🧮 algebra

1. The problem is to find the formula for a ratio. 2. A ratio compares two quantities by division.

1. **State the problem:** We want to prove by contradiction that if $a$ is rational ($a \in \mathbb{Q}$) and $b$ is irrational ($b \notin \mathbb{Q}$), then $a + 2b$ is also irrati

1. We are asked to find the equation of the graph labeled $y = h(x)$ based on the provided description and the points noted. 2. From the description, there are two curves: one open

1. Let's analyze the given graph description to understand the function $y = h(x)$. 2. The graph has two connected curved segments separated near $x = -2$:

1. **State the problem:** We have two box sizes, small and large, selling identical chocolate pieces.

1. Solve for $x$ in the equation $S = \frac{2x + t}{r}$. Multiply both sides by $r$ to get: $$rS = 2x + t$$

1. मान ज्ञात कीजिए : (i) $3^{-2} = \frac{1}{3^2} = \frac{1}{9}$

1. **State the problem:** We have an initial alloy of silver and copper with unknown weight $x$ kg. 2. When $x$ kg of this alloy is mixed with 3 kg of pure silver, the new alloy co

1. সমসাময়িক হার চক্রবৃদ্ধি মূলধনের সমস্যাটি বিবেচনা করা হল যেখানের ১ বছরে বৃদ্ধি $19500$ টাকা এবং ২ বছরে বৃদ্ধি $20280$ টাকা। 2. হার নির্ণয়ের সূত্র: মূলধন $P$ ও হারের $r$ জন্য চক

1. We are asked to calculate $60 - (15\% \times 60)$. 2. First, convert 15% to decimal: $15\% = 0.15$.

1. Let's define variables for the populations in 1970: - Let the male population in 1970 be $M$.

1. The problem is to factor the expression $x^2$. 2. Factoring means expressing the expression as a product of simpler expressions.

1. **State the problem:** Car A is moving north at 45 kph. Car B starts 12 minutes (which is \(\frac{12}{60}=0.2\) hours) later at 54 kph. We need to find how long it takes Car B t

1. **State the problem:** We have two numbers, let's call the larger number $x$ and the smaller number $y$.

1. **State the problem:** We have 9000 liters of a 30% acid solution. We want to add water to reduce the acid concentration to 20%. 2. **Find the amount of acid in the initial solu

1. **State the problem:** Kaye is currently 24 years old and her cousin Pia is 9 years old. We need to find in how many years Kaye's age will be double Pia's age. 2. **Define varia

1. **State the problem:** Joy is 9 years older than Leo. Three years ago, the sum of their ages was 29. We need to find Joy's current age.

1. **State the problem:** Sam, Ton, and Paul together can finish a job in 3 hours. Sam alone can finish in 6 hours, and Ton alone in 8 hours. We need to find how long Paul alone wi

1. **State the problem:** Ben and Kevin start driving towards each other from two points 120 km apart. Ben drives at 45 kph and Kevin at 35 kph. We need to find the time when they

1. **State the problem:** We are given a rectangle whose width is thrice the length, and the width is equal to the side of a square.

1. **State the problem:** Roy is 13 years older than Sam. In 5 years, the sum of Roy’s age and twice Sam’s age will be 79. We need to find Sam’s current age. 2. **Define variables: