🧮 algebra

1. The problem asks to find the value of 8 raised to the power of $\frac{1}{3}$ using rational exponents. 2. The formula for rational exponents is $a^{\frac{m}{n}} = \sqrt[n]{a^m}$

1. The problem asks to find the value of $8^{\frac{1}{3}}$. 2. The expression $a^{\frac{m}{n}}$ means the $n$th root of $a$ raised to the $m$th power, or equivalently, $\left(\sqrt

1. **Problem:** If the 4th term of an Arithmetic Progression (AP) is 14 and its 12th term is 70, find the 1st and 5th terms. 2. **Formula for the nth term of an AP:**

1. **Problem:** Write any three Arithmetic Progressions (AP) with common difference $d=5$. 2. **Formula:** An AP is defined as $a, a+d, a+2d, \dots$ where $a$ is the first term and

1. Problem: Oblicz pierwiastek z wyrażenia $4n^2 + 7$. 2. Wzór: Pierwiastek kwadratowy z sumy to $$\sqrt{4n^2 + 7}$$.

1. **State the problem:** Simplify the expression $$\frac{x^2 - 7x + 12}{x^2 - 3x} \div \frac{x - 4}{x + 1}$$. 2. **Rewrite division as multiplication:** Dividing by a fraction is

1. Diberikan fungsi $f : \mathbb{R} \to \mathbb{R}$ yang memenuhi relasi: $$f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(x) + 6x$$

1. **State the problem:** Solve for $x$ in the equation $$\frac{x-1}{x} - \frac{2x+1}{3x} = \frac{2}{3}.$$\n\n2. **Identify the formula and rules:** To solve equations with fractio

1. El problema es factorizar la expresión $5x - 10$. 2. Para factorizar, buscamos un factor común en ambos términos.

1. **State the problem:** We are given the line equation $3x - 2y = 10$ (call this line $L1$).

1. The problem is to convert the improper fraction $-\frac{1}{7}$ into a mixed number. 2. A mixed number consists of an integer part and a proper fraction part.

1. The problem is to find the result of multiplying all the numbers from 1 to 9, which is called the factorial of 9, denoted as $9!$. 2. The factorial of a positive integer $n$ is

1. The problem is to find the formulas for the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) of two numbers. 2. The HCF (also called GCD - Greatest Common Diviso

1. **State the problem:** Simplify the expression $6 - \frac{1}{7} \div \frac{3}{14}$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiply

1. **State the problem:** A person pays 6000 per year towards a debt for 4 years, then pays 15000 per year. We want to find the year when the debt is completely paid off.

1. The problem is to find the values of $x$ and $y$. 2. To solve for $x$ and $y$, we need an equation or system of equations involving these variables.

1. **State the problem:** We need to plot the lines $y=3x-11$ and $y=-2x+4$ by completing their tables of values, then use the graph to solve the simultaneous equations. 2. **Compl

1. **State the problem:** We need to write a quadratic function representing a bridge with the following conditions: - Width (distance between x-intercepts) is 5

1. **Problem:** Solve the system of linear equations: $$\begin{cases} x + 2y + 2z = 13 \\ 2x + 3y + z = 11 \\ 4x + 0.5z = 2 \end{cases}$$

1. **Problem Statement:** Find a combination of numbers from the given list that add up to a total of $2681231.00$. 2. **Understanding the Problem:** This is a subset sum problem w

1. **Problem statement:** Given the points $K(0,1,4)$, $K(8,7,7)$, and $K(4,3,3)$ labeled as $C$, $B$, and $A$ respectively, and the equation $z = 3 + 2i$ with real numbers $p$ and