🧮 algebra

1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the equation that relates $y$ to $x$. 2. **Given table:**

1. **State the problem:** We have a rectangular farmland with length $2$ mi and width $1.5$ mi.

1. **State the problem:** We need to find the total amount of protein an athlete eats in 9 weeks if she eats 0.2 kg per week. 2. **Formula:** Total protein = protein per week \( \t

1. The problem is to simplify the expression $\sin 6 + x \cdot 9$. 2. Here, $\sin 6$ means the sine of 6 radians (or degrees if specified, but usually radians).

1. **Problem 1:** X sells two articles for Rs. 4000 each with no loss and no gain overall. One article is sold at a gain of 25%. Find the loss percentage on the other article. 2. *

1. **Problem Statement:** X sells two articles for $4000$ each with no overall loss or gain. One article is sold at a gain of $25\%$. We need to find the loss percentage on the oth

1. **State the problem:** We want to find how many times $5.34 \times 10^5$ is larger or smaller than $5.34 \times 10^{-2}$. 2. **Formula used:** To find the factor by which one nu

1. The problem is to express the fraction $\frac{7}{2}$ in the form $3 \times \frac{1}{2}$ or a similar mixed number format. 2. First, recognize that $\frac{7}{2}$ is an improper f

1. The problem is to express the fraction $\frac{5}{2}$ in the form $2 \times \frac{1}{2}$ or a similar mixed number format. 2. First, understand that $\frac{5}{2}$ is an improper

1. **State the problem:** We need to find the total capacity of the container in gallons. 2. **Define variables:** Let $C$ be the total capacity of the container in gallons.

1. **State the problem:** We want to find the number of minutes $m$ for which the cost of the two plans is the same. 2. **Define variables and costs:**

1. **State the problem:** Solve the equation $$8n - 1.4 = -6.3$$ for $$n$$. 2. **Add $$1.4$$ to both sides** to isolate the term with $$n$$:

1. مسئله: معادله درجه دوم $$x^2 - 5x + 6 = 0$$ را حل کنید. 2. مسئله: مقدار عبارت جبری $$\frac{3x^2 - 2x + 1}{x - 1}$$ را برای $$x = 2$$ محاسبه کنید.

1. **State the problem:** Simplify the polynomial expression $$(a^{2} - 8a - 6) - (4a^{2} - 6a - 9)$$. 2. **Remove the brackets:** When removing the brackets, distribute the minus

1. **State the problem:** We want to simplify the expression $$\left( \frac{3}{5} \right)^{-8} \div \left( \frac{3}{5} \right)^{-4}$$ and express it using a positive exponent.

1. **State the problem:** We need to determine which pairs of expressions are equivalent. 2. **Recall exponent rules:**

1. **State the problem:** Determine which ordered pair(s) satisfy the equation $$-7x + 3y = 2$$. 2. **Recall the rule:** To check if an ordered pair $(x,y)$ is a solution, substitu

1. **State the problem:** We need to determine which ordered pair(s) satisfy the equation $$3x + 3y = -x + 5y$$. 2. **Rewrite the equation:**

1. **State the problem:** We want to find a combination of points from Shards, Heroes, SSR, and SR that sum exactly to $12,062,000$ points.

1. **State the problem:** We need to compare two transport options for a school trip with 168 students and 12 teachers (total $168 + 12 = 180$ people). We will write cost expressio

1. **State the problem:** We need to factor the expression $$36 - 27x$$ completely. 2. **Identify the greatest common factor (GCF):** The coefficients are 36 and 27. The GCF of 36