🧮 algebra

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

1. Stating the problem: We are given the system of equations $$5x + y = 13$$ and $$5xy = 13$$, and asked to find the value of $$12.5x^2 + y^2$$ given that $$xy = 10$$. 2. Step 1: A

1. The problem is to analyze the given equations and solve for the variables involved.\n2. Identify each equation and write down what is known and what needs to be found.\n3. Use a

1. The problem involves finding the total marks for 5 tests given that the mean score for 2 tests is 75. 2. Mean score is calculated as total marks divided by the number of tests.

1. The problem asks to find the fraction of the cake Wetsho left for himself after sharing with his three friends. 2. Wetsho gave Toto \(\frac{1}{6}\), Phatsimo \(\frac{2}{5}\), an

1. The problem asks for the Least Common Multiple (LCM) of the numbers 5, 3, and 6. 2. Recall that the LCM of a set of integers is the smallest positive integer that is divisible b

1. Problem: An object is thrown upward with height given by $$h = -16t^2 + 96t$$. Find $t$ when $h=144$ feet. 2. Set the height equal to 144: $$-16t^2 + 96t = 144$$.

1. Problem (d): Calculate $\frac{2}{3} \times \left(1 \frac{1}{4} - \frac{5}{8}\right)$.\n 2. Convert mixed number to improper fraction: $1 \frac{1}{4} = \frac{5}{4}$.\n

1. **First problem statement:** Find the new quadratic equation whose roots are $\alpha - 2\beta$ and $\beta - 2\alpha$, given the roots $\alpha$ and $\beta$ of $x^2 + 3x - 7 = 0$.

1. Problem a: Calculate the total future profits from a tool whose net return decreases by 10% annually, starting from 400 this year. 2. Since the return decreases by 10% per year,