🧮 algebra

1. Stating the Problem: Find the equation of the straight line passing through the points $(3, y)$ and $(4, 5)$.

1. Let's clarify what a negative exponent means. When you see an expression like $a^{-n}$ where $a \neq 0$ and $n > 0$, it means the reciprocal of $a^n$. 2. Specifically, $a^{-n} =

1. The problem is to find the ratio $x:y$ given the equation $2x = 3y$. 2. Start by expressing $x$ in terms of $y$: from $2x = 3y$, divide both sides by $2$ to get $x = \frac{3y}{2

1. Bài toán cho biết số học sinh tham quan là một số $x$ nằm trong khoảng từ 1200 đến 1500. 2. Nếu thuê xe 30 chỗ thì dư 21 chỗ, nghĩa là số ghế nhiều hơn số học sinh 21, nên ta có

**Problem:** Given the equation:

1. Énonçons le problème : comprendre et résoudre des problèmes sur les proportions. 2. Une proportion est une égalité entre deux rapports : $$\frac{a}{b} = \frac{c}{d}$$ où $b \neq

1. **State the problem:** Sarah is making bracelets using 2 beads of each color (red, green, blue). She wants to make 4 bracelets of each color and we need to find the total number

1. **State the problem:** We need to evaluate the expression $3^{15} - 2 \times 9^6$. 2. **Rewrite terms in terms of base 3:** Note that $9 = 3^2$, so $9^6 = (3^2)^6$.

1. First, understand the problem: We need to find the sum of all prime factors of $N$ given that $\log_3 \log_5 \left(\frac{N}{2}\right) = 6$. 2. Start by isolating the inner logar

1. The problem asks to find the values of $a$ and $b$ given the set notation ${a,b}$. 2. However, the input does not specify any equations, expressions, or conditions involving $a$

1. Stating the problem: We are given the function $y = -3x + 7$ and will analyze its properties. 2. This is a linear function with slope $-3$ and y-intercept $7$.

1. **State the problem:** Simplify the expression $$exy \left( \frac{y^2}{x} - \frac{2y}{x^2} + \frac{2}{x^3} \right)$$ and understand the next steps. 2. **Distribute the terms:**

1. **State the problem:** Gemechu bought sheep and sold them for 4650 birr. He made a 7% profit on the selling price. We need to find how much he originally paid for the sheep.

1. We are asked to factorize the expression $$(2x + 9)^2 - (x + 4)^2$$. 2. Recognize this as a difference of squares, which has the formula $$a^2 - b^2 = (a - b)(a + b)$$.

1. Let's start with the equation given: $$2x^2 + 2x^2 = (ab)^2$$

1. Stated problem: Simplify the expression $2x^2 + 2x^2$. 2. Identify like terms: Both terms contain $x^2$ and can be added together.

1. Énonçons le problème : factoriser l'expression $ (2x + 5)(6x + 4) $. 2. L'expression est un produit de deux binômes. Pour factoriser, on peut développer et simplifier, puis cher

1. Express each of the following in the form $a - bi$.\\ a) Simplify $\frac{i}{3 - i}$. Multiply numerator and denominator by the conjugate $3 + i$ to get:\\

1. **State the problem:** We need to show the value of the expression $4^5 \cdot 64^3 \cdot 2^3$. 2. **Rewrite bases in terms of prime factors:**

1. **State the problem:** We have 40 questions. \nFraction of multiple choice questions is $\frac{2}{5}$. \nFraction of true or false questions is $\frac{1}{4}$. \nWe need to find

### Exercice 1: Finding limits of sequences 1. **Problem:** Find the limit of \( u_n = \frac{\sin(n)}{n^{2} + 3} \).