🧮 algebra

1. State the problem: Simplify the expression and verify the equation $$\frac{(-4)\times 11\times 23\times \sqrt{26}}{(-38)^{-2}\times 1444} = 2^3 \times 11 \times 23$$. 2. Simplif

1. State the problem: Find the value of $k$ such that $5 - \frac{6}{k} = -13$. 2. Start by isolating the term with $k$:

1. لنبدأ بتحديد نوع المعادلات الرياضية التي تريد حلها. هل هي معادلات خطية، تربيعية، أو معادلات من نوع آخر؟ 2. مثال: حل المعادلة التربيعية $ax^2 + bx + c = 0$، حيث $a\neq 0$.

1. The problem is to simplify the expression $\sqrt{x}32 - \sqrt{x}50$ in terms of surds. 2. First, recognize that $\sqrt{x}32$ and $\sqrt{x}50$ should be written as $32\sqrt{x}$ a

1. The problem is to convert the time durations 30 minutes and 2 hours into a ratio. 2. First, convert all times to the same unit for an accurate ratio comparison. Since 1 hour = 6

1. **State the problem:** We are asked to solve and analyze the function $y = -x + 5$. 2. **Rewrite the equation:** The function is a linear equation, where the slope is $-1$ and t

1. **State the problem:** Simplify the expression $$2 - \sqrt{27} + \frac{(12a^2b^3)^{-1} \times (\sqrt{3} ab)^3}{(4^{-1} a) \times (202b)^0}$$. 2. **Simplify each part step-by-ste

1. Solve the equation $x + \sqrt{x} = \frac{6}{25}$. First, let $y = \sqrt{x}$, then $x = y^2$. Substitute:

1. **Problem statement:** Simplify each of the expressions given. \(\text{(a) } \left(a^8 b^{12}\right)^2 \div \left(a^5 b^7\right)^3 \)

1. The problem is to simplify the expression $\frac{2x}{t} \times \frac{1}{2x}$.\n\n2. Write the expression as a single fraction: $$\frac{2x}{t} \times \frac{1}{2x} = \frac{2x \tim

1. Simplify $\frac{(a^8 b^{12})^2}{(a^5 b^7)^3}$: Apply power rule: $(x^m)^n = x^{mn}$.

1. დავიმახსოვროთ, რომ საერთო გამყოფი (GCD) - არის ორ მთელი რიცხვის ყველაზე დიდი რიცხვი, რომელიც ორივეს ভাগდება მთელიებით. 2. მოცემულია ორი რიცხვა: 120 და 676.

1. დავასახელოთ პრობლემა: უნდა ვიპოვოთ რიცხვების 18 და 24 საერთო გამყოფი. 2. საერთო გამყოფის (საუკეთესო საერთო გამყოფის) მოძებნა: უნდა გავარკვიოთ რიცხვების ძირითადი გამყოფები და ვიპ

1. Let's first write down the given function: $$g(t) = \sqrt{3} - t - \sqrt{2} + t$$

1. **State the problem:** We have the function $$f(x) = \frac{x + 4}{x^2 - 9}$$ and we want to analyze its components and behavior. 2. **Factor the denominator:** The denominator i

1. **State the problem:** Given the function $f(x) = 3x^2 - x + 2$, we need to find the values of $f(2)$, $f(-2)$, $f(a)$, $f(-a)$, $f(a+1)$, $2f(a)$, $f(2a)$, $f(a^2)$, $[f(a)]^2$

1. **Problem statement:** Given a graph of a function $f$, answer the following: (a) Find $f(1)$.

1. Stating the problem: Simplify the expression $$\frac{6}{4} - \frac{3}{5} + \left( \frac{4}{2} \cdot \frac{3}{7} y \sqrt{3ab} \right) 3 - 9 - 2 \sqrt{3}$$

1. **State the problem:** Analyze the rational function $$f(x) = \frac{x + 4}{x^2 - 9}$$ by identifying its domain, vertical asymptotes, horizontal asymptote, and intercepts. 2. **

1. Given the function $f(x) = 3x^2 - x + 2$, we need to find the values of $f(2)$, $f(-2)$, $f(a)$, $f(-a)$, $f(a+1)$, $2f(a)$, $f(2a)$, $f(a^2)$, $[f(a)]^2$, and $f(a+h)$.\n\n2. C

1. **State the problem:** We are analyzing a function $f$ based on its graph.