🧮 algebra

1. **Problem Statement:** Solve the algebraic equation $2x + 3 = 11$ for $x$. 2. **Formula and Rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. We do

1. **State the problem:** Express $27^5$ as a power of 3. 2. **Recall the base relationship:** We know that $27 = 3^3$ because $3^3 = 3 \times 3 \times 3 = 27$.

1. The problem is to express $8^4$ with base 2. 2. Recall that $8$ can be written as a power of 2: $8 = 2^3$.

1. Let's clarify the problem you are working on to understand why you might be getting a loss of 12,000. 2. Typically, a loss is calculated as the difference between cost price and

1. The problem is to solve for $x$ in the equation $q2$. 2. Since $q2$ is not a standard algebraic expression or equation, we need to clarify or rewrite it in a solvable form.

1. **State the problem:** A dealer bought 12 refrigerators at 15000 each and repaired all at 30000 total. He sold each refrigerator at 17200. We need to find if he made a loss or g

1. **State the problem:** Simplify the expression $$(x^x+3)(2x^4)$$. 2. **Recall the distributive property:** When multiplying a sum by a term, multiply each addend by the term:

1. **Problem Statement:** Explain how to determine if a relation is linear, quadratic, or exponential given a table of values, an equation, or a graph, and provide real-life exampl

1. **Problem 7a:** Find the energy produced by wind turbines in 1992. Given the model: $$E = 6.49(1.058)^t$$ where $t$ is years since 1980.

1. **State the problem:** We have a bacterial culture starting with 1000 bacteria, modeled by the formula $$N = 1000 \times 2^{\frac{t}{5}}$$ where $N$ is the number of bacteria af

1. **Evaluate the expression $5^{-3}$ as a fraction or integer.** Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$.

1. **State the problem:** Find the equation of the straight line passing through the points $(0,6)$ and $(2,0)$ in the form $y = mx + c$. 2. **Formula used:** The equation of a lin

1. Diberikan dua persamaan dengan bilangan real positif $a$ dan $b$: $$a - 12b = 11 - \frac{100}{a}$$

1. **Stating the problem:** Solve the equation $$a - \frac{12}{b} = 4 - \frac{100}{a}$$ for $a$ given $b$ or vice versa. 2. **Understanding the equation:** The equation involves fr

1. **State the problem:** Solve the equation $$1 - \frac{1}{1 - x} = \frac{2}{x^2 - 1}$$ for $x$. 2. **Rewrite the equation and identify denominators:** Note that $x^2 - 1 = (x-1)(

1. **State the problem:** Solve for $x$ in the equation $$\frac{1 - x^2}{1 - x} = \frac{2}{1}.$$\n\n2. **Recall the formula and rules:** We want to solve the equation by simplifyin

1. **Problem 1: Solve the system using Gauss Elimination Method** Given system:

1. **State the problem:** We need to compare $A = n$ and $B = 12$ given the equation $n^{11} = 11^n$. 2. **Analyze the equation:** The equation $n^{11} = 11^n$ means the number $n$

1. Diberikan sistem persamaan dengan bilangan real positif $a$ dan $b$: $$a - 12b = 11 - \frac{100}{a}$$

1. **State the problem:** Given the equation $x^{-1} = \frac{\sqrt{2}}{6}$, find the value of $x$. 2. **Recall the rule:** $x^{-1}$ means the reciprocal of $x$, so $x^{-1} = \frac{

1. **Problem statement:** Simplify the algebraic expressions given: A = (4x - 1)(5x - 3)(4x - 1)