🧮 algebra

1. **Problem Statement:** Draw the graph of the equation $$|x - 4| = y$$.

1. **State the problem:** Simplify the expression $$(2 - i)(3 - i)$$ where $i$ is the imaginary unit with the property $i^2 = -1$. 2. **Use the distributive property (FOIL method):

1. **Problem Statement:** Find the zeroes of the quadratic polynomial $x^2 - 2x - 8$ and verify the relationship between the zeroes and the coefficients. 2. **Formula and Important

1. **State the problem:** Solve the equation stepwise (the user did not specify the exact equation, so I will demonstrate solving a common algebraic equation: $2x + 3 = 11$. 2. **F

1. **Problem:** Solve the equation $$y^2 - 1 = 0$$. 2. **Formula and rules:** This is a quadratic equation in terms of $y$. We can use the difference of squares factorization:

1. Diberikan persamaan: $$3 + 6 \times 2L - 10 + 2 = 10L$$ 2. Langkah pertama adalah menyelesaikan operasi perkalian dan menyederhanakan persamaan.

1. **Problem statement:** A sales representative has a monthly salary of 5000 TK. He earns a 5% commission on sales below 60000 TK, 8% commission on sales above 60000 TK, and a 100

1. **Problem 41:** Calculate $$0.2^{\log_3\left(4+1+\frac{1}{3}+...\right)}$$. 2. **Problem 42:** Calculate $$(0.125)^{\log_2\sqrt{1-\frac{1}{2}+\frac{1}{3}+...}}$$.

1. **State the problem:** Given the equation $z = \frac{e^y}{x}$, we want to understand or manipulate this expression. 2. **Formula and rules:** The expression involves the exponen

1. The problem is to simplify the expression $$7000\left(1-\left[\frac{1+0.12}{1+0.15}\right]^{\frac{9}{0.15-0.12}}\right)$$. 2. First, calculate the base inside the brackets: $$\f

1. **Énoncé du problème :** On considère la fonction $f$ définie par $f(x) = x + \frac{1}{x-2}$.

1. Diketahui persamaan: $$2m - 4 = n$$

1. Let's solve a simple algebra problem using normal terms. 2. Suppose we want to solve for $x$ in the equation $2x + 3 = 7$.

1. Let's start by stating the problem: solving quadratic simultaneous equations means finding values of variables that satisfy two equations, where at least one is quadratic. 2. A

1. **Problem statement:** You have 15,000 đồng and buy 41 Christmas hats at 8,000 đồng each. After buying, you have 7,000 đồng left. Among your money, the number of 10,000 đồng bil

1. The problem is to draw a hyperbolic diagram for the function $y = x^2$. 2. The function $y = x^2$ is a parabola, not a hyperbola. A hyperbola has the form $\frac{x^2}{a^2} - \fr

1. The problem is to classify the equation based on the discriminant $\Delta$ and understand its nature. 2. The discriminant $\Delta$ is given as $\Delta = x^2$.

1. **State the problem:** Max fills a bathtub with water. After 5 minutes, there are 11 gallons, and after 10 minutes, there are 22 gallons. We need to find an equation relating ga

1. The problem involves evaluating the expression $$\log_{125} \left((0.25)^{\log_{16} \left(\frac{1}{3} + \frac{1}{8} + \frac{1}{4} + \ldots \right)}\right).$$ 2. First, simplify

1. Problem 41: Calculate $$0.2 \log_2(4+1+3+\dots)$$. The series inside the log is unclear, assuming it means sum of powers or terms, clarify if needed. 2. Problem 42: Calculate $$

1. Problem 31: Simplify the expression $$\frac{2\log_3^2 2 - \log_3 8 - \log_2 3 \cdot \log_3 8}{2\log_3 2 + \log_3 8}$$