🧮 algebra

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

1. Masalah yang diberikan adalah memeriksa apakah cara penyelesaian metode substitusi pada sistem persamaan linear sudah benar. 2. Metode substitusi melibatkan menyelesaikan satu p

1. Masalah: Gunakan metode substitusi untuk menyelesaikan sistem persamaan linear. 2. Metode substitusi melibatkan langkah-langkah berikut:

1. We are given the system of equations: $$\begin{cases} 2x + 3y = 2 \\ 2x - 3y = 14 \end{cases}$$

1. **State the problem:** We need to compute the balance from the total palay produced over 5 years and the selling price per cavan.

1. **State the problem:** Solve the system of equations using the inverse matrix method: $$\begin{cases} x - y + z = 8 \\ 2x + y - 3z = -15 \\ x + y + z = 4 \end{cases}$$

1. مسئله: حل معادله $\sqrt{x+8} - \sqrt{x+2} = 1$. 2. برای حل این معادله، ابتدا هر دو طرف را به گونه‌ای ساده می‌کنیم که بتوانیم رادیکال‌ها را حذف کنیم. قانون مهم: برای حذف رادیکال‌

1. مسئله: نمودار تابع پله‌ای $$f(x) = 1 - \left\lfloor \frac{x}{3} \right\rfloor$$ را در بازه $$(-3, 3]$$ رسم کنیم. 2. تعریف تابع پله‌ای: تابع $$\left\lfloor x \right\rfloor$$ مقدا