🧮 algebra

1. **Stating the problem:** We need to understand and possibly simplify or interpret the number given in scientific notation: $1.8181293 \times 10^{12}$.

1. **State the problem:** Solve the equation $$\frac{(Cx - 1)^2}{3} - \frac{x - 2}{2} = 2$$ for $x$. 2. **Rewrite the equation:** Multiply both sides by the least common denominato

1. We beginnen met het probleem: los de vergelijking $2x + 3 = 11$ op. 2. De formule die we gebruiken is de basisregel van algebra: om $x$ te isoleren, moeten we eerst de constante

1. The problem is to convert and understand the relationships between fractions, decimals, and percentages given in the table. 2. Let's analyze the first row: "gekürzter Bruch" (re

1. The problem is to verify the solutions $2\sqrt{31}$ and $-2\sqrt{31}$ for an equation, likely involving a square root. 2. Recall that if $x = \pm 2\sqrt{31}$, then $x^2 = (2\sqr

1. **Problema 3.1: Encontrar as expressões analíticas das funções lineares f, g e h.** Para uma função linear do tipo $f(x) = mx + b$, precisamos determinar o coeficiente angular $

1. **State the problem:** We are given two linear equations: $$y = \frac{2}{3}x + 2$$

1. **State the problem:** Mark's car gets 30 miles per gallon and Jodi's car gets 21 miles per gallon. Both used a whole number of gallons to travel from their home to the theater.

1. The problem is to solve the system of equations. However, the system is not provided in the message, so I cannot solve it without the equations. Please provide the system of equ

1. **Stating the problem:** We are given the function $$f(x) = \frac{1}{6}x^3 + \frac{3}{2}ax^2 - 36a^2x + 10$$ where $$a \in \mathbb{R}^+$$ (positive real numbers).

1. **Problem:** Find the roots of the polynomial $f(x) = x^4 - 10x^3 + 20x^2 + 19x - 12$. 2. **Step 1: Use synthetic division to factor the polynomial.**

1. **Problem statement:** Löse die Gleichung $$16 = ?$$

1. **問題の説明** 与えられた和 $$\sum_{k=1}^n (-x)^{k-1}$$ を $x, n$ の式で表す。

1. **State the problem:** Given $p=100000$ and the equation $p^2 + 2pq + q^2 = 1$, find the value of $q$. 2. **Recall the formula:** The equation $p^2 + 2pq + q^2 = 1$ can be recog

1. **State the problem:** Solve the equation $$(-4) + (-1) + 2 + 5 + \ldots + x = 437$$ where the terms form an arithmetic sequence. 2. **Identify the sequence:** The terms are $$-

1. The problem asks if $\log(7/5)$ divided by $\log(3/4)$ is the same as $\lg(7/5)/\lg(3/4)$. 2. Here, $\lg$ typically denotes the logarithm base 10, and $\log$ without a base ofte

1. **State the problem:** Simplify the expression $$5^{3 - \log_2 25} + 3^{2 - \log_3 3} - 4^{4 - \log_2 5}.$$\n\n2. **Recall logarithm and exponent rules:**\n- $a^{m-n} = \frac{a^

1. **State the problem:** Solve the equation $5 \cdot 6^x = 7 \cdot 8^x$ for $x$. 2. **Rewrite the equation:** We want to isolate $x$. Start by dividing both sides by $7 \cdot 6^x$

1. Het probleem is om gelijknamige breuken te rangschikken, dat wil zeggen breuken met dezelfde noemer. 2. Bij gelijknamige breuken vergelijken we alleen de tellers, omdat de noeme

1. **State the problem:** We want to understand how to go from the equation $$(\ln 3)(\ln 3 + \ln x) = (\ln 4)(\ln 4 + \ln x)$$

1. **Problem statement:** Löse die Gleichung $$ (x - 29)(-2x + 14) = 0 $$ und finde die Werte von $x_1$ und $x_2$. 2. **Formel und Regel:** Wenn das Produkt zweier Faktoren null is