🧮 algebra

1. **State the problem:** We are given the linear system:

1. **State the problem:** Solve the inequality $$\frac{x - 5}{x - 4} < 0$$ and express the solution set in interval notation. 2. **Identify critical points:** The numerator $$x - 5

1. **State the problem:** Solve the inequality $$\frac{x - 2}{x - 1} \leq 0$$ and express the solution set in interval notation. 2. **Rewrite the inequality:** Move all terms to th

1. **State the problem:** Solve the inequality $$\frac{x-8}{x+3} > 0$$ and express the solution set in interval notation. 2. **Identify critical points:** The numerator $$x-8=0$$ w

1. **Problem a:** George invested $2000 in two accounts. One earned 4.5% interest, the other lost 2%, with a net gain of $38. Find the amount invested in each account. 2. **Formula

1. **State the problem:** Solve the inequality $$\frac{x-2}{x-8} > 0$$ and express the solution set in interval notation. 2. **Rewrite the inequality:** Define $$f(x) = \frac{x-2}{

1. **State the problem:** Solve the inequality $$-5x^2 - 5x > 0$$ and express the solution set in interval notation. 2. **Rewrite the inequality:** Factor out the common factor $$-

1. **State the problem:** Determine the ratio of engines to box cars for Hiroshi who has $4$ engines and $18$ box cars. 2. **Write the ratio as a fraction:** The ratio of engines t

1. **State the problem:** Solve the inequality $$x^2 - 12x + 27 > 0$$ and express the solution set in interval notation. 2. **Find the boundary points:** Solve the equation $$x^2 -

1. **State the problem:** Solve the system of linear equations by graphing: $$\ell_1: y = -x - 2$$

1. **State the problem:** Solve the system of linear equations by graphing: $$\ell_1: y = -x - 2$$

1. To plot points on a coordinate plane, you need to understand the directions: up, down, left, and right. 2. The horizontal axis is called the $x$-axis. Moving right means increas

1. **State the problem:** We have two lines given by the equations $$2x - 3y = -6$$ and $$y = \frac{5}{3}x - 1$$. We want to know where to graph the points for these lines on a coo

1. **State the problem:** We want to find how many doughnuts are in 4 dozen if 1 dozen has 12 doughnuts.

1. **State the problem:** We have a total of $$200$$ tickets sold with a ratio of children's tickets to adult tickets as $$2:3$$. We need to find how many more adult tickets than c

1. **State the problem:** Evaluate the expression $$\frac{-\frac{2}{3}(6 + 9) - (-3)(-4)}{\frac{1}{2}}$$. 2. **Simplify inside the parentheses:**

1. **State the problem:** We need to find which function has a vertical asymptote at $x=3$ and a slant (oblique) asymptote at $y=3x+7$. 2. **Recall vertical asymptote rule:** Verti

1. **State the problem:** We need to find a function from the given options that has: - A vertical asymptote at $x = 1$

1. **State the problem:** Find the equation of the line passing through points $(-2, 8)$ and $(1, -1)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1, y_1)$ and

1. **State the problem:** We need to find the value of $f(-1)$ for the given piecewise function. 2. **Identify which piece to use:** Since $-1 \leq 0$, we use the first piece of th

1. **State the problem:** We want to find the function that represents the height $h(t)$ of a leaf falling from a branch 12 feet high, falling at a rate of 0.25 feet per second.