🧮 algebra

1. State the problem: We are given the set $S = \{(x,y) \mid x,y \in \mathbb{R} \text{ and } y = 2x - 2\}$, which represents points $(x,y)$ in the real plane satisfying the linear

1. **Problem restatement:** We want to find the value of $a$ such that the line $2x - 3y = 6$ passes through points $(9,-4)$ and $(6,a)$. 2. **Substitute first point into the line

1. First, let's clarify what the "simple method" means in general terms: it's a straightforward approach to solving a problem without complicated steps. 2. For example, if you're s

1. Stating the problem: We have functions $f(x) = ax + 5$ and functions $f \circ g(x) = 8x + 13$, and are given that $g \circ f(5) = 8a$. We need to find the value of $a$. 2. Expre

1. The problem states that the cube root of $a$ equals the square root of 5, i.e., $\sqrt[3]{a} = \sqrt{5}$. 2. We want to find the value of $a$. To do this, we can cube both sides

1. The problem states: Given the function $y = 4x + 2$, find its characteristics and interpret its meaning. 2. This is a linear function where $y$ depends on $x$ with a slope of 4

1. Diberikan persamaan: $$2(2^x - 1)x^2 + (2x^2 - 2)x = 2^{x+1} - 2$$

1. **Aljafna (Equations)** - **Title:** Algebraic Equations

1. **State the problem:** We need to find two costs related to the garden: the cost of repairing the garden floor and the cost of constructing a wall around it. 2. **Given data:**

1. **State the problem:** Simplify the expression $9 - 2\sqrt{14}$. 2. **Identify the terms:** Here, $9$ is a constant and $2\sqrt{14}$ is an irrational number. Since they are unli

1. Given polynomial $p(x) = mx^3 - 29x^2 + 39x + n$ with factor $3x - 1$ and remainder 6 when divided by $x - 1$. Step 1: Since $3x - 1$ is a factor, $p(\frac{1}{3}) = 0$. Substitu

1. Solve the equation $n - (3 + 2n) = -6$. Start by distributing and combining like terms:

1. **State the problem:** Solve the equation $$\sqrt[3]{x+1}+\sqrt[3]{-x+1}=2$$. 2. **Set variables:** Let $$a=\sqrt[3]{x+1}$$ and $$b=\sqrt[3]{-x+1}$$.

1. **Stating the problem:** The retailer buys a radio for rs. 225 and has overhead expenses of rs. 15. He sells the radio for rs. 300. We need to determine his profit.

1. نُعطى أن الحد الخامس $a_5 = 8$ والحد الثامن عشر $a_{18} = -31$ لمتتابعة حسابية. 2. صيغة الحد العام للمتتابعة الحسابية هي:

1. **Stating the problem:** The cost of 10 articles equals the selling price of 9 articles. We need to find the profit or loss percentage. 2. **Let the cost price (CP) of one artic

1. Solve for question 1: solution is provided. 2. Solve for question 2: solution is provided.

1. **Problem 1: Find the approximate percentage increase in total number of downloads from April to May**. Given data:

1. Stating the problem: Simplify the expression $$(\sqrt{7} - \sqrt{2})^{2}$$. 2. Recall the algebraic identity for the square of a difference: $$ (a - b)^2 = a^2 - 2ab + b^2 $$.

1. **State the problem:** Simplify the expression $3\sqrt{75} + \sqrt{45} + 2\sqrt{20}$. 2. **Simplify each radical:**

1. Stating the problem: Fully simplify both expressions separately, then add or multiply as required.\n\n2. Simplify the radicals part: \n\n\tFor $3\sqrt{75} + \sqrt{45} + 2\sqrt{2