Which relationships have the same constant of proportionality between yyy and xxx as the equation 3y=27x3y=27x3, y, equals, 27, x? Choose 3 answers: Choose 3 answers: (Choice A) A y=9xy=9xy, equals, 9, x (Choice B) B 2y=18x2y=18x2, y, equals, 18, x (Choice C) C (Choice D) D xxx yyy 333 \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction 666 \dfrac{2}{3} 3 2 start fraction, 2, divided by, 3, end fraction 999 111 (Choice E) E xxx yyy 222 181818 444 272727 666 363636

A, B and C

Step-by-step explanation:

In the equation: 3y=27x

Making y the subject of the equation, we have:

The constant of proportionality between y and x  is 9.

We want to determine which relationships have the same constant of proportionality 9.

Option A

y=9x

The constant of proportionality is 9.

Option B

2y=18x

Divide both sides by 2 to obtain: y=9x

The constant of proportionality is 9.

Option C

x=3, y=1/3

Substitution into y=kx gives:

1/3=3k

k=9

The constant of proportionality is 9.

Option D

x=6, y=2/3

Substitution into y=kx gives:

2/3=6k

k=2/3*6=4

The constant of proportionality is 4.

Option E

When x=2, y=18

Substitution into y=kx gives:

18=2k

k=9

However, when x=4, y=27

Substitution into y=kx gives:

27=4k

k=6.75

This is not a proportional relation since the constant of proportionality is not equal.

The correct options are A, B and C

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).

391.6 is the correct answer