Afilm set designer is using white and colored tiles in a pattern to create paths of different lengths. if x is the length of the path in feet, the number of colored tiles needed to make it is calculated using the rule

(8x2y2)(3xy)

where y represents the number of white tiles.

which simplified expression represents the number of colored tiles used for a path of length x feet?
• 24x3y3
• 11x3y3
• 24x2y2
• 11x2y2

So this question is asking for the area which needs to be covered with colored tiles. Given the expression above, what we are going to do is to multiply the expressions. So the simplified expression that will represent the number of colored tiles used for a path of length x feet is this:
(8x2y2)(3xy)
24x3y3. So the correct answer would be the first option.
Hope this answer helps. Thanks for posting your question.

a) (-2,-6)

b) (3, -5)

c) (3 ,2)

d) (8,-9)

Step-by-step explanation:

a) You have to use the Rotation Matrix, which is and it has to be multiplied by (x,y) which is equal to (2,6)

Then after the multiplication you´ll obtain (-2,-6)

b) You have to use the Rotation Matrix which is and multiplied for the vector (5,3) you´ll obtain (3, -5)

c) The Rotation Matrix for a rotation of 90° is given by and again after the multiplication you´ll obtain (3,2)

d) The Rotation Matrix is given by  hence after the multiplication fo the roation matrix and the vector you´ll obtain (8,-9)

The answer of 5 and 6 is the matrix that I already wrote down on the excercises.