🧮 algebra

1. The problem is to solve pairs by the square method, which likely means solving quadratic equations or finding pairs of numbers related by squares. 2. The general formula for sol

1. **State the problem:** Solve the equation $$2x + 2^2 = 16$$ for $$x$$. 2. **Rewrite the equation:** Recall that $$2^2 = 4$$, so the equation becomes:

1. **State the problem:** Find the expression for $\tan^{-1}(\sqrt{x})$. 2. **Recall the definition:** The function $\tan^{-1}(y)$, also called arctangent, gives the angle whose ta

1. **State the problem:** We need to find the value of $$v = \sqrt{\frac{a}{b}}$$ where $$a = 6.43$$ (correct to 2 decimal places) and $$b = 5.514$$ (correct to 3 decimal places),

1. **State the problem:** We need to rationalise the denominator of the expression $$\frac{15}{\sqrt{5}}$$ and simplify the result. 2. **Recall the formula and rule:** To rationali

1. **State the problem:** Rationalise the denominator of the expression $$\frac{10 + \sqrt{5}}{4\sqrt{5}}$$ and simplify the result. 2. **Recall the formula and rule:** To rational

1. **Problem statement:** Simplify the expression $$\left(\frac{1}{\sqrt{2}} + \sqrt{2}\right)\left(\frac{1}{\sqrt{2}} - \sqrt{2}\right)$$. 2. **Formula used:** This is a product o

1. **State the problem:** We have a library with an initial number of books $12,000$ and it adds $250$ books every month. We want to model this growth linearly.

1. **State the problem:** We have a linear growth model for the number of cars sold weekly. Given $P_0 = 7$ and $P_1 = 9$, find: (a) The recursive formula for $P_n$.

1. **State the problem:** Solve the equation $$-6=\frac{e}{6} - 7$$ for $e$. 2. **Add 7 to both sides** to isolate the fraction term:

1. **State the problem:** We are given the perimeter formula for a rectangle:

1. **State the problem:** We need to find an equation for the total cost $C$ of a call lasting $M$ minutes, where the first minute costs 5 and each additional minute costs 2.

1. **Problem:** Solve the system of linear equations: $$7x + 9y = 119$$

1. **State the problem:** We need to find the equation of the line $l_1$ that passes through point $B(8, -16)$ and is perpendicular to the line segment $AB$ where $A = (0,0)$ and $

1. **State the problem:** We need to find the equation of the line $l_1$ that passes through point $A(2,0)$ and is perpendicular to the line segment $AB$ where $B(3,1)$. 2. **Find

1. The user asked for an example. 2. Since the request is vague, let's provide a simple algebra example.

1. **State the problem:** We are given $a = 2020$ and $b = 92$.

1. **State the problem:** Find the GCD of $a=252$ and $b=198$ using the Euclidean algorithm and express it as $sa + tb$ where $s,t \in \mathbb{Z}$. Then find the LCM of 252 and 198

1. ปัญหาคือหาค่าของ $a \times b$ เมื่อให้สมการ $a+b=6$ และ $a-b=10$ 2. ใช้สมการสองตัวนี้แก้หาค่า $a$ และ $b$ โดยบวกสมการทั้งสองเข้าด้วยกันเพื่อกำจัด $b$:

1. **State the problem:** Prove that the quadratic expression $x^2 + 5x + 6$ can be factored as $(x + 2)(x + 3)$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx +

1. **Problem 1 (top-left): Simplify $$\frac{6x^2 - x - 2}{2x^2 + 3x + 1} \times \frac{2x^2 + x - 1}{3x^2 + 10x - 8}$$. 2. **Factor all polynomials:**