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EleoNora [17]
3 years ago
15

Which table shows a proportional relationship between a and b? a b 3 9 4 12 5 20 a b 20 25 24 30 32 40 a b 4 12 5 15 6 24 a b 3

4 6 9 12 16
Mathematics
1 answer:
umka21 [38]3 years ago
8 0
When the second number is divided by the first, the result is ...

First table
   9/3 = 3
   12/4 = 3
   20/5 = 4 . . . . result is not consistent. NOT a proportional relationship

Second table
   25/20 = 1.25
   30/24 = 1.25
   40/32 = 1.25 . . . . result is consistent. A PROPORTIONAL RELATIONSHIP

Third table
   12/4 = 3
   15/5 = 3
   24/6 = 4 . . . . result is not consistent. NOT a proportional relationship

Fourth table
   4/3 ≈ 1.33
   9/6 = 1.5
   16/12 ≈ 1.33 . . . . result is not consistent. NOT a proportional relationship
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Solution

Step 1: Horizontal shift. AAA is shifted 333 units to the right because (6)-(3)=\tealD{+3}(6)−(3)=+3left parenthesis, 6, right parenthesis, minus, left parenthesis, 3, right parenthesis, equals, start color #01a995, plus, 3, end color #01a995.

Step 2: Vertical shift. AAA is shifted 999 units down because (-2)-(7)=\maroonD{-9}(−2)−(7)=−9left parenthesis, minus, 2, right parenthesis, minus, left parenthesis, 7, right parenthesis, equals, start color #ca337c, minus, 9, end color #ca337c.

The answer: AAA is mapped onto A'A

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A, prime under a translation by \langle \tealD{3},\maroonD{-9} \rangle⟨3,−9⟩open angle, start color #01a995, 3, end color #01a995, comma, start color #ca337c, minus, 9, end color #ca337c, close angle.

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