🧮 algebra

1. Énoncé du problème : On a deux fonctions définies sur \(\mathbb{R}\) : \(f(x) = x - 5\) et \(g(x) = x^2 - x + 2\). On doit trouver les expressions de \(h(x)\) pour plusieurs com

1. **State the problem:** Solve the equation $$\frac{4y}{5} + 6 \frac{9}{12} = 11 \frac{11}{20}$$ for $y$. 2. **Convert mixed numbers to improper fractions:**

1. პრობლემა: გვსურს გავიგოთ, როგორ უნდა მოვაგვაროთ ალგებრული ამოცანა ყველაზე მარტივი ხერხით. 2. ალგებრული ამოცანების მოსაგვარებლად ყველაზე მარტივი ხერხი არის:

1. **Énoncé du problème :** Soient $x$ et $y$ deux nombres réels tels que $x \geq 2$, $y \leq 1$ et $x - y = 4$.

1. დავიწყოთ პრობლემის აღწერით: საწვავის ფასმა მოიმატა 40%-ით. 2. თუ საწყისი ფასი იყო $P$, მაშინ ფასის ზრდის შემდეგ ახალი ფასი იქნება $P + 0.40P = 1.40P$.

1. Factorise $x^2 - 6x + 8$. We look for two numbers that multiply to $8$ and add to $-6$. These are $-4$ and $-2$.

1. Factorise $ax - ay$: $$ax - ay = a(x - y)$$

1. Das Problem lautet: Löse die Gleichung $$2x + 3 = 7$$. 2. Die verwendete Formel ist die lineare Gleichung in der Form $$ax + b = c$$, wobei wir $x$ isolieren wollen.

1. **State the problem:** Simplify the expression $$\left(\frac{4a^{-2} b^{3}}{8a^{4} b^{-4}}\right)^{-2}$$. 2. **Recall the rules:**

1. **State the problem:** Evaluate the expression $2 + 1 \times 2$ and verify if it equals any of the given numbers (5, 8, 12, 16, 21). 2. **Recall the order of operations:** Multi

1. **State the problem:** We need to analyze and simplify the function $$y = \frac{\sqrt{1 + x^2 - 4}}{x}$$ and understand its domain and behavior. 2. **Simplify the expression ins

1. El problema nos pide encontrar la función inversa de la función lineal dada $$v(t) = 3t + 5$$. 2. La función inversa, denotada como $$t(v)$$, nos permite encontrar el tiempo $$t

1. The problem is to identify rational numbers from a given set. 2. A rational number is any number that can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q \ne

1. The problem is to evaluate the expression $4.94 \times 10x^{-3}$. 2. This expression involves multiplication and an exponent with a variable $x$.

1. Planteamos el problema: El costo de energía $C(h)$ es directamente proporcional a las horas de funcionamiento $h$ de la máquina. 2. La fórmula para una relación directamente pro

1. مسئله: شما پرسیده‌اید که عدد 1/2 آخر یک عبارت یا محاسبه از کجا آمده است. 2. برای توضیح این موضوع، باید بدانیم که 1/2 معمولاً به معنی نصف یا تقسیم بر 2 است.

1. **State the problem:** Simplify the algebraic expression $$\frac{2}{-3q+5} + 2q - 3$$. 2. **Rewrite the expression:** The expression is $$\frac{2}{-3q+5} + 2q - 3$$.

1. El problema nos pide encontrar la composición de funciones $ (f \circ g)(x) $, que significa aplicar primero $ g(x) $ y luego $ f $ al resultado. 2. Las funciones dadas son:

1. **State the problem:** We are given the vector function $$\vec{y} = (x - 2)(x + 1)z$$ and need to understand or analyze it. 2. **Understand the expression:** The function involv

1. **State the problem:** Simplify the expression $$\frac{-2}{-3q+5} + \frac{2q-3}{1}$$. 2. **Rewrite the expression:** The expression is $$\frac{-2}{-3q+5} + (2q-3)$$.

1. The problem states the formula: $T = \frac{k}{n}$. 2. This formula means that $T$ is directly proportional to $k$ and inversely proportional to $n$.