🧮 algebra

1. **State the problem:** Elizabeth's subtotal is $x$ dollars. A tax of 6% is added, and then a tip of 21% is applied to the total after tax. 2. **Write the formula for tax:** Tax

1. **State the problem:** We have two lines, Line A passing through points (3, 6) and (5, -2), and Line B passing through points (2, 5) and (8, k). We need to find the value of $k$

1. **State the problem:** We need to find the equation of a line perpendicular to line A, which passes through points (2, -5) and (10, -1), and this perpendicular line must pass th

1. The problem gives us two lines: $$y = -5x + 2$$ and $$y = -5x + 6$$. 2. We want to find out if these lines intersect or not.

1. **State the problem:** We have two equations: $$x = 4y + 8$$

1. **State the problem:** A student starts with 50 and buys $x$ reusable water bottles, each costing 6. After buying, the student has 14 left. We need to find $x$. 2. **Set up the

1. **State the problem:** We need to find the current size of the graduating class at Arlington High School, given that it was 100 students a generation ago and is now 26% larger.

1. The problem involves analyzing the behavior of the amount of coffee in the pot over time, represented by $y$ as a function of time $x$. 2. We observe that the graphs start at th

1. **State the problem:** Solve the equation $$8x^2 - 7x + 9 = 2x^2 + 6x + 7$$ for $x$. 2. **Bring all terms to one side:** Subtract $2x^2 + 6x + 7$ from both sides to set the equa

1. **State the problem:** Solve the quadratic equation $8x^2 - 7x + 9 = 2x^2 + 6x + 7$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Find the domain of the function $$f(x) = \frac{1}{\frac{12}{x-5} - 2}$$. 2. **Recall domain rules:** The domain of a function includes all real numbers ex

1. The problem asks to determine values for $A$ and $B$ such that the system of equations $$\begin{cases} 12x + Ay = 8 \\ Ax + By = 4 \end{cases}$$

1. **Problem:** Determine which point lies on the line given by the equation $$2x - 3y = 7$$. 2. **Formula and rule:** To check if a point $ (x, y) $ lies on the line, substitute t

1. **Problem:** Determine which point lies on the line given by the equation $$2x - 3y = 7$$. 2. **Formula and rule:** To check if a point $ (x, y) $ lies on a line, substitute the

1. **State the problem:** Solve the equation $5 - 6(2x + 2) = -2(6x + 5) + 4$ using the method of drawing a vertical line under the equal sign to keep both sides balanced. 2. **Dis

1. **State the problem:** Simplify the expression $$\frac{(8x^6y^{-3})^{\frac{1}{3}}}{\sqrt{16x^8}}$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $5 - 6(2x + 2) = -2(6x + 5) + 4$ using the method of drawing a vertical line under the equal sign to keep both sides balanced. 2. **Dis

1. **State the problem:** We need to find the value of $a$ in the equation $$\left(x^{\frac{1}{2}}\right)^3 \sqrt{x} = x^a$$ given that $x > 0$. 2. **Recall exponent rules:**

1. The problem is to simplify the expression $$(243x^4)^{\frac{4}{5}}$$. 2. We use the power of a product rule: $$(ab)^m = a^m b^m$$.

1. **State the problem:** Evaluate the expression $125^{-\frac{2}{3}}$. 2. **Recall the rule for negative and fractional exponents:**

1. **State the problem:** We need to find the first four terms of a sequence starting at $\frac{5}{6}$ where each term is obtained by adding $\frac{2}{3}$ to the previous term. 2.