🧮 algebra

1. **Probleemstelling:** Gegeven is de lijn $k: \frac{x}{250} + \frac{y}{350} = 1$. De vergelijking moet herschreven worden in de vorm $35x + 25y = c$ en $c$ moet worden berekend.

1. **Énoncé du problème :** Nous avons deux modèles pour l'évolution de la concentration en principe actif d'un médicament dans le sang.

1. The problem asks to identify the dependent quantities from the table showing Kenzi's weekly allowance savings. 2. In a table showing a relationship between two quantities, the i

1. **State the problem:** Factor the expression $$147(2x-5)^2 - 48(2y+1)^2$$. 2. **Recognize the formula:** This is a difference of squares, which follows the rule:

1. The problem is to evaluate the expression $0/2$. 2. Division by a nonzero number is defined as splitting the numerator into that many parts.

1. **State the problem:** Solve the quadratic equation $$x^2 + 2x - 35 = 0$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an equation of

1. **State the problem:** Factor the quadratic expression $120x^2 - 52x - 224$. 2. **Formula and rules:** To factor a quadratic $ax^2 + bx + c$, find two numbers that multiply to $

1. **State the problem:** We are given the equation $$x^2 + y^2 - 4y + 4 = 100$$ and need to identify the shape and its properties. 2. **Rewrite the equation:** Notice that the ter

1. **State the problem:** We are given the polynomial function $$f(x) = -6x^5 - 3x^4 + 2x - 1$$ and we want to analyze or solve it depending on the context (e.g., find roots, evalu

1. **Problem statement:** Alan cycled from P to Q (64 km) starting at 10:00, stopped for a break, then continued to arrive at 15:00. Brendan started at 12:00 from P to Q, passing A

1. **Problem statement:** We are given a cubic polynomial function $f(x) = ax^3 + bx^2 + cx + d$ with the following conditions:

1. **State the problem:** We are given the equation $$2kv(v+w) - (1 + k(v+w)^2) = 0$$ and want to understand or simplify it after differentiation. 2. **Rewrite the equation:** The

1. **Problem statement:** Vervollständigen Sie die Tabelle für ganzrationale Funktionen 3. und 4. Grades.

1. **State the problem:** We need to substitute $$t = \frac{-x + \sqrt{x^2 + 2y^2}}{2y}$$ into the equation $$x + 2ty = 8t^2 + 4$$ and show that the result simplifies to $$\frac{x}

1. **Stating the problem:** A car travels from point A to point B at an unknown speed $v$ km/h (unloaded), and returns from B to A at 60 km/h (loaded). The average speed for the en

1. **State the problem:** We are given a piecewise function defined as $$y=\begin{cases} x+6 & \text{if } -6 \leq x \leq -2 \\ x^{2} & \text{if } -2 < x < 3 \\ -x+12 & \text{if } x

1. **State the problem:** We have a piecewise function defined as $$f(x) = \begin{cases} -\frac{x}{2} + 6 & \text{for } -10 \leq x \leq -4 \\ \frac{10}{3} & \text{for } -4 < x < 3

1. Problem G 1 a) Partialbruchzerlegung von $$f(s) = \frac{1}{(s-2)(s+2)}$$ 2. Die Funktion ist ein Bruch mit zwei Linearfaktoren im Nenner. Die Partialbruchzerlegung hat die Form:

1. **Stating the problem:** We have a drug dosage problem where a 20 mg tablet is taken once daily, and the drug amount decreases by 30% each day. The amount left after $n$ days is

1. **Stating the problem:** We are given two lines and need to find the two possible values of $m$ such that the area of the triangle formed is a certain value (assumed given or to

1. **State the problem:** We are given two points $(4,0)$ and $(0,2)$ and need to find the equation of the line passing through these points. 2. **Formula used:** The slope-interce