🧮 algebra

1. **State the problem:** We are given two linear equations: $$3x - 4y = 8$$

1. **Probleemstelling:** We bekijken lineaire verbanden en formules uit verschillende contexten zoals lijnen, gewichten, kosten en percentages. 2. **Belangrijke formules en regels:

1. **State the problem:** Find the equation of the line passing through points $(2,5)$ and $(5,-1)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x

1. El problema es factorizar la expresión $$a^2x^3 - 9x^3 + 1125 - 125a^2$$. 2. Primero, agrupamos términos para facilitar la factorización:

1. **Problem Statement:** Analyze the function $y=\log_2(x)$. 2. **Domain:** The logarithm is defined for positive arguments only, so $x>0$.

1. Problem: Analyze the function $y = \log_2(x)$. - Domain: $x > 0$ because the logarithm is only defined for positive numbers.

1. **State the problem:** Find the center and radius of the circle given by the equation $$x^2 + y^2 - 6x - 12y + 29 = 0$$. 2. **Formula and rules:** The general form of a circle's

1. **State the problem:** Find the center and radius of the circle given by the equation $$x^2 + y^2 - 10x + 10y + 25 = 0$$. 2. **Formula and rules:** The general form of a circle'

1. **Problem:** Divide $x^2 - 13x - 48$ by $x + 3$ using long division. 2. **Formula and rules:** For polynomial long division, divide the leading term of the dividend by the leadi

1. **Problem:** Natasha’s flat screen television was originally purchased for 300. The value decreases by 7% each year. Find the value after 5 years. 2. **Formula:** The value afte

1. **State the problem:** We are given a table showing the number of tickets purchased and the corresponding number of entries in a raffle drawing. We need to find the rule that re

1. **State the problem.** Alan spent $\frac{7}{10}$ of his allowance on food, then spent half of what was left on stationery, and he had $3$ left.

1. **State the problem.** Alan spent $\frac{7}{10}$ of his allowance on food, then spent half of what was left on stationery, and he had $3$ left.

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. **State the problem:** We have three types of fruits represented by variables: red apple ($A$), bunch of bananas ($B$), and coconut half ($C$). We are given two equations: - Cen

1. **State the problem:** Solve the linear equation $$16 - 2t = 5t + 9$$ for the variable $t$. 2. **Write down the formula and rules:** To solve for $t$, we want to isolate $t$ on

1. **State the problem:** We want to graph the quadratic function $$y = x^2 + 5x + 6$$. 2. **Formula and important rules:** A quadratic function is generally written as $$y = ax^2

1. **State the problem:** Solve the equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the equation:**

1. 문제: \(\left(\frac{4}{2\sqrt{2}}\right)^{2+\sqrt{2}}\)의 값을 구하시오. 2. 사용 공식 및 규칙: 지수법칙에 따라 \(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}\)이고, \(\sqrt{2} = 2^{1/2}\)임을 이용합니다.

1. 문제: $9^{\frac{1}{4}} \times 3^{-\frac{1}{2}}$의 값을 구하세요. 2. 사용되는 공식 및 규칙:

1. The problem asks how to get the numbers 1, 27, 35, 44, 52 from 172 and then find the corresponding numbers for 180. 2. First, let's understand the relationship between 172 and t