🧮 algebra

1. **State the problem:** We need to solve for $x$ given an equation where the answer is 114. 2. **Identify the equation:** Since the exact equation is not provided, let's assume a

1. **State the problem:** Simplify the expression $x^2 - \sqrt{x}$. 2. **Recall the definitions:**

1. **Stating the problem:** We need to determine the two correct rules when dividing two integers with different signs (one positive, one negative).

1. **Problem Statement:** Determine if the set of vectors of the form $nx + my$ where $n, m$ are integers and $x, y$ are vectors, forms a subgroup of the group of translations. 2.

1. **Problem Statement:** Identify the graph of an odd function among the given four graphs. 2. **Definition of Odd Function:** A function $f(x)$ is odd if it satisfies the conditi

1. The problem asks to find the graph of an even function. 2. An even function satisfies the property $$f(-x) = f(x)$$ for all $x$ in its domain.

1. **State the problem:** A drink-seller had 520 cups in total: small (S), medium (M), and large (L). She used 34 small cups and 20% of medium cups. Then she increased large cups b

1. The problem is to convert the fraction $\frac{54}{60}$ into a percentage. 2. To convert a fraction to a percentage, use the formula:

1. The problem is to convert the fraction $\frac{53}{60}$ into a percentage. 2. The formula to convert a fraction to a percentage is:

1. **State the problem:** We have a cubic polynomial $$h x^3 + 7 x^2 - 48 x + 49$$ that leaves the same remainder when divided by $$x + k$$ and $$x - k$$. We need to find possible

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: $$0.5x + 2y = 10$$