🧮 algebra

1. **State the problem:** Solve the equation $$\frac{1}{20} = \frac{1}{90 - x} + \frac{1}{x}$$ for $x$. 2. **Use the formula:** To solve equations involving sums of fractions, find

1. The problem states that a quantity is 15% more in October compared to a previous value. 2. To find the new value after a 15% increase, we use the formula:

1. **State the problem:** We know that the number of cars registered in October is 100%.

1. **State the problem:** Solve for $b$ in the equation $16 = \frac{5}{3}(40) + b$. 2. **Write the formula and explain:** We want to isolate $b$ on one side. The equation is of the

1. Stating the problem: Simplify the expression $$\frac{1}{4} \div \left(3^2 \times \frac{1}{9}\right) + \frac{3}{2} \div \frac{2}{3}$$. 2. Recall the rules: Division by a fraction

1. The problem involves simplifying expressions with square roots and cube roots. 2. For the first expression $\sqrt{25} \sqrt{6}$, use the property $\sqrt{a} \sqrt{b} = \sqrt{ab}$

1. **State the problem:** We have three commodities: agriculture (A), manufacturing (M), and transportation (T). Each requires certain units of the others to produce one unit. We w

1. **State the problem:** Solve the inequality $1.2x - 6 \geq 0$. 2. **Write the inequality:**

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。