Let W, X, Y and Z be full column rank real matrices. What are the conditions (if any) on W, X, Y and Z, such that there exists a real matrix A such that A X = Z and YT A = W T ? Find all such A when the conditions are satisfied. How many linearly independent equations were there? What was the dimensionality of the left and right nullspaces? Did the rank-nullity theorem hold? The previous exercise can provide a simple way to approach this problem.

Two parallel lines are crossed by a transversal. what is the value of x? x = 40 x = 70 x = 110 x = 130

Trent wants to buy 2 packs of trading cards for 3 dollars each. the trading card packs that trent normally buys tend to come in packs of 6, 10, 12, or 15 cards. after selecting 2 packs, trent found that the first pack of cards cost 25 cents per card, and the second pack cost 30 cents per card. trent uses this information to write the equations below in order to compare c, the number of cards in each pack.

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)) =