🧮 algebra

1. ප්‍රශ්නය කියවමු: අපට සෙවිය යුතුය $x$ සඳහා සමානතාවය $2x + 3 = 11$. 2. සමානතාව විසඳීමේ සූත්‍රය: සරල රේඛීය සමානතාවයක් විසඳීමේදී, අපි $x$ වෙනුවට වෙනත් සියලු අගයන් වෙනස් කරමු.

1. The problem is to solve exercise 4.1. Since the user did not specify the exact problem, I will assume it is a common algebraic problem such as solving a linear equation. 2. Let'

1. **Stating the problem:** We are given the function $$f(x) = \frac{1}{\sqrt{2x - 1}}$$ and need to analyze its domain and behavior. 2. **Formula and rules:** The function involve

1. Problem 31: Find the sum of all integer solutions to the inequality $$4^{\log_2 x} + x^2 < 32$$. 2. Recall the property: $$4^{\log_2 x} = (2^2)^{\log_2 x} = 2^{2 \log_2 x} = 2^{

1. **Problem:** Find the square root of 3721. 2. **Formula:** The square root of a number $a$ is a number $b$ such that $$b^2 = a$$.

1. Problem: Find the square root of 3721. 2. Formula: To find the square root of a number $N$, find a number $x$ such that $x^2 = N$.

1. **State the problem:** We are given $N = 2 \times 3^4 \times y^3$ and need to find $3N^2$ expressed as a product of prime factors in index form, in terms of $y$. 2. **Recall the

1. **State the problem:** Add the mixed numbers and fractions: $5 \frac{3}{10} + \frac{1}{12}$. 2. **Convert mixed number to improper fraction:**

1. **Problem:** Solve $\frac{4}{3} + \frac{2}{5}$. 2. **Formula:** To add fractions with unlike denominators, find the least common denominator (LCD), convert each fraction, then a

1. **Stating the problem:** Find the next term in the sequence: KM2, IP5, GS8, EV11, ?

1. **State the problem:** Olive invested some money at 6% per year and three times that amount at 8% per year. The total annual return from both investments is 2400.

1. **Problem statement:** We want to find the condition under which a composite function has an inverse. 2. **Recall definitions:**

1. **State the problem:** Wendy bought 9 notebooks and 4 ballpens for 225, and Peter bought 8 notebooks and 6 ballpens for 222. We need to find the price of one notebook and one ba

1. **Problem statement:** Given the sequence A-BBC-AAB-CCA-BBCC, find the next sequence from options (A) ACBA, (B) BACB, (C) ABBA, (D) CABA. 2. **Understanding the problem:** The s

1. **State the problem:** Solve the equation or expression given by the user. Since no specific equation was provided, please provide the exact problem to solve. 2. **Formula and r

1. **State the problem:** Given the formula $$P_m = \frac{1}{p \times \sqrt[3]{p^2}}$$, find the value of $m$ in terms of $p$. 2. **Rewrite the expression:** The denominator is $p

1. Problem: Two machines pack bricks at rates 24000 and 12000 bricks per hour. Find time to pack 12000 bricks together. 2. Formula: Total rate = sum of individual rates. Time = Tot

1. **State the problem:** Find the slope of the line passing through the points $(0,1)$ and $(3,-1)$.\n\n2. **Formula for slope:** The slope $m$ of a line through points $(x_1,y_1)

1. **State the problem:** Find the slope of the line passing through the points $(-6, 0)$ and $(-3, -3)$.\n\n2. **Formula for slope:** The slope $m$ of a line through points $(x_1,

1. The problem is to solve the equation $\frac{2x+4}{x+2} = 3$ for $x$. 2. We start by stating the formula and rules: To solve a rational equation, multiply both sides by the denom

1. Bài toán yêu cầu tìm các số nguyên $x, y, z$ thỏa mãn phương trình $$x^2 + y^2 + z^2 = 2xyz.$$ 2. Đây là một phương trình Diophantine, tức là ta tìm nghiệm nguyên.