📘 algebra, geometry, arithmetic

1. **Problem 1: Total prize money distribution** The winner receives half of the total prize money, and the second runner-up receives one-fourth of the winner's amount. The winner'

1. Problem 17: Given the operation $a \otimes b = \frac{a^2}{b}$ for all nonzero numbers, find $[(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]$. 2. Use the definition of the

1. Problem: Find the circumference of a truck tyre with diameter 70 cm. The formula for circumference is $$C = \pi d$$ where $d$ is diameter.

1. **Problem 20:** Represent the inequality $2 \leq Q < 6$ on the number line. - This means $Q$ includes 2 and all numbers up to but not including 6.

1. Problem 9: A clock loses 18 seconds every hour. It was set correctly at 8:00 am Monday. Find the time the clock shows at 11:20 am Saturday. 2. Calculate total hours from 8:00 am

1. Solve the quadratic equation $2x^2 - 5x + 3 = 0$ using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a=2$, $b=-5$, $c=3$. Calculate the discriminant: $\D

1. Problem: Solve for $m$ in the equation $42m - 1 = 64$. Step 1: Add 1 to both sides: $42m = 65$.

1. Simplify $4^{5a+3b} + 3(2a-b)$. Step 1: Recognize $4^{5a+3b}$ is an exponential term that cannot be simplified further without values for $a$ and $b$.