Answer:
Conjecture : 2xy / ( x + y ) ≤ √xy
Step-by-step explanation:
Harmonic mean of x and y = 2xy/( x + y )
<u>Formulate a conjecture about their relative sizes </u>
we will achieve this by computing harmonic and geometric means
Geometric mean = √xy
harmonic mean = 2xy/( x + y )
Conjecture : 2xy / ( x + y ) ≤ √xy
attached below is the proof
Answer:
9 books on each shelf
Step-by-step explanation:
43 + 29 = 72 books total
72/8 = 9 books per shelf
1) No. 28/21 does not end up being equal to 2.
2) No. 45/5 does not equal 18/2
3) No. For something to be proportional, it should at least have the smaller number in the same place.
4) No. 25/12 does not equal 53/40
5) Yes. 4/2 is equal to 14/7
6) Yes. 4/1 is equla to 12/3
7) No. For something to be proportional, it should at least have the smaller number in the same place.
8) No. 44/9 is not equal to 36/11
9) Yes. 10/5 is equal to 16/8
10) Yes. 24/12 is equal to 14/7
11) No. 24/4 is not equal to 42/9
12) Yes. Both equal 1.
13) Yes. 20/5 is equal to 44/11
14) No. 44/40 is not equal to 34/30
15) Yes . 40/4 is equal to 10/1
16) Yes. 36/4 is equal to 45/5
17) No. 16/2 is not equal to 13/1
18) No. 38/9 is not equal to 28/7
19) Yes. This is a common proportion.
20) Yes. 50/25 is equal to 2.
21) Yes. 36/24 is equal to 3/2.
22) Yes. 18/12 is equal to 42/28
23) No. 33/42 is not equal to 27/37
24) No. 34/7 is not 4
25) Yes. The second proportion listed is half of the first
26) Yes. This is proportional.
27) Yes. This is proportional.
28) Yes. This is proportional.
29) No. This is not proportional.
30) No. This is not proportional
31) Yes. This is proportional.
32) Yes. This is proportional
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I hope this helped. I left the last few unsolved so you could follow the patterns to find them out!
Not sure how to do it in this form but in slope intercept form for example if the slope was -4/3 the perpendicular would be 3/4 it’s the negative reciprocal of the answer
A plane has two dimensions and extends infinitely in both dimensions.
