🧮 algebra

1. **State the problem:** We are given the linear function $$y = \frac{2}{3}x - 5$$ and a table with values of $$x$$: -9, 0, 3, 6. We need to find the corresponding values of $$y$$

1. Stating the problem: Simplify the expression $$a^{-7} b^{2} c^{-1} = \frac{2 n^{-5} p^{0}}{m^{-2}}$$. 2. Recall the rules of exponents:

1. **State the problem:** Simplify the expression $$2x^{8}y^{15} - \frac{40x^{10}y^{24}}{5x^{2}y^{9}}$$. 2. **Recall the rules:**

1. The problem is to convert the improper fraction $\frac{33}{28}$ into a mixed number. 2. An improper fraction has a numerator larger than the denominator. To convert it, divide t

1. **State the problem:** Match each situation (a, b, c, d) to one of the graphs (A, B, C) based on the description of the graph and the situation. 2. **Analyze each graph:**

1. The problem is understanding why the factorial expression $(N+1)!$ remains as is, instead of simplifying to $(N+1) - 1$. 2. Recall the definition of factorial: for any positive

1. **State the problem:** Simplify and solve the equation $\frac{x+x+x}{x} = 10$. 2. **Understand the expression:** The numerator is $x+x+x$, which is $3x$.

1. **State the problem:** Factor the expression $$9x^2 - 16$$ completely. 2. **Recognize the form:** This is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b

1. **State the problem:** Show that $k \times k! = (k + 1)! - k!$ and then use this to sum the series $1 \times 1! + 2 \times 2! + 3 \times 3! + \cdots + n \times n!$.

1. **State the problem:** Factor the expression $$9x^2 - 16$$ completely. 2. **Recognize the form:** This is a difference of squares because $$9x^2 = (3x)^2$$ and $$16 = 4^2$$.

1. **State the problem:** We need to evaluate the expression $\left(3(5)-4(-2)\right)^2$. 2. **Apply the order of operations:** First, calculate the products inside the parentheses

1. **State the problem:** Simplify the expression $$2j(7j^2k^2 + jk^2 + 5k) - 9k(-2j^2k^2 + 2k^2 + 3j)$$. 2. **Distribute each term:**

1. **State the problem:** Ethan earned 188.40 for 12 hours of work. We need to find how much he earned per hour. 2. **Formula:** The unit rate (earnings per hour) is calculated by

1. **State the problem:** Solve the equation $$\frac{x}{6} = 4$$ for $x$. 2. **Recall the formula:** To solve for $x$ when it is divided by a number, multiply both sides of the equ

1. **State the problem:** We need to find the horizontal and vertical asymptotes, new reference points, domain, and range of the function $$f(x) = \frac{2x^2 - 4x}{x^2 + 4x + 4}$$

1. The problem is to analyze the function $g(x) = -8(3)^x$. 2. This is an exponential function of the form $g(x) = a \cdot b^x$ where $a = -8$ and $b = 3$.

1. **State the problem:** We are given the function $f(x) = \frac{3}{5} 4^x$ and need to write the limit statements for its left and right end behaviors. 2. **Recall the behavior o

1. **State the problem:** Simplify or analyze the expression $$\frac{5}{2} x^6 - \frac{1}{2} x^4$$. 2. **Identify the terms:** The expression has two terms: $$\frac{5}{2} x^6$$ and

1. **State the problem:** Simplify the expression $9m^7 - 3m^2$. 2. **Identify common factors:** Both terms have a common factor of $3m^2$.

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + 2y = 5 \\ 5x + 6y = 9 \end{cases}$$

1. **State the problem:** Solve the system of equations using Gauss-Jordan elimination: $$\begin{cases} x + y - z = -1 \\ -x + 5y + 19z = 9 \\ -5x + 5y + 3z = 8 \end{cases}$$