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.

The factorization of 8x3 -125 is (2x-5)(jx2 +kx+25)

One expression below in undefined, and the other expression has a well defined value. which expression is undefined and explain why it has no value. which expression is defined? what is the value of that expression and how do you know? what is a different expression using a trig inverse function that is also undefined?

Someone answer this asap rn for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =