William is planning to create a rectangular mosaic which measures 120 cm by 144 cm. the mosaic will be covered completely with square pieces of colored glass. william has decided that he will purchase only one size of glass squares, and he does not plan to cut any of the pieces. if the art supply store only sells the glass squares in whole-number side lengths (measured in centimeters), find the smallest number of squares which william could use for his mosaic.

30

Step-by-step explanation:

We need to find the greatest common factor of 120 and 144.

First, write the prime factorization of both:

120 = 2³×3×5

144 = 2⁴×3²

Both have 2³ and 3 in common, so the GCF is:

GCF = 2³×3

GCF = 24

So the side length is 24 cm.  The number of squares along the width is:

120 / 24 = 5

And the number of squares along the length:

144 / 24 = 6

So the number of squares need to fill the entire area is 5×6 = 30.  This is the least number of squares with whole-number side lengths that he can use.

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92

answer: 180 degrees clockwise

step-by-step explanation: