🧮 algebra

1. **State the problem:** Find the Greatest Common Factor (GCF) of 108 and 100. 2. **Formula and rules:** The GCF of two numbers is the largest number that divides both without lea

1. **Problem:** If the LCM of $m$ and 53 is 1279, find the value of $m$. 2. **Formula and rules:** For two numbers $a$ and $b$, the Least Common Multiple (LCM) and Greatest Common

1. **State the problem:** A phone originally priced at 120000 has increased to 124800. We need to find the percentage increase. 2. **Formula for percentage increase:**

1. **Stating the problem:** We have a car priced at 1800 rials initially, and after two years, its price decreases to 1600 rials. We need to find the percentage decrease in price.

1. **State the problem:** We want to show that $$\sum_{r=3}^n \frac{1}{r(r-2)} = \frac{3}{4} - \frac{1}{2n-2} - \frac{1}{2n}$$

1. **State the problem:** Simplify the expression $$\left(\frac{y}{x^2}\right)^3 \left(\frac{x}{y^2}\right)^2$$. 2. **Recall the power of a quotient rule:** For any nonzero $a$ and

1. **Problem Statement:** Given a geometric series where the 4th term is 10 and the 7th term is 80, find: i. The common ratio $r$

1. نبدأ بحل التمرين الثاني: دالة الخط المستقيم $f(x) = mx + b$ مع استثناء النقطة $x = -3$ من المجال. 2. الدالة خطية بشكل عام، وصيغتها $f(x) = mx + b$ حيث $m$ هو الميل و$b$ هو الجزء

1. Problem 102: Given $\lg 2 = a$ and $\log_2 7 = b$, express $\lg 56$ in terms of $a$ and $b$. Step 1: Write $56$ as $56 = 7 \times 8 = 7 \times 2^3$.

1. Problem 90: Given $\log_2 = a$ and $\log_{10} = b$, express $\log_{78.4}$ in terms of $a$ and $b$. Step 1: Use change of base formula: $\log_{78.4} = \frac{\log 78.4}{\log 10}$.

1. Problem 76: Given $a = \log_6 108$, express $\log_2 3$ in terms of $a$. 2. Use the change of base formula: $\log_b c = \frac{\log_k c}{\log_k b}$ for any base $k$.

1. Problem 76: Given $a = \log_6 108$, express $\log_2 3$ in terms of $a$. 2. Use the change of base formula: $\log_b x = \frac{\log_k x}{\log_k b}$ for any base $k$.

1. समस्या: एक चुनाव में कुल 24000 वोट डाले गए हैं, जिनमें से 20.833% वोट अवैध हैं। विजेता को 17000 वैध वोट मिले हैं। हमें हारने वाले को मिले वैध वोटों का प्रतिशत ज्ञात करना है। 2.

1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula or factorization to solve quadratic equations. Here, factorization is simpler.

1. **State the problem:** We are given two functions: $$S(x) = \frac{525}{x}$$

1. **State the problem:** Find the solution set of the inequality $X > 0$.

1. **Stating the problem:** Solve the system of linear equations using the substitution method: $$\begin{cases} 2x + 3y = 2 \\ 2x - 3y = 14 \end{cases}$$

1. **State the problem:** We need to analyze the function given by $$y = \frac{3 - x}{x + 2}$$. 2. **Formula and rules:** This is a rational function where the numerator is $3 - x$

1. **State the problem:** Find the area enclosed by the graphs of \(y = x^2 - 2x + 1\), \(y = x^2 - 4x + 4\), and the x-axis. 2. **Rewrite the functions:**

1. **State the problem:** Find the area enclosed by the graphs of $y=x^2-2x+1$, $y=x^2-4x+4$, and the x-axis. 2. **Rewrite the functions:**

1. **Problem statement:** Demi and Maisy start moving towards each other from points $S$ and $T$ respectively. Maisy starts 1 hour after Demi and moves at double Demi's speed. When