🧮 algebra

1. **State the problem:** Solve the equation $3 = 0$. 2. **Analyze the equation:** The equation $3 = 0$ is a simple equality statement.

1. The problem states that the $n^{th}$ term of a sequence is given by the formula $a_n = 4n^2$. 2. We need to find the first three terms of the sequence, which means we will calcu

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Write the formula and rules:** To simplify a rational expression, factor numerator and denominator a

1. Problem: Convert the simultaneous linear equations into matrix form. 2. The matrix form of simultaneous linear equations $ax + by = c$ and $dx + ey = f$ is:

1. **State the problem:** Determine which category correctly describes the number $\sqrt{5}$. The options are: A. whole number

1. **State the problem:** อลิสมีเงินได้สุทธิ 560,000 บาท และถูกหักภาษี ณ ที่จ่าย 7,000 บาท ต้องหาว่าเมื่อยื่นแบบแสดงรายการภาษีเงินได้ จะต้องชำระภาษีเพิ่มหรือได้รับเงินภาษีคืนเท่าไร

1. Muammo: Sizdan algebraik ifodani yechish yoki hisoblash so'ralmoqda. 2. Formulalar va qoidalar: Muammo aniq ko'rsatilmagan, shuning uchun iltimos, aniq masalani taqdim eting.

1. **State the problem:** Solve the inequality $$\frac{2x - 5}{x + 3} \geq 1$$. 2. **Rewrite the inequality:** Subtract 1 from both sides to get a single rational expression:

1. The problem involves understanding the function $f(a)$ defined as: $$

1. **State the problem:** Paola is twice the age of Nat. In 3 years, Paola will be 5 years older than Nat. We need to find their current ages. 2. **Define variables:** Let $N$ be N

1. Problem: Find vertical and horizontal asymptotes, intercepts, domain, and range of the rational function with vertical asymptotes at $x=-2$ and $x=2$, and horizontal asymptotes

1. **Problem Statement:** Given vertical asymptotes at $x = -2$ and $x = 2$, a horizontal asymptote at $y = 1$, no $x$-intercepts, a $y$-intercept at $y = 0$, and domain and range

1. **State the problem:** Vi pays 255 for some shirts and dresses. Each shirt costs 15 and each dress costs 35. Vi buys 9 items in total. We need to find how many shirts and dresse

1. Planteamos el problema: calcular el límite $$\lim_{x \to 2} \frac{\sqrt[3]{x-1} - 1}{\sqrt[4]{x-1} - 1}$$. 2. Para resolver límites con raíces y expresiones que tienden a 0 en n

1. **State the problem:** Solve the inequality $$6^x - 9 \cdot 2^x + 3^{x+2} - 9^x > 0.$$\n\n2. **Rewrite terms to express bases consistently:** Note that $$6^x = (2 \cdot 3)^x = 2

1. **State the problem:** Solve the equation $\lg(x^2) - \lg^2(-x) = 3$ for $x$. 2. **Recall the definitions and domain restrictions:**

1. **Problem:** Factorise the algebraic expressions given. 2. **Formula/Rule:** To factorise expressions, look for common factors or use grouping methods.

1. **Stating the problem:** We are given two points on a line representing the investment amount $A$ over time $t$: $(3, 16500)$ and $(6, 18000)$. We want to find the linear equati

1. **State the problem:** We are given the cost of hiring a surfboard which includes an up-front fee plus an hourly rate. The cost for 3 hours is 50 and for 7 hours is 90. We need

1. **State the problem:** Simplify the expression $\frac{x}{2} \div \frac{1}{2}$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying b

1. **State the problem:** Simplify the expression $\frac{x}{2} \div \frac{1}{2}$.\n\n2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplyin