QUESTION 1: A mechant has 120 litres and 180 litres of two kinds of oil. He wants to sell the oil by filling the two kinds in tins of equal volumes. Find the greater volume of such a tin. QUESTION 2: Difference between a number and its positive square root is 12 Find the number.

QUESTION 3: A piece of iron rod costs $60. If the rod was 2 meter shorter and each meter cost $1 more, the cost will remain unchanged what is the length of the rod.

QUENTION 4: The sides of an equilateral triangle are reduced by 12 units, 13 units and 14 units respectively and a right-angle triangle is formed Find the length of each side of the equilateral triangle
QUESTION 5: One of the diagonals of a rectangle a 20 cm long. The difference between lts length and its width is 4 cm find the area of the rectangle

1 H C F of 120 and 180 is 2

120/2 = 60

180/2 = 90

Total number of tins = 60+90 = 150

2 16 - √16 =12. So,correct ans is 16.

3 as the new price for each metre is now rs.1 therefore the length of rod should be 60 meters so that it costs rs.60.

and we know the new length is two minus the actual length so,

the actual length of rod=60+2

=62 meters

4 New sides of new Δ=x-12; x-13; x-14.

(x-12) side is the longest side in the right angled Δ

ACCORDING TO THE PYTHAGORAS THEORAM

(x-13)² + (x-14)²= (X-12)²

after opening the brackets...

x² + 169 - 26x + x² + 196 - 28x = x² + 144 - 24x

2x² + 365 - 54x = x² + 144 -24x

2x²- x² + 365 - 144 - 54x + 24x= 0

x² - 30x + 221 =0

x² -17x -13x + 221=0

x(x-17) -13(x-17)= 0

(x-13)(x-17)=0

x-13=0 or x-17=0

x=13 x=17

x ≠13 (because if x is 13 then side (x-13) of Δ would be zero

which is imposiible)

x= 17 units

we need the options

step-by-step explanation:

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: