and exponent), combine the

1. **State the problem:** Simplify the complex fraction $$\frac{5 + 2i}{-2 - 5i}$$ where $i$ is the imaginary unit with $i^2 = -1$. 2. **Formula and rule:** To simplify a fraction

1. Problemstellung: Wir sollen äquivalente Gleichungen zu den gegebenen Gleichungen finden und zuordnen. 2. Wichtig: Zwei Gleichungen sind äquivalent, wenn sie dieselbe Lösungsmeng

1. **State the problem:** We need to find which expressions are equivalent to the quadratic expression $$x^2 + 4x + 3$$. 2. **Recall the formula:** A quadratic expression $$ax^2 +

1. We are given multiple linear equations to solve for $x$. 2. The general approach for solving linear equations is to isolate $x$ on one side by performing inverse operations such

1. **Problem statement:** We are given two lines: - Line $g$ in parametric form: $$\mathbf{X} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} + t \cdot \begin{pmatrix} 1 \\ 4 \end{pmatrix}$

1. Das Problem besteht darin, die algebraischen Begriffe im Zusammenhang mit der Oberfläche $O$ eines Zylinders zu verstehen und zu überprüfen, welche Aussagen korrekt sind. 2. Die

1. Das Problem besteht darin, die algebraischen Begriffe und Umformungen für die Oberfläche $O$ eines Zylinders zu verstehen. 2. Die gegebene Formel für die Oberfläche lautet:

1. **State the problem:** Simplify the expression $$ (x + y + 2)(2x - y - 1) - (x + 2)(y - 3) $$. 2. **Recall the distributive property:** To multiply two binomials or polynomials,

1. **Problemstellung:** Gegeben sind $f$ Frauen und $m$ Männer in einem Elektrogeschäft.

1. **State the problem:** Solve the system of linear equations using the inverse matrix method and Cramer's rule. Given equations:

1. The problem is to understand and verify inequalities involving negative and positive numbers, especially temperatures. 2. Important rule: On the number line, numbers to the righ

1. The problem asks to sketch and graph the solution sets of quadratic inequalities such as $$y \geq 2(x - 3)^2 - 8$$ and others. 2. The general form of a quadratic inequality is $

1. **Exercice 1** **a. Résoudre l'inéquation** $(-1 - x)(4x + 4) < 0$

1. **Exercice 1** **a. Résoudre l'inéquation** $(-1 - x)(4x + 4) < 0$

1. **State the problem:** We need to find the equation of a line in slope-intercept form $y=mx+b$ that matches the graphed line. 2. **Recall the slope-intercept form:** The equatio

1. **Problem 8:** A truck rental agency offers two plans: - Plan A: $85$ per week plus $0.30$ per mile driven.

1. **State the problems:** We have three expressions to simplify: