🧮 algebra

1. Problem: Find the 50th term of the sequence defined by $4n+3$ given the 100th term is 403. 2. Formula: The $n^{th}$ term of the sequence is given by $T_n = 4n + 3$.

1. **Problem:** If the $100^{th}$ term of the sequence defined by $4n+3$ is 403, find the $50^{th}$ term. 2. **Formula:** The $n^{th}$ term of the sequence is given by:

1. **بيان المسألة:** لدينا دالة عددية $f$ معرفة على المجال $[-4;4]$ مع تمثيل بياني معطى. 2. **تحديد قيم $f(0)$ و $f(-3)$ و $f(1)$:**

1. ปัญหาคือการหาค่าเครื่องหมาย ? ในเลขฐานสิบหก $1A?_{16}$ ที่มีค่าเท่ากับ $419_{10}$ ในฐานสิบ 2. สูตรแปลงเลขฐานสิบหกเป็นฐานสิบคือ $\text{ค่าฐานสิบ} = \sum (\text{หลัก} \times 16^{\

1. ปัญหาคือการหาค่าของเครื่องหมาย \(?\) ในเลขฐาน 16 ที่ทำให้ \(1A?_{16} = 41910_{10}\) 2. เรารู้ว่าเลขฐาน 16 มีค่าตัวเลขตั้งแต่ 0-9 และ A-F (A=10, B=11, ..., F=15)

1. The problem is to solve a grade 10 level algebra question. Since no specific problem was given, let's consider a common algebra problem: solving a linear equation. 2. Suppose th

1. **State the problem:** We are given that $x^2 - px + q$ is a factor of the cubic polynomial $x^3 + 3px^2 + 3qx + r$. We need to show that $q = -2p^2$. 2. **Use the factorization

1. **State the problem:** We are given that $x^2 - px + 2$ is a factor of the cubic polynomial $x^3 + 3px^2 + 3qx + r$. We need to show that $q = -2p^2$. 2. **Use the factorization

1. **State the problem:** Solve the system of linear equations: $$\frac{2x-7}{2} - \frac{2(x-y)}{3} = 0$$

1. **State the problem:** Simplify the expression $$\frac{X+\frac{2x}{x-2}}{1+\frac{4}{x^2}-4}$$. 2. **Rewrite the expression:** The numerator is $$X + \frac{2x}{x-2}$$ and the den

1. Bài toán yêu cầu tìm các số nguyên $x,y$ thỏa mãn phương trình $$5x^2 - 32y = 193.$$\n\n2. Ta có thể viết lại phương trình dưới dạng $$32y = 5x^2 - 193.$$\n\n3. Do $y$ là số ngu

1. **State the problem:** Simplify the given expression clearly with steps. 2. **Identify the expression:** Since the user did not provide a specific expression, please provide the

1. **State the problem:** We have two inequalities involving an unknown value $x$: - $3 + x \leq 5$

1. **State the problem:** Express the rational function $$\frac{x^4 - 1}{x^2 - 1}$$ in partial fractions. 2. **Recall the formula and rules:** Partial fraction decomposition is use

1. **State the problem:** We are given the first three terms in ascending powers of $x$ in the expansion of $ (3 + px)^n $ as $243 + 810x + qx^2$. We need to find the values of $n$

1. **State the problem:** We are given the first three terms in ascending powers of $x$ in the expansion of $$(3+px)^n$$ as $$243 + 810x + qx^2$$. We need to find the values of $n$

1. The problem is to calculate $3 \times a$. 2. The multiplication of a number by a variable is expressed as $3a$.

1. **State the problem:** We need to solve the equation $$p(x) = (x-2)(3x-4)(2x-5) = 5$$ for $x$. 2. **Rewrite the equation:** Set the product equal to 5:

1. **State the problem:** Find the values of $x$ such that $p(x) = 5$ where $p(x) = 6x^3 - 35x^2 - 34x - 45$. 2. **Set up the equation:**

1. **State the problem:** We need to find the values of $x$ such that $p(x) = 5$ where $p(x) = 6x^3 - 35x^2 - 34x - 45$. 2. **Set up the equation:**

1. **Problem:** Find the slope and y-intercept of the line passing through points (0, 4) and (2, 0). 2. **Formula:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2,