🧮 algebra

1. The problem is to determine which graph correctly represents the system of linear inequalities: $$4x - 3y \leq 12$$

1. **Problem Statement:** Given the sequence -2, 7, 16, 25, 34, find the formula the engineer used to determine the assigned values, where $n$ is the number of times the program wa

1. **State the problem:** We need to graph the system of inequalities: $$y \leq -\frac{1}{3}x + 2$$

1. We are asked to add pairs of fractions. The general formula for adding fractions is: $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ are integers and $b,d \ne

1. The problem is to add the fractions $\frac{2}{3}$ and $\frac{3}{4}$.\n\n2. To add fractions, we need a common denominator. The denominators here are 3 and 4. The least common de

1. Задачата е да се съкратят дробките и да се сравнят дробите. 2. За съкращаване на дроби използваме правилото: съкращаваме числителя и знаменателя с общия им най-голям общ делител

1. **State the problem:** Simplify the ratio $$\frac{25w^4}{45w^7}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{9w^5}{36w}$$. 2. **Recall the rules:** When simplifying fractions with variables, divide coefficients and subtract exponen

1. The problem asks for the reciprocal (مقلوب) of the number inside the image, which is $\sqrt{3} - 2$. 2. The reciprocal of a number $x$ is $\frac{1}{x}$.

1. المشكلة: إيجاد قيمة التعبير الجبري \( \sqrt{3} - 2 \). 2. القاعدة: الجذر التربيعي \( \sqrt{a} \) هو العدد الذي إذا ضرب في نفسه يعطي \( a \).

1. **State the problem:** We need to find the Creperie's productivity in crepes per minute before and after changes, and then calculate the percentage improvement. 2. **Formula for

1. **Problem statement:** 14 workers can build a wall in 42 days. We need to find how many days 1 worker will take to build the same wall. 2. **Formula and concept:** The amount of

1. **State the problem:** Simplify the expression $$\frac{3x^2 y^3 z^{-1}}{y^{-2} z^3 \cdot (x^{-1} y^3)^{-3}}$$. 2. **Recall the rules:**

1. The problem asks to complete sentences about percentage change and absolute change. 2. For percentage increase, the rule is: To increase a value by $p\%$, multiply by $1 + \frac

1. **State the problem:** Simplify the complex fraction $\frac{13+9i}{-2-i}$. 2. **Formula and rule:** To divide complex numbers, multiply numerator and denominator by the conjugat

1. نبدأ ببيان المسألة: لدينا عددان حقيقيان $a$ و $b$ حيث $$b = 2 + 3\sqrt{5}, \quad a = 2 + \sqrt{3}$$

1. **State the problem:** Simplify the expression $$\left( \frac{6 x^{-4} y^{5} z^{4}}{2 x^{0} y^{0} z} \right)^2$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the complex fraction $$\frac{-28-11i}{10-9i}$$ where $i$ is the imaginary unit with $i^2 = -1$. 2. **Formula and rule:** To simplify a complex fr

1. **State the problem:** We need to determine if each equation relating hours (h), days (d), months (m), and years (y) is always true, sometimes true, or false. 2. **Recall the de

1. **State the problem:** We are given that $x$ varies inversely as $y$, and when $x=5$, $y=30$. We need to find the value of $y$ when $x=3$. 2. **Recall the formula for inverse va

1. El problema consiste en graficar las funciones por tramos de dos empresas, Emelec S.A. y Power Sierra S.A., definidas para diferentes intervalos de $x$. 2. Para cada empresa, se