🧮 algebra

1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$

1. **State the problem:** We are given the function $$f(x) = \frac{x^{2}}{\sqrt{x^{2} + 2x - 3}}$$ and need to analyze it, including its domain and behavior. 2. **Identify the doma

1. **State the problem:** Add the fractions $\frac{1}{2}$ and $\frac{1}{2}$.\n\n2. **Formula used:** When adding fractions with the same denominator, add the numerators and keep th

1. **State the problem:** We are given the function $f(x) = \sqrt{2x^2 - 9x - 5}$ and asked to analyze it. 2. **Understand the domain:** Since $f(x)$ involves a square root, the ex

1. **Stating the problem:** We have two functions: $f(x) = x^2$ and $g(x) = 2x + 1$. We need to find the following combined functions:

1. **State the problem:** Given two functions $f(x) = x^2$ and $g(x) = 2x + 1$, find the following combined functions: $(f+g)(x)$, $(f-g)(x)$, $(fg)(x)$, and $(f/g)(x)$. 2. **Recal

1. **Problem Statement:** You asked why the term $50t$ was added when simplifying the profit equation in problem b.

1. **State the problem:** Kelly and Sarah need at least 12 dollars in change using quarters and dimes. They also need at least six more quarters than dimes.

1. We are given points on a line: (2, -10), (5, 8), (8, 26), and (11, 44). 2. The problem asks for the slope of the line passing through these points.

1. **State the problem:** Kelly and Sarah need at least 12 dollars in change using quarters and dimes. Let $x$ be the number of quarters and $y$ be the number of dimes. 2. **Transl

1. **State the problem:** We are given four points on a line: $(30,45)$, $(33,33)$, $(36,21)$, and $(39,9)$. We need to find the slope of the line passing through these points. 2.

1. We are given a set of points $(x, y)$: $(4, 24)$, $(5, 19)$, $(6, 14)$, and $(7, 9)$. We need to find the slope of the line passing through these points. 2. The formula for the

1. The problem is to find the slope of the line passing through the points given in the table: (3,7), (8,5), (13,3), and (18,1). 2. The formula for the slope $m$ between two points

1. **State the problem:** We are given points on a line: (3,20), (7,16), (11,12), and (15,8). We need to find the slope of the line passing through these points. 2. **Formula for s

1. **State the problem:** We are given a quadratic equation for profit $P$ in terms of $b$, the number of skateboards (in thousands): $$P = -2b^2 + 14b - 20$$

1. **Problem Statement:** A theatre group models revenue with $R = -50(t - 2)(t - 3)$ where $t$ is ticket price. They know revenue is maximized at $t=3$ with $R=450$ and $R=400$ at

1. **State the problem:** Simplify the expression $(1,4:5+19:20)*2-1,5$. 2. **Clarify notation:** The commas likely represent decimal points, so rewrite as $(1.4 \div 5 + 19 \div 2

1. **State the problem:** Calculate the value of the expression $\left(1,\frac{4}{5}+\frac{19}{20}\right)\times 2 - 1.5$. 2. **Clarify the expression:** The comma seems to separate

1. The problem is to find the inverse of a function, which means finding a function that "undoes" the original function. 2. The general formula for finding the inverse of a functio

1. **Stating the problem:** Solve question 5 (assuming it is an algebraic equation or expression to solve). 2. **Formula and rules:** Since the exact problem is not provided, I wil

1. The problem is to write the expression minus(bminus2c)minus3a without brackets. 2. First, understand that "minus" means a negative sign, so the expression is: