🧮 algebra

1. **State the problem:** Determine whether the function $f(x) = \frac{x^2}{x^2 + 4}$ is even, odd, or neither. 2. **Recall definitions:**

1. **State the problem:** Solve the equation $$9 = 2y - y^2 - 6x - x^2$$ for $x$ and $y$ or analyze its form. 2. **Rewrite the equation:** Move all terms to one side to get a stand

1. **State the problem:** We are given the equation $$16 + x^2 + y^2 - 8x - 6y = 0$$ and need to identify the geometric shape it represents and find its center and radius if it is

1. **State the problem:** Solve the equation $$x^2 + 3x + 4\sqrt{x^2 + 3x - 6} = 18$$ for $x$. 2. **Introduce substitution:** Let $$y = \sqrt{x^2 + 3x - 6}$$. Then $$y^2 = x^2 + 3x

1. **State the problem:** We are given the equation $y^2 + 4x - 20 - 2y = -x^2$ and asked to analyze it as a circle.

1. **Problem Statement:** A computer training course lasts 15 days. Practical training starts at 75 minutes on day 1 and increases by 15 minutes each subsequent day.

1. **State the problem:** Simplify the expression $2(3x-2)(3x-2)$. 2. **Formula and rules:** When multiplying expressions like $(a-b)(a-b)$, use the formula for the square of a bin

1. **Problem Statement:** We are given a budget constraint and minimum purchase requirements for a pizza party.

1. Problem statement: Prove that $\sqrt[3]{3}$ is irrational. 2. Formula and concept: A number is irrational if it cannot be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$

1. **Problem Statement:** Find the Highest Common Factor (H.C.F) of 144 and 96. 2. **Formula and Concept:** The H.C.F (also called GCD) of two numbers is the largest number that di

1. **State the problem:** Find the Highest Common Factor (HCF) of 144 and 96. 2. **Formula and rules:** The HCF of two numbers is the largest number that divides both without leavi

1. **State the problem:** We need to find the Highest Common Factor (HCF) of 144 and 96. 2. **Formula and rules:** The HCF of two numbers is the largest number that divides both wi

1. **State the problem:** Solve the equation $$x^{0.95} \times 760 = 18.5x$$ for $x$. 2. **Rewrite the equation:** We have $$760x^{0.95} = 18.5x$$.

1. Let's analyze the given expression: $\frac{42}{2} = \frac{21}{3} = 7$. 2. First, calculate each fraction separately.

1. **Stating the problem:** We want to understand what prime factorization is and how to find the prime factors of a number. 2. **Definition:** Prime factorization is expressing a

1. **Stating the problem:** (a) Alvin runs 5 km in two sessions. In the first session, his average speed is $x$ km/h. In the second session, his speed is reduced by 2 km/h, and he

1. Problem 30: A snail climbs a 10 m pole, climbing 5 m during the day and sliding down 4 m at night. How many days until it reaches the top? - Each full day (day + night) the snai

1. The problem is to solve the equation or expression given by the user, but since no specific equation or expression was provided, I cannot solve a particular problem. 2. To resol

1. **Problem 1:** Solve the equation $$\left\lceil 2\lfloor x \rfloor + \Delta + 2\right\rceil = 1$$. - Here, $\lfloor x \rfloor$ is the floor function (greatest integer less than

1. **Problem 1:** Solve the equation $[x] + x + [x] = 1$, where $[x]$ denotes the floor function (greatest integer less than or equal to $x$). 2. **Step 1:** Let $n = [x]$, then th

1. **State the problem:** We are given two functions: $$f(x) = 3x^2 - 5x + 7$$