🧮 algebra

1. **State the problem:** We start with 972 infected people, and the virus spreads at a rate of 15% per day. We want to find how many people will be infected after 13 days. 2. **Fo

1. **State the problem:** Simplify the expression $$ (112128.28-60x^2)(46135.98-28.03x^2) - (-46135.98)^2 $$. 2. **Recall the formula:** We will expand the product of two binomials

1. The problem asks: What is the degree of the polynomial $5z^3 - 2z^4 - 9z^2 + z$? 2. The degree of a polynomial is the highest power of the variable in the expression.

1. **State the problem:** You want to reach the number 0.6328125 starting from some initial value (assumed 0) by applying a sequence of allowed functions one by one without order o

1. The problem is to find the sum of $\frac{3}{4} + \frac{1}{10}$.\n\n2. To add fractions, we need a common denominator. The denominators are 4 and 10. The least common denominator

1. **State the problem:** We want to find the value of $\frac{3}{5} - \frac{1}{3}$. 2. **Find a common denominator:** The denominators are 5 and 3. The least common denominator (LC

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): $$P = -2b^2 + 14b - 20$$