🧮 algebra

1. **Problem Statement:** Find all possible rational zeros of the polynomial \(x^3 - 5x + 4\) using the Rational Root Theorem and then find the actual rational zeros. 2. **Rational

1. **State the problem:** We are given the ratio of goals scored by Arjun, Simon, and Kath as $2:5:8$. Simon scored 12 more goals than Arjun. We need to find how many goals Kath sc

1. The problem is to understand the function $h(n)$ given by the values $2, -1, 1, 1, 0$. 2. Since $h(n)$ is given as a sequence of values, we interpret it as $h(1)=2$, $h(2)=-1$,

1. **State the problem:** Identify the vertical and horizontal asymptotes of the function $$g(x) = \frac{1}{x - 1} - 5$$. 2. **Vertical asymptote:** Vertical asymptotes occur where

1. **State the problem:** Solve the equation $$\frac{6x}{x - 2} = \frac{4x + 4}{x - 2}$$. 2. **Important note:** The denominator $$x - 2$$ cannot be zero, so $$x \neq 2$$.

1. **Stating the problem:** Calculate the sale price when the original price is 230 and the sale price is 92. 2. **Formula used:** The absolute change is calculated as $$\text{Abso

1. The problem involves understanding the function $$f(x) = \sqrt{x} + \sin(x)$$ and the graph labeled as cm(x) with a length scale of 2 cm. 2. We start by analyzing each component

1. Het probleem is om de som van de zijden te controleren en te corrigeren als er een 2 vergeten is bij de horizontale zijden. 2. De gegeven zijden zijn: 2, 1, 1, 2, 2, 1, 1.

1. **Stating the problem:** We want to analyze the function $$f(x) = \frac{\sqrt{x} + \sin(x)}{\cos(x)}$$ and understand its behavior, including points where it is defined and its

1. The problem asks to find the expanded form of the expression $\left(x+5\right)^2$ using algebraic identities. 2. We use the identity for the square of a binomial: $$\left(a+b\ri

1. **State the problem:** Find the Highest Common Factor (HCF) of 12 and 18 using the division method. 2. **Explain the division method:** The division method (also known as the Eu

1. Let's start by stating the problem: We want to understand what a linear equation is and how to work with it. 2. A linear equation in one variable is an equation that can be writ

1. Problem statement: You asked for a clear, beginner-friendly, step-by-step guide to Functions and Their Graphs so you can understand from the basics. 2. What is a function: A fun

1. **Problem:** Add the linear expressions (12x + 5) + (-10x - 3). 2. **Formula:** To add linear expressions, combine like terms (terms with the same variable) by adding their coef

1. **State the problem:** A ball bounces to a height of 3 meters initially, and each subsequent bounce reaches a height 10% lower than the previous one. We need to find the total h

1. **State the problem:** A ball bounces to a height of 3 meters initially, and each subsequent bounce reaches a height 10% lower than the previous one. We need to find the total h

1. Bài toán yêu cầu giải hệ phương trình: $$\begin{cases} x - 2y = 1 \\ 2x + y = 2 \end{cases}$$

1. **State the problem:** Simplify the expression involving two rational expressions: $$\frac{5}{(x-3)(x+1)} \quad \text{and} \quad \frac{x+1}{(x-2)(x+4)}$$

1. **State the problem:** We are given the linear equation $3x - 2y + 6 = 0$ and the point $(-3, -3)$. We want to check if the point lies on the line. 2. **Recall the rule:** A poi

1. The problem is to find the value of the expression $-6 + 6$. 2. This is a simple addition problem involving integers.

1. The problem is to simplify the expression $- + + = ?$. 2. However, the expression as given is incomplete or unclear because it contains only plus and minus signs without numbers