🧮 algebra

1. **State the problem:** Pablo shares 525 cupcakes in the ratio 3 : 4 between his bakery and a supermarket. We need to find how many cupcakes the supermarket gets. 2. **Understand

1. The problem is to solve the equation $x^2 = 9$ over the real numbers $\mathbb{R}$. 2. The general formula to solve $x^2 = a$ is:

1. Das Problem besteht darin, das lineare Gleichungssystem zu lösen: $$y = 1.5x - 1$$

1. **Problemstellung:** Gegeben sind die Punkte $P(2|1)$ und $Q(-4|10)$, die auf einer Geraden liegen. Gesucht ist die Funktionsgleichung der Geraden in der Form $y = mx + b$. 2. *

1. **State the problem:** Vani wants to treat 12 friends with either bubble tea or ice-cream cones.

1. **State the problem:** Vani wants to treat 12 friends with either bubble tea or ice-cream cones. 2. **Define variables:** Let $x$ be the number of bubble teas and $y$ be the num

1. **State the problem:** Solve the compound inequality $$d-5 < \frac{2d}{5} \leq \frac{d}{2} + \frac{1}{5}$$. 2. **Break the compound inequality into two parts:**

1. **State the problem:** We have two types of energy drinks: 2-Liter jugs costing 4 each and 0.5-Liter bottles costing 1.5 each.

1. **State the problem:** We have two types of energy drinks: 2-Liter jugs costing 4 each and 0.5-Liter bottles costing 1.5 each.

1. **State the problem:** Solve the simultaneous equations: a) $y = 4x - 10$

1. **State the problem:** Solve the system of linear equations: $$0.5x + 2y = 10$$

1. **Problem statement:** Given the family of functions defined for $k > 0$ by $$f_k(x) = \frac{1}{2k} \cdot x^2 \cdot (x - 2k)^2,$$

1. **Problemstellung:** Löse das Gleichungssystem $$2^y = 2 \cdot 4^x$$

1. **Problem statement:** We have two functions \(y = x - |x - 1| + 2\) and \(y = |x|\) to plot on the same graph. Also, solve the inequality \(|x| + |x - 2| \leq x + 4\) and find

1. The problem states that we must use the answer from part one to solve the current problem. 2. To proceed, identify the answer from part one, denote it as $x$.

1. **State the problem:** We need to find the number of solutions to the equation $$x^4 = 3 - 20x^2$$.

1. **Problem statement:** Berechnen Sie die Nullstellen der quadratischen Funktion $h(x) = x^2 + 6x + 9$. 2. **Formel:** Die Nullstellen einer quadratischen Funktion $ax^2 + bx + c

1. The problem is to evaluate the logarithm of a fraction, specifically $\log \frac{2}{ }$. However, the denominator is missing, so the expression is incomplete. 2. The logarithm o

1. Problem: Löse die Gleichung $m + 5 = 11$ nach $m$ auf. 2. Formel: Um eine Variable zu isolieren, subtrahiere die Zahl auf der gleichen Seite wie die Variable von beiden Seiten d

1. **State the problem:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$.

1. **Problem statement:** Alice wants to buy the same number of apples, oranges, and pears. Apples come in packs of 12, oranges in packs of 7, and pears in packs of 9. We need to f