🧮 algebra

1. The problem is to understand and analyze the equation $\operatorname{sug}(an) + i g'(ga) = dih$. 2. First, identify the components: $\operatorname{sug}(an)$ appears to be a func

1. **State the problem:** Find the values of $x$, $y$, and $z$ such that the vector $(x y, x + y, z - 1)$ equals $(4, 2, 3)$. 2. **Set up equations:** Since the vectors are equal,

1. **State the problem:** Find $x$, $y$, and $z$ such that the vector $(x y, x + y, z - 1) = (4, 2, 3)$. 2. **Use the definition of equality of vectors:** Corresponding components

1. **State the problem:** Find the value of the limit $$\lim_{x \to +\infty} \frac{2^{-x}}{2^x}$$. 2. **Recall the properties of exponents:**

1. **State the problem:** Simplify the expression $-y4 - y4$. 2. **Understand the terms:** Here, $y4$ means $y \times 4$ or simply $4y$.

1. **State the problem:** We are given the function $$y = e^{\sqrt{7x^2 - 1}}$$ and want to understand its behavior. 2. **Recall the formula and rules:** The function involves an e

1. **State the problem:** Nadia needs to buy guttering to cover the perimeter of an L-shaped roof with given side lengths. 2. **Identify the sides:** The roof has four sides with l

1. The problem asks us to determine whether the sequence \(a_n\) is increasing or decreasing by comparing \(a_{n+1}\) and \(a_n\). 2. To analyze this, we use the rule:

1. **State the problem:** We have a sequence defined by the formula $a_n = \frac{n + 2}{4n}$ for any natural number $n$. We need to find the first three terms of this sequence. 2.

1. Problem statement: $g(x)=\frac{-2x^2+7}{\sqrt{x^3+5x+6}-\sqrt{6}}$.\n2. Strategy: Rationalize the denominator by multiplying numerator and denominator by the conjugate $\sqrt{x^

1. **Problem Statement:** Find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of the numbers 18, 20, and 10. 2. **Formulas and Rules:**

1. **State the problem:** We have a rectangle where the length is 5 cm greater than the width. The area of the rectangle is 84 cm². We need to find the length and the width. 2. **F

1. **State the problem:** Fully factorize the expression $1 - 81y^4$. 2. **Recognize the form:** This is a difference of squares since $1 = 1^2$ and $81y^4 = (9y^2)^2$.

1. **State the problem:** We need to find the percentage of all animals treated during the weekend that were guinea pigs. 2. **Given data:**

1. **State the problem:** We have a pie chart showing sales of electronic devices in April with total sales of 900 units. The central angle for tablets is 50°. 2. **Find the number

1. **State the problem:** Convert the quadratic equation $y = x^2 - 4x + 6$ into vertex form. 2. **Recall the vertex form:** The vertex form of a quadratic is $$y = a(x-h)^2 + k$$

1. **Problem:** Znajdź równanie osi symetrii paraboli f(x) = x^2 + bx + c, która przechodzi przez punkty A(-4,29) i B(1,-6). 2. **Wzór funkcji kwadratowej:** $$f(x) = x^2 + bx + c$

1. مسئله را بیان می‌کنیم: می‌خواهیم عبارت $ (4x^2 + 4xy + y^2) (4x^2 - 4xy + y^2) $ را ساده کنیم.

1. مسئله: ضرب دو چندجمله‌ای $x^2 + 5x + 6$ و $x^2 + 5x + 4$ را پیدا کنید. 2. فرمول: برای ضرب دو چندجمله‌ای، هر جمله از چندجمله‌ای اول را در هر جمله از چندجمله‌ای دوم ضرب می‌کنیم و

1. **Problem statement:** The length of a rectangle is 7 cm longer than its width. The perimeter of the rectangle is 74 cm. We need to find the length and the area of the rectangle

1. **State the problem:** Solve for $x$ in the equation $5x - 7 = 17 - 3(2 - x)$. 2. **Write down the equation:**