Use the Law of Detachment to make a valid conclusion in the true situation. Alex goes to the park every Sunday evening. Today is Sunday.

For which of the values of a and b will the following pair of linear equations has infinitely many solutions x + 2y = 1; (a - b)x + (a + b)y = a + b - 2
a) a = - 3 , b = 1
b) a = 3 , b = 1
c) a = 2 , b = 2
d) None of the above

Describe the pattern in the numbers. Write the next number in the pattern.
3,  1, 1/3, 1/9, …

In An academic contest, the Correct answer earns 12 points and the incorrect answer loses 5 points. In the final round, School A starts with 165 points and gives the same number of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied. Find
b) How many answers did each school get correct in the final round?

Classify the linear equations x = 2y and, y = 2x as having one solution, no solution or infinitely many solutions.

In An academic contest, the Correct answer earns 12 points and the incorrect answer loses 5 points. In the final round, School A starts with 165 points and gives the same number of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied. Find
a) Frame the equation which models the scoring in the final round and the outcome of the contest?

Use the Law of Detachment to make a valid conclusion in the true situation. If two lines are perpendicular, they form a right angle.

Classify the linear equations x - 3y = 3 , 3x - 9y = 2 as having one solution , no solution or infinitely many solutions .

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.