🧮 algebra

1. **Problem:** Find the number of ways to arrange the letters of the word \textbf{MATHEMATICS}. 2. **Understanding the problem:** The word MATHEMATICS has 11 letters with some let

1. The problem is to understand the variable $t$ and its role in an equation or context. 2. Since no specific equation or context is given, $t$ is typically used as a variable repr

1. **State the problem:** Find the x-intercepts of the parabola given by the equation $$y = -2x^2 + 6x - 4$$. The x-intercepts occur where $$y=0$$. 2. **Set the equation to zero:**

1. **State the problem:** Simplify the expression $$\left(\frac{1}{2}a + \frac{2}{3}\right)\left(4a - \frac{3}{2}b\right)$$. 2. **Recall the distributive property:** To multiply tw

1. **State the problem:** Solve for $x$ in terms of $n$ given the equation:

1. **State the problem:** Jane is thinking of a number $x$. Two more than seven times her number is the same as sixteen less than nine times her number. 2. **Translate the problem

1. نبدأ ببيان المشكلة: لدينا كثيرة حدود $f(x)$ وباقي قسمة $f(x)$ على $(x-3)$ يساوي 4، وباقي قسمة $f(x)$ على $(x+2)$ يساوي 9. المطلوب هو إيجاد باقي قسمة $f(x)$ على حاصل ضرب $(x-3)(x

1. **State the problem:** We have a square with side length $s$ and an equilateral triangle with side length $t$. Their perimeters are equal, and the sum of one side of the square

1. **State the problem:** We are given two numbers where one number is twice the other, and their sum is 51. We need to find these two numbers. 2. **Set variables:** Let the smalle

1. **Problem:** Simplify the rational expression \(\frac{2x^2 y^5}{3x^3 y^2}\). 2. **Formula and rules:** To simplify a fraction with variables, divide numerator and denominator by

1. **Énoncé du problème :** Résoudre dans $\mathbb{R}$ l'équation $$x^2 - 1 + 4(x^2 - 1) + 4x - 4 = 0.$$ 2. **Formule et règles importantes :** On va d'abord développer et simplifi

1. **Stating the problem:** We are asked to write the algebraic expression for the ratio of the area of square EFGH to the area of rectangle ABCD.

1. **State the problem:** Find the ratio $a : b$ given the identity $$x(2x + b) + a(x + 1) \equiv 2x^2 + 8cx + 2c$$ where $a$, $b$, and $c$ are non-zero constants.

1. Problem: Find the natural number $n$ such that the equality $\left(1 + \frac{z}{3} x\right)^n \cdot (3 + n x)^2 = 9 + 84 x + \ldots$

1. Problem: Solve the system of equations using substitution and elimination methods. Given:

1. **State the problem:** We are given the function $f(x) = 6x2074$ and need to understand or simplify it. 2. **Analyze the function:** The expression $6x2074$ appears to be a mult

1. The problem is to understand the function notation $F(X)$ and what it represents. 2. In mathematics, $F(X)$ denotes a function named $F$ with $X$ as the input variable.

1. **State the problem:** We are given the function $$y = - (0.8)^x - 5$$ and want to understand its behavior and graph shape. 2. **Formula and rules:** This is an exponential func

1. **State the problem:** We are given the function $$y = - (0.8)^x + 5$$ and want to understand its behavior. 2. **Identify the function type:** This is an exponential function of

1. The problem is to understand the difference between the number 2 and the variable $z$. 2. In mathematics, $2$ is a constant number, which means it always represents the same val

1. **State the problem:** We want to find the number of loaves of White, Wholemeal, and Multigrain bread produced given the total amounts of flour, yeast, and water used. 2. **Set