🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{3x - 1}{1 - 3x}$$. 2. **Recall the rule:** When you have a fraction with a numerator and denominator that are negatives or

1. **Problem:** Find the asymptotes of the rational function $$y = \frac{x^2 + 12x + 35}{3x^2 + 19x + 20}$$. 2. **Vertical asymptotes:** These occur where the denominator is zero (

1. The problem states that the sequence $a_n = 3^n$ for $n \geq 2$ satisfies the recurrence relation: $$2a_{n-1} - a_{n-2} = a_n$$

1. **State the problem:** Max starts with $9.89236 \times 10^{923738393930237303939227837338388}$ candy bars and gives away $5.35 \times 10^{8227383738389272}$ candy bars. We need

1. The problem is to solve for the constants in an equation or expression, but the specific equation is missing from your message. 2. To solve for constants, we typically need an e

1. The problem is to solve the second question of q2, but since the exact question is not provided, I will assume a typical algebraic problem for demonstration. 2. Let's consider t

1. **Problem:** Find the value of $$(256)^{0.16} \times (256)^{0.09}$$. 2. **Formula:** When multiplying powers with the same base, add the exponents:

1. **State the problem:** Find the domains of the functions $$f(x) = \sqrt[4]{x - 9}$$ and $$g(x) = \sqrt[3]{3x - 9}$$ and express them in interval notation. 2. **Recall domain rul

1. **State the problem:** Find the domains of the functions $$f(x) = \sqrt[4]{x} - 9$$ and $$g(x) = \sqrt[3]{3x} - 9$$ and write the answers in interval notation. 2. **Recall domai

1. **State the problem:** Find the domains of the functions $f(x) = \sqrt[3]{2x+6}$ and $g(x) = \sqrt[4]{2x+2}$. 2. **Recall domain rules for radicals:**

1. **State the problem:** Find the domains of the functions $$f(x) = \sqrt[4]{3x - 3}$$ and $$g(x) = \sqrt[3]{x + 3}$$ and express them in interval notation. 2. **Recall domain rul

1. **Problem statement:** We have two numbers that add up to 415. One number is a two-digit number (between 10 and 99), and the other is a three-digit number (between 100 and 999).

1. **State the problem:** Solve the equation $w - 3 = \sqrt{5w - 19}$ for $w$. 2. **Understand the equation:** The equation involves a square root. To solve it, we will isolate the

1. **State the problem:** Solve the quadratic equation $$3x^2 + 2x - 21 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^2 + bx + c = 0$$ is $$x = \frac{-b \pm \s

1. **State the problem:** Solve for real number $y$ in the equation $$y - 2 = \sqrt{10 - 3y}.$$\n\n2. **Understand the equation:** The right side is a square root, so the expressio

1. **State the problem:** Solve for $v$ in the equation $$\sqrt{-3v + 40} = v - 4.$$\n\n2. **Understand the domain:** The expression inside the square root must be non-negative, so

1. **State the problem:** Solve the equation $$2^{-115x - 15} = (2^9)^{-13x + 14}$$ for $x$. 2. **Use the property of exponents:** Recall that $(a^m)^n = a^{mn}$.

1. **Problem Statement:** We are given the height of a ball during a slam dunk modeled by the quadratic function:

1. **Stating the problem:** We are given the equation $[x] - \{x\} = \frac{x}{3}$, where $[x]$ is the greatest integer function (floor function) and $\{x\}$ is the fractional part

1. **State the problem:** Simplify the expression $$\frac{16x^{40}y^{18}x^{14}}{y^{18}w^{14}}^{19} = 16^4 x^A y^B w^C$$ and identify the integers $A$, $B$, $C$, and $D$. 2. **Rewri

1. **Problem Statement:** Given the graph of $y=\frac{1}{f(x)}$, we need to sketch $y=f(x)$, determine the equation of $f(x)$, and state any asymptotes. 2. **Understanding Reciproc