Here's a problem that occurs in automatic program analysis. for a set of variables x1; : : : ; xn, you are given some equality constraints, of the form xi = xj and some disequality constraints,

of the form xi 6= xj . is it possible to satisfy all of them?

for instance, the constraints

x1 = x2; x2 = x3; x3 = x4; x1 6= x4

cannot be satis ed. give an ef cient algorithm that takes as input mconstraints over n variables

and decides whether the constraints can be satisfied.

cut 138 centimeters off

step-by-step explanation:

250-112 = 138

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

yes

step-by-step explanation:

yes

answer: c.  

step-by-step explanation:

mixtures containing substances that get attracted to magnet can be separated using a magnet. we can separate iron from a mixture of sand and iron, as only iron attracts to the magnet.