🧮 algebra

1. **State the problem:** A farmer wants to enclose two adjacent rectangular plots for sheep and one for cattle along a river, using 240 yards of fencing. The river forms one side,

1. **State the problem:** Solve the equation $ (x-1)^2 = 2(x-1) $. 2. **Rewrite the equation:** The equation is $ (x-1)^2 = 2(x-1) $.

1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}.$$\n\n2. **Use the given information:** We know

1. Let's start by understanding what percentage profit and loss mean. 2. Percentage profit occurs when the selling price (SP) of an item is more than its cost price (CP). The formu

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: