🧮 algebra

1. **Problem statement:** A diamond necklace's selling price increases by 5% each year. The price in 2000 was 36000.

1. The problem is to express the equation $6x + 7y = ?$ in a meaningful way. 2. This is a linear expression with two variables $x$ and $y$. Without additional information, such as

1. The problem asks which expression is equivalent to $5x^2 - 8$. 2. To check equivalence, we simplify each given expression and compare it to $5x^2 - 8$.

1. **State the problem:** Simplify the expression $$\frac{2}{3}y + 14 - \frac{1}{6}y - 8$$. 2. **Combine like terms:** The terms involving $y$ are $$\frac{2}{3}y$$ and $$-\frac{1}{

1. **State the problem:** Simplify the expression $$\frac{3}{5}x + 19 - \frac{3}{20}x - 7$$. 2. **Combine like terms:** Group the terms with $x$ and the constant terms separately.

1. Let's start by stating the problem: understanding logarithmic and exponential equations. 2. Exponential equations have the form $y = a^x$, where $a$ is a positive constant not e

1. Let's state the problem: We want to solve an algebraic problem using a simple method. 2. The simple method often involves isolating the variable on one side of the equation. For

1. **State the problem:** We want to find the least number of copies sold so that the publishing company makes a positive profit.

1. **State the problem:** Solve the equation $$\frac{x - 4}{2022} + \frac{x - 3}{2023} + \frac{x - 2}{2024} = 3.$$\n\n2. **Formula and approach:** To solve this linear equation, we

1. **State the problem:** Solve the equation $$\frac{x - 4}{2022} + \frac{x - 3}{2023} + \frac{x - 2}{2024} - 3 = 3$$ for $x$. 2. **Rewrite the equation:** Move the constant term o

1. **Problem Statement:** A publishing company has a cost of Le 0.38 per copy and revenue of Le 0.35 per copy. Dealers get Le 0.3 of the revenue. Advertising revenue is 10% of deal

1. **Problem:** A company produces product X at a unit cost of 10. Fixed costs are 450000, and each unit sells for 25. How many units must be sold to make a positive profit of 5100

1. **Problem:** Show that the middle term in the expansion of $ (1+x)^{2n} $ is given by $$ \frac{1 \times 3 \times 5 \times \cdots \times (2n - 1)}{n!} x^n $$

1. **Problem:** Show that the middle term in the expansion of $ (1 + x)^{2n} $ is given by $$ \frac{1 \times 3 \times 5 \times \cdots \times (2n - 1) \times 2^n \times x^n}{n!} $$

1. **State the problem:** We need to find a possible whole number length of a race track that rounds to 300 km when rounded to the nearest 100 km and rounds to 250 km when rounded

1. **State the problem:** Harley needs to cut the grass on a rectangular field that is 100 meters long and 90 meters wide. She cuts grass at a rate of 30 square meters per minute.

1. **State the problem:** We need to find the value of $A$ given three balancing scales involving bananas, pears, lemons, and peas. 2. **Assign variables:** Let

1. **State the problem:** Simplify the expression $$\frac{(2a)^2}{4a}$$. 2. **Recall the formula and rules:** When raising a product to a power, apply the exponent to each factor:

1. **State the problem:** Simplify the expression $$\frac{3 + \sqrt{5} + \sqrt{44}}{2}$$. 2. **Recall the rules:** The square root of a product can be simplified as $$\sqrt{a \time

1. The problem is to understand the topic of Surds, which are irrational roots that cannot be simplified to remove the root. 2. A surd is an expression containing a root, such as $

1. **State the problem:** We are given the first four terms of a sequence: 19, 23, 27, 31. We need to find the formula for the nth term of this sequence. 2. **Identify the type of