🧮 algebra

1. **State the problem:** Callie's company has fixed monthly expenses of $3200 and variable costs of $2.40 per pillow. Each pillow sells for $18. We want to find the number of pill

1. Problemi: Zgjidh ekuacionin linear $2x + 3 = 7$. 2. Formula dhe rregullat: Për të zgjidhur ekuacionet lineare, qëllimi është të izolosh $x$ në njërën anë të ekuacionit duke krye

1. Problem: Berechne günstig den Ausdruck a) $-12,6 - (+250) - (+7,4)$. 2. Wir verwenden das Kommutativgesetz der Addition, das besagt, dass die Reihenfolge der Summanden vertausch

1. **Stating the problem:** We need to describe the slopes of parallel and perpendicular lines and determine the relationship between line segments AB and CD for given points.

1. **State the problem:** Determine if the line segments AB and CD are parallel, perpendicular, or neither for the points given in problem 18: A(-4, 3), B(2, -12), C(10, 5), and D(

1. **Problem statement for 4.60:** Vis at $(x - 1)$ er en faktor i $P(x) = x^3 + 4x^2 + x - 6$.

1. **State the problem:** Simplify the expression $$\sqrt[3]{-64x^6y^9}$$. 2. **Recall the cube root properties:**

1. **State the problem:** Simplify the expression $$\frac{x^3}{x^{1/2}}$$ and find the value of $a$ such that $$\frac{x^3}{x^{1/2}} = x^a$$. 2. **Recall the exponent rule:** When d

1. **Problem statement:** Solve the system of equations $$2x + y = 10$$

1. **Problem statement:** Given the function $g(x) = \frac{1}{9}x^3 - 3x$, analyze its properties as requested in parts a) to g). 2. **Part a) Graph sketch:** The function is cubic

1. **Stating the problem:** Finn stigningstallet til linja som går gjennom punktene (1, 1) og (4, 7). 2. **Formel for stigningstall:** Stigningstallet $m$ mellom to punkter $(x_1,

1. **State the problem:** We need to expand and simplify the expression $(-7x+2)(-3x-4)$. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL method

1. **State the problem:** Simplify the expression $$(9x+3)(-2x-2)$$. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Find the zeros (roots) of the quadratic function given in vertex form: $$a(x-h)^2 + k = 0$$ 2. **Formula and rules:** The zeros of a quadratic are the val

1. Énonçons le problème : Trouver les coefficients du polynôme caractéristique d'une matrice donnée en utilisant la méthode des coefficients. 2. Le polynôme caractéristique $p(\lam

1. Énonçons le problème : On cherche à vérifier le calcul du polynôme caractéristique $\chi_A(\lambda)$ de la matrice symétrique donnée et à comprendre pourquoi le résultat ne corr

1. **Problem statement:** Stelle eine Gleichung auf und löse mit quadratischer Ergänzung: Das doppelte Quadrat einer Zahl ist um eins größer als die Differenz aus dem 24-fachen der

1. **State the problem:** A boat travels 25 km upstream in 5 hours and returns downstream in 0.5 hours. We need to find the speed of the boat in still water ($b$) and the speed of

1. **State the problem:** We are given the formula for the Ponderal Index: $$P = \frac{M}{h^3}$$ where $P$ is the Ponderal Index, $M$ is the mass (weight), and $h$ is the height.

1. **Stel het probleem vast:** We willen de richtingsgetallen (richtingsvector) van de rechte $f$ vinden, gegeven in parametervergelijking: $$f : \begin{cases} x = 1 + 2k \\ y = 10

1. **Problemstellung:** Wir sollen 1 Liter der neuen Sorte PLOP mit 50% Gesamtfruchtgehalt und 20% Maracujaanteil aus den drei Mischgetränken A, B und C mischen. 2. **Gegebene Fruc