bruce retiled his kitchen. originally, he bought three boxes of tile with the same number of tiles in each. he ran out of tile and had to go back to get three extra boxes of tile. however, he only used two tiles from the last box to finish the job.

felicia also retiled her kitchen. she bought five boxes of tile with the same number of tiles that were in each as bruce’s boxes. she also ran out of tile. she had to go back to the store and get an extra five tiles to finish the job.

in this activity, you will determine whether bruce and felicia used the same number of tiles and whose tiles cover the most area per tile.

write an expression for the number of tiles bruce used and an expression for the number of tiles felicia used. use x to represent the number of tiles in a box.

5x+2=5x+5

For Bruce, 5 represents the number of boxes, and the 2 represents the number of tiles he used from the box.

For Felicia, 5 represents the 5 boxes she used, and the other 5 is used for the tiles she bought on her own.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: