🧮 algebra

1. The problem provides a function $f(x,y)$ with values at specific points in a grid format. 2. We want to understand or analyze the function values given at points $(x,y)$ where $

1. **State the problem:** Solve for $x$ in the equation $$2^x + x = 5.$$\n\n2. **Rewrite the equation:** We want to isolate $x$ but the equation mixes an exponential and a linear t

1. **Problem Statement:** Find the quotient function when dividing two functions, for example, given $f(x)$ and $g(x)$, find $\frac{f(x)}{g(x)}$. 2. **Formula:** The quotient of tw

1. The problem involves solving the equation $$5^x = x^5$$ and analyzing the quadratic equation $$x^2 - nx = 0$$ where $$x = n$$ is a parameter. 2. First, consider the quadratic eq

1. **Stating the problem:** We are given the equation $$5^x = x^e$$ and asked to analyze it along with the related expressions and graph. 2. **Understanding the equation:** The equ

1. **Énoncé du problème :** Développer puis réduire les expressions suivantes : A = (x + 2)(3x + 4)

1. **State the problem:** Simplify the expression \(\frac{\frac{v-5}{v^2-25}}{\frac{11-v}{v-11}}\). 2. **Identify the components:** The numerator is \(\frac{v-5}{v^2-25}\) and the

1. **State the problem:** Find the domain of the function $$f(x) = \frac{x}{\sqrt{3x - x}}$$. 2. **Simplify the expression inside the square root:**

1. Rozwiązać równania macierzowe. **a)** Dane jest równanie macierzowe $$X \cdot \begin{bmatrix}2 & 1 & 5 \\ 1 & 3 & 1\end{bmatrix} = \begin{bmatrix}-1 & -8 & 2 \\ 8 & 14 & 14\end{

1. **State the problem:** Simplify the expression \( \frac{(2y^2 - 10y)(y + 5)}{(y^2 + 10y + 25) \cdot 6} \). 2. **Identify and factor expressions:**

1. **State the problem:** Simplify the expression $y^2 + 10y + 25$. 2. **Formula and rules:** This is a quadratic expression. We can try to factor it using the perfect square trino

1. **State the problem:** Find the least common multiple (LCM) of 60 and 72. 2. **Formula and rules:** The LCM of two numbers is the smallest positive integer that is divisible by

1. **State the problem:** Find the highest common factor (HCF) of 56 and 84. 2. **Formula and rules:** The HCF of two numbers is the largest number that divides both without leavin

1. **State the problem:** We need to find the result of dividing $\frac{1}{2}$ by another number or expression. Since the user only said "1/2 divide," we assume the problem is to d

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + y + z = 3 \\ x + 2y + 3z = 4 \\ x + 4y + 9z = 6 \end{cases}$$

1. The problem is to determine if a given number is a perfect square. 2. A perfect square is an integer that can be expressed as $n^2$ where $n$ is an integer.

1. **State the problem:** You currently have a budget of 100 per month for office snacks, and you want to increase this amount by 50% for next year. 2. **Formula used:** To increas

1. **State the problem:** Simplify the expression $$\frac{x + 5}{x - 4} - \frac{x - 2}{x}$$ by subtracting the two rational expressions. 2. **Find a common denominator:** The denom

1. **State the problem:** Add the rational expressions $$\frac{5}{x-7} + \frac{x-3}{x-4}$$ and simplify the result as much as possible. 2. **Formula and rules:** To add rational ex

1. **State the problem:** Add the rational expressions $\frac{5}{x-7} + \frac{x-3}{x-4}$ and simplify the result. 2. **Find a common denominator:** The denominators are $x-7$ and $

1. The problem is to find the value of an expression or solve an equation where the answer is given as 24. 2. Since the answer is 24, let's consider a simple example: solving for $