🧮 algebra

1. The problem asks to identify the rational numbers from the list: $-5$, $\sqrt{x64}$, $2.1$, $\sqrt{11}$, $\frac{2}{5}$, $2\pi$. 2. Recall that a rational number is any number th

1. **State the problem:** Arrange the numbers $0.19 \times 10^4$, $0.019 \times 10^3$, $1.9 \times 10^2$, and $10.9 \times 10^3$ from smallest to largest. 2. **Recall the rule:** T

1. **State the problem:** We are given the numbers $0.19 \times 10^4$, $0.019 \times 10^3$, $1.9 \times 10^2$, and $10.9 \times 10^3$. We want to express each number in standard de

1. **State the problem:** Solve the equation $$\frac{5}{24 - 3x} = -6x$$. 2. **Formula and rules:** To solve for $x$, multiply both sides by the denominator to clear the fraction,

1. **State the problem:** Arrange the numbers $0.19 \times 10^0$, $0.019 \times 10^1$, $1.9 \times 10^2$, and $10.9 \times 10^3$ in order from smallest to largest. 2. **Convert eac

1. **Problem statement:** Evaluate the expressions: a) $5^{-3}$

1. The problem is to evaluate the expression $5^{-3}$. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$ and $n$ is a positive integer.

1. The problem is to evaluate the expression correctly. Since no specific expression was given, let's consider a general approach to evaluating algebraic expressions. 2. The formul

1. **Énoncé du problème :** Calculer une fraction d’un nombre consiste à multiplier cette fraction par le nombre donné. 2. **Formule utilisée :** Pour calculer $\frac{a}{b}$ de $c$

1. Data je jednačina $3x - 7 = 11$. 2. Cilj je da nađemo vrednost promenljive $x$.

1. **State the problem:** We are given the rational expression $$\frac{2x - 3}{x + 4}$$ and want to understand its behavior and graph. 2. **Formula and rules:** This is a rational

1. **State the problem:** We are given the relationship between the number of steps per minute $n$ and the pace length $P$ in metres for men as $$\frac{n}{P} = 140.$$ We need to fi

1. Planteamos el problema: Factorizar la expresión $$(x^3 - 6x^2y + 5y^3)(x^3 + x^2y + y^3)$$ y determinar si se puede factorizar más. 2. Observamos que la expresión es un producto

1. **State the problem:** We are asked to evaluate expressions where we start with a negative number and then add or subtract another number, making the result more negative. This

1. The problem involves adding or subtracting negative numbers, which is called "Case 3" where you start with a negative number and make it more negative. 2. Rule #1 states: Adding

1. **Problem:** Simplify $$\frac{\sqrt[4]{z^5}}{\sqrt[4]{z}}$$ using the Quotient of Powers Property. 2. **Formula:** The Quotient of Powers Property states $$\frac{a^m}{a^n} = a^{

1. **State the problem:** Simplify expressions using the Quotient of Powers Property and write answers in rational form. 2. **Recall the Quotient of Powers Property:** For any nonz

1. **State the problem:** Find the sum of all whole numbers from 1 to 20. 2. **Formula used:** The sum of the first $n$ whole numbers is given by the arithmetic series formula:

1. **State the problem:** Write a recursive formula for the sequence $6, 4, \frac{8}{3}, \frac{16}{9}, \ldots$. 2. **Identify the pattern:** To find a recursive formula, we need to

1. The problem appears to be about simplifying or evaluating an expression involving $x$ and plus/minus signs, but the exact expression is unclear from the input. 2. Since the inpu

1. **State the problem:** Simplify the rational expression $$\frac{75 - 3v^2}{v^2 + v - 30}$$. 2. **Factor the numerator and denominator:**