Describe the pattern in the numbers. Write the next number in the pattern. 1, 3/4, 1/2, 1/4, …

Classify the equation 2x + 1 - 4 = -2x - 3 as having one solution , no solution or infinitely many solutions .

The Price of Stock A at 9 A.M was 12.73 .Since then the price has been increasing at the rate of Rs 0.06 per hour. At noon , the price of stock B was Rs 13.48 .It begins to decrease at the rate of Rs 0.14 per hour. If the stocks continue to increase and decrease at the same rates, in how many hours will the prices of the stocks be the same?

The equation is defined as a mathematical statement with at least two terms containing variables or numbers that are equal.
Let's take an example:
Assume the hours are "h" when attempting to equalize,
As per the given question, we can write the equation as:
12.73 + 0.06h = 13.48 - 0.14h
Rearrange the terms of h in the above equation,
0.06h + 0.14h = 13.48- 12.73
In the above equation, combine the corresponding terms,
0.2h = 0.75
Divide both sides by 0.2
h = 0.75/0.2
h = 3.75
Thus, the stock prices will be the same in 3.75 hours.

Use the Law of Detachment to make a valid conclusion in the true situation. If two angles have the same measure, then they are congruent

Classify the equation 3x - x + 4 = 4(2x - 1) as having one solution , no solution or infinitely many solutions .

The Population of one town is 43,425. About 125 people move out of the town each month. Each month 200 people on average move into town. A nearby town has a population of 45000. It has no one moving in and an average of 150 people moving away every month. In about how many months will the population of the towns be equal ?

The Weight of Abhi’s dog can be found using the expression 2(x+3), where x is the number of weeks. The weight of tarun’s dog can be found using the expression3(x + 1), where x is the number. Will the dogs ever be the same weight ? explain.

Make and test a conjecture about the sum of two even numbers.

How many solutions does this equation have 2(6x+9-3x) = 5x+21

Solve the equation -2.6b + 4 = 0.9b - 17

Sunil has Rs 450 in her savings account . she deposits Rs 40 each month. Arun has Rs 975 in his checking account. He writes a check for Rs 45.90 each month for his cell phone bill. He also writes a check for Rs 19.55 each month for his water bill. After how many months will Sunil and Arun have the same amount of money in their accounts ?

Vihan’s class is making care packages to give to victims of a natural disaster. Vihan packs one box in 5 minutes and has already packed 12 boxes. His friend Simaran packs one box in 7 minutes and has already packed 18 boxes. How many more minutes does each need to work in order to have packed the same number of boxes?

Make a conjecture about the number of diagonals of a pentagon. Write a conjecture for the general case.

Express  as a power with base 3.

Arun and Kiran work in a banquet hall. Arun earns a 20% commission on his food sales. Kiran earns a weekly salary of Rs 625 plus a 10% commission on his food sales . What amount of food sales will result in Arun and Kiran earning the same amount for the week ?

Make a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.