🧮 algebra

1. **State the problem:** We want to graph the function $$f(x) = \frac{3}{x^2 - 1}$$. 2. **Recall the function behavior:** The function has vertical asymptotes where the denominato

1. **State the problem:** We need to find the domain of the function $$f(x) = \frac{3}{x^2 - 1}$$. 2. **Recall the domain rules:** The domain of a function includes all real number

1. The problem is to evaluate the expression $6^{6^6}$. 2. This is an example of a power tower or tetration, where the exponent itself is an exponentiation.

1. **Problem 7: Calculate one interior angle of a regular polygon with 10 sides. The formula for the measure of one interior angle of a regular polygon with $n$ sides is:

1. **State the problem:** Calculate the annual fixed costs given monthly fixed costs using an Excel formula with cell references. 2. **Formula used:** Annual fixed cost = Monthly f

1. **State the problem:** We need to find the cost of 6 kg of lemons given a linear relationship between mass and cost shown by the graph from (0,0) to (5,14.5). 2. **Identify the

1. نبدأ بحل السؤال الأول: اكتب الحد الرابع في مفكوك $$\left(s + \frac{1}{s}\right)^n$$ حسب أسس $$s$$ التنازلية. 2. نستخدم صيغة الحد العام لمفكوك ذات الحدين:

1. **State the problem:** We are given the function $$f(x) = (x - 1) \cdot (x + 1) \cdot (x + 5)$$ and we want to simplify it or understand its expanded form. 2. **Recall the formu

1. **State the problem:** Find the domain and range of the function $$f(x) = \sqrt{5x - 10}$$ and express them in set notation. 2. **Domain:** The expression inside the square root

1. **State the problem:** Find the domain and range of the function $$f(x) = \sqrt{x + 8}$$. 2. **Domain:** The expression inside the square root must be non-negative because the s

1. **State the problem:** Find the domain and range of the function $$f(x) = \frac{4x+1}{x-7}$$ in set notation. 2. **Find the domain:** The domain is all real numbers $$x$$ for wh

1. **State the problem:** We are given the linear equation $$y = \frac{2}{3}x + 10$$ and we want to understand its properties and graph it. 2. **Formula and explanation:** This is

1. **State the problem:** We need to calculate $\frac{5}{6} \div \frac{2}{3}$. 2. **Recall the division of fractions rule:** Dividing by a fraction is the same as multiplying by it

1. **Problem:** Find the domain and range of the function $$g(x) = 3x^2 - 1$$. 2. **Domain:** Since $$g(x)$$ is a polynomial, it is defined for all real numbers.

1. **Masalah:** Sederhanakan ekspresi $$\left(\frac{a^3 b^{2/3}}{b^{2/3} a^2}\right)^{3/4}$$. 2. **Gunakan aturan pangkat:** $$\frac{a^m}{a^n} = a^{m-n}$$ dan $$(x^m)^n = x^{mn}$$.

1. **Nyatakan masalah:** Seorang freelancer dibayar $200.000$ untuk proyek pertama. Setiap proyek berikutnya, bayarannya naik $8\%$ dari proyek sebelumnya. Kita diminta mencari bes

1. **State the problem:** Solve the equation $$\frac{1}{x^3} = 1$$ for $$x$$. 2. **Recall the rule:** If $$\frac{1}{x^3} = 1$$, then multiplying both sides by $$x^3$$ (assuming $$x

1. **State the problem:** Solve the equation $$x = \frac{1}{x^2}$$ for $x$. 2. **Rewrite the equation:** Multiply both sides by $$x^2$$ to eliminate the denominator:

1. Selesaikan soal berikut: ### a. $\left(\frac{x^{-5}y^4}{xy^3}\right)^{-2}\cdot\left(\frac{x^7y^{-3}}{x^{-4}y^6}\right)^{-\frac{1}{2}}$

1. **State the problem:** Factor the quadratic expression $$4x^2 - 28x + 40$$ completely.\n\n2. **Identify the greatest common factor (GCF):** The coefficients are 4, -28, and 40.

1. **Stating the problem:** Calculate the value of the expression $0,5 \times \frac{2}{7} - 1$. 2. **Convert decimal to fraction:** Note that $0,5$ is the same as $\frac{1}{2}$.