🧮 algebra

1. **State the problem:** We need to find the monthly revenue function $R(x)$ for a city where each resident pays a base fee plus a variable fee depending on water usage.

1. **Problem Statement:** We are given one line equation and points on a graph forming a quadrilateral. We need to find the equations of the other three lines connecting the points

1. **State the problem:** We are given the equation $$\frac{x}{5} + \frac{y}{2} = 1$$ and asked to analyze it. 2. **Rewrite the equation:** To better understand the line, multiply

1. **State the problem:** We need to find how many times greater the volume of the large dog crate is compared to the small dog crate. 2. **Recall the formula for volume of a recta

1. **State the problem:** Lenny paid 12.5% tax on the motorcycle, which added 1437.50 to the price. We need to find the original price before tax. 2. **Formula:** Tax amount = Tax

1. The problem asks for an expression representing 108 divided by the sum of 2 and 7. 2. The sum of 2 and 7 is calculated as $2 + 7$.

1. **State the problem:** Solve the two-step equation $$4(y - 81) = -20$$ for $y$. 2. **Understand the equation:** This is a two-step equation where $y$ is inside parentheses multi

1. **State the problem:** Solve for $s$ in the equation $$\frac{s - 37}{-8} = -6.$$\n\n2. **Formula and rules:** To solve for $s$, we need to isolate $s$ on one side. Since $s$ is

1. **State the problem:** We have the function $f(x) = 10 \left(\frac{1}{5}\right)^x$. We need to find its domain, range, asymptotes, and the average rate of change from $x = -2$ t

1. The problem is to understand if we can multiply the expression $(4x+10)$ by 3 to get 15 as a common denominator on the left side. 2. When dealing with fractions or expressions,

1. The problem asks to find the slope of the line passing through the points $(-2, -2)$ and $(1, 1)$. 2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_

1. **State the problem:** Solve the equation $$\frac{45 - 2x}{15} - \frac{4x + 10}{5} = \frac{15 - 14x}{9}$$ for $x$. 2. **Identify the formula and rules:** To solve equations with

1. The problem asks for the coefficient in the expression $11 + 5x - 7$. 2. A coefficient is the numerical factor multiplied by a variable in an algebraic term.

1. The problem asks us to identify the variable in the expression $13x + 52$. 2. In algebra, a variable is a symbol that represents an unknown or changeable value.

1. **State the problem:** Evaluate the expression $y^2 - 5$ when $y = 3$. 2. **Write the expression:**

1. The problem asks us to evaluate the expression $13i$ when $i=2$. 2. The expression is a simple multiplication of the constant 13 by the variable $i$.

1. The problem asks us to evaluate the expression $7b$ when $b=6$. 2. The expression is a simple multiplication: $7b$ means $7 \times b$.

1. The problem is to evaluate the expression $ (4 - 1) \cdot 5 $. 2. According to the order of operations (PEMDAS), we first solve the expression inside the parentheses.

1. **State the problem:** Evaluate the expression $9 + (8 - 3) \cdot 2$ using the order of operations (PEMDAS). 2. **Recall the order of operations:**

1. **Problem Statement:** Determine whether each function (A, B, and C) is linear or nonlinear based on their representations (table, graph, equation) and justify the answers. 2. *

1. The problem asks whether the given curve is the graph of a function. 2. A function must pass the vertical line test: any vertical line drawn through the graph should intersect i