🧮 algebra

1. **Problem Statement:** A sheet of paper is folded exactly in half once, resulting in 2 equal parts. Then it is folded a second time, resulting in 4 equal parts, and so on. How m

1. **State the problem:** Find the slope of the line passing through the points (2,3) and (5,7). 2. **Formula:** The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is giv

1. **Problem:** Find the slope of the line passing through the points (2,3) and (5,7). 2. **Formula:** The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:

1. **Stating the problem:** Find the slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ using the formula for slope.

1. **Problem Statement:** Simplify each expression using modular arithmetic. 2. **Formula and Explanation:** The expression $a \mod m$ means the remainder when $a$ is divided by $m

1. **Problem Statement:** We have a cubic polynomial $p(x)$.

1. **State the problem:** Simplify or analyze the expression $$ (2x^2 + 3) \cos(x^2) + \tan(5x^2) $$. 2. **Recall the functions involved:**

1. **State the problem:** We are given that 22% of a rope is 55 metres long, and we need to find the full length of the rope. 2. **Formula used:** Percentage means part of a whole.

1. **State the problem:** Calculate the value of the expression $$\frac{13}{25} + \frac{7}{70} + \frac{2}{5} \times \frac{8}{70}$$. 2. **Recall the order of operations:** Multiplic

1. **Problem statement:** A girl receives $n$ cedis each week as pocket money. She saves this money for 5 weeks and then buys a present costing 7900 cedis. 2. **Expression for the

1. **Problem Statement:** Draw addition (\oplus) and multiplication (\otimes) tables for the set \{2,4,6,8\} modulo 9.

Let's solve the first question step by step! 🎉 **Problem:** Solve for $x$ if $x + \log_2(2^x - 6) = 4$

1. مسئله اول: محاسبه مجموع دنباله حسابی با فرمول $$S_n = \frac{n}{2} (a + l)$$ که در آن $$n$$ تعداد جملات، $$a$$ جمله اول و $$l$$ جمله آخر است. 2. مسئله دوم: حل معادله $$x^2 (104 +

1. مسئله را بیان می‌کنیم: در دنباله حسابی داریم $a_1=51$ و $a_8=58$. می‌خواهیم تعداد جملات لازم برای جمع تا حاصل آن از 493 بیشتر شود را پیدا کنیم. 2. فرمول جمله عمومی دنباله حسابی:

1. **Problem Statement:** Given the function $$F(x) = \frac{x + 5}{2 - x}$$, find: i) Turning point (x, y)

1. **Problem Statement:** Verify whether the matrix multiplication $AB$ equals $BA$ for the given matrices: $$A = \begin{bmatrix}1 & 3 \\ 4 & 5\end{bmatrix}, \quad B = \begin{bmatr

1. **Problem Statement:** Solve for $x$ in the equation $x + \log_2(2^x - 6) = 4$. 2. **Formula and Rules:** Recall that $\log_b(a)$ is the logarithm base $b$ of $a$, and the domai

1. **Problem:** Given $a = \sqrt{5 + 2}$ and $b = \sqrt{5 - 2}$, find $a^2 - b^2$. 2. **Formula and rules:** Recall the difference of squares formula: $a^2 - b^2 = (a - b)(a + b)$.

1. The problem is to find the value of the expression or solve the given algebraic problem (please provide the specific problem for detailed steps). 2. Generally, for algebraic pro

1. **State the problem:** Find three-digit numbers such that the number itself is 21 times the sum of its digits. 2. **Define variables:** Let the three-digit number be $100a + 10b

1. **Problem Statement:** Prove that the map $\rho : \mathbb{Z}[i] \to \mathbb{Z}/10\mathbb{Z}$ defined by $\rho(a + bi) = [a + 7b]$ is a homomorphism and find its kernel. 2. **Rec