Stores x, y, and z each sell a certain item that has a given list price. stores x and y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while store z is located in a state with no sales tax and gives no discounts. store x applies its discount first and then charges tax on the discounted price, while store y adds the tax first and then applies the discount to the price with tax. if x and y are the prices, with tax and discount, charged by stores x and y, respectively, and z is the price charged by store z, which of the following statements correctly describes the relationship among x, y, and z ? a. x=y=z
b. x=y c. x d. x e. y

B. x=y

Step-by-step explanation:

Store X applies its discount of 5% first and then charges tax of 5% on the discounted price. The discount is 5/100× x = 0.05x. The new amount is x - 0.05x = 0.95x

Tax charged on 0.95x = 5/100× 0.95x = 0.0475

Final amount at store x = 0.95x + 0.0475x = 0.9975x

Store Y adds the tax first and then applies the discount to the price with tax.

Tax charged on y = 5/100× y = 0.05y.

Price with tax = y + 0.05y = 1.05y

5% discount on 1.05y = 5/100 × 1.05y = 0.0525y

Final amount at store y = 1.05y - 0.0525y = 0.9975y

The final price at store Z remains z

The final prices at store X and store Y are 0.9975 of the initial prices. Therefore, X = Y describes the relationship among x, y, and z

step-by-step explanation: 4 cause 2+2=4

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4