🧮 algebra

1. **State the problem:** Solve the equation $$5y + 6 = 8y - 12$$ and check the solution. 2. **Write down the formula and rules:** To solve for $y$, we need to isolate $y$ on one s

1. **State the problem:** Find the points of exclusion, vertical asymptotes, zeros (x-intercepts), factor the expression, and analyze the end behavior and asymptote type for the fu

1. **State the problem:** We want to analyze the rational function $$y = \frac{x^2 + 7x - 11}{x^2 + 16}$$ to find points of exclusion, vertical asymptotes, zeros (x-intercepts), an

1. The problem is to understand the function $f(t) = 1200 \cdot 2^t$ and find its value for a given $t$ or describe its behavior. 2. This is an exponential function where the base

1. The problem states that an influencer has 800,000 followers and is losing followers at a rate of 28% each month. 2. Since the followers are decreasing, this is an exponential de

1. **State the problem:** Find the slope of the line passing through the points $(-4, 0)$ and $(0, 2)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and

1. **State the problem:** Find the slope of the line passing through the points $(-6, 0)$ and $(-3, -3)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ an

1. The problem is to understand how to correctly handle an exponent of 3 when it moves from the numerator (top) to the denominator (bottom) or vice versa. 2. The key rule is: when

1. **State the problem:** Simplify the expression $$\frac{(e'f^3 g)^{-3}}{10 e^0 f g^{-4}}$$ where the numerator and denominator are enclosed in curved brackets. 2. **Recall expone

1. **Problem Statement:** Find all vertical asymptotes of the given functions by identifying where the denominator is zero and verifying by plugging values near those points. 2. **

1. Stating the problem: Calculate the value of $0.6 \times \frac{2}{7} + \frac{4}{5}$. 2. Convert the decimal to a fraction: $0.6 = \frac{6}{10} = \frac{3}{5}$.

1. Vamos resolver a equação do segundo grau dada: $f(x) = x^2 + 3x + 2$. 2. A fórmula geral para encontrar as raízes de uma equação quadrática $ax^2 + bx + c = 0$ é:

1. The problem is to simplify the expression $0.4 \times 3 \frac{a}{b}$. 2. First, rewrite the mixed expression clearly: $0.4 \times 3 \times \frac{a}{b}$.

1. **Problem:** Find the value of $t$ in the equation $3^{2t} = 9$. 2. **Formula and rules:** Recall that $9 = 3^2$, so we can write the equation as $3^{2t} = 3^2$.

1. **State the problem:** Solve the equation $6q + 3q - q = 24$ for $q$. 2. **Combine like terms:** Add the coefficients of $q$ on the left side.

1. **Stating the problem:** We are given a list of fractions and mixed numbers and asked to solve or simplify them. Since no specific operation is mentioned, we will convert all mi

1. The problem is to find the equation of the line passing through the points $(-1, 2)$ and $(3, 4)$. 2. The formula to find the slope $m$ of a line passing through two points $(x_

1. The problem is to understand how to solve equations or problems without using the lambda notation. 2. Lambda (\lambda) is often used in advanced math or programming to represent

1. The problem states that the cost of plums is proportional to the number of pounds bought, with a constant of proportionality of 2. 2. The formula for proportional relationships

1. **Problem Statement:** Find all vertical asymptotes of the given functions. Vertical asymptotes occur where the denominator is zero and the numerator is non-zero. 2. **Function

1. **State the problem:** Sketch the graph of the function $f(x) = -x^2 - 3x - 2$. 2. **Domain:** The domain of any quadratic function is all real numbers, so $\text{Domain} = (-\i