Which fractions are equivalent to 4/9?

Answer:

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 Proportional relationships y = 9x, 2y = 18x, and y = (1/3)x have the same constant of proportionality as the equation 3y = 27x.

The equation 3y = 27x represents a proportional relationship between y and x with a constant of proportionality of 9. To determine which relationships have the same constant of proportionality, we can compare the ratios of y to x in the given options.

A) y = 9x: The ratio of y to x is 9, which is the same as the constant of proportionality in the original equation. So, this option has the same constant of proportionality.

B) 2y = 18x: Dividing both sides of the equation by 2, we get y = 9x, which has the same constant of proportionality. Therefore, this option also has the same constant of proportionality.

D) y = (1/3)x: The ratio of y to x is 1/3, which is different from the constant of proportionality in the original equation. Therefore, this option does not have the same constant of proportionality.

So, the correct answers are A) y = 9x, B) 2y = 18x, and D) y = (1/3)x.

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The equivalent value of the expression (1/2 x 15) is 7.5.

What is algebraic expression?                      

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations.

Given is to solve the expression as -

1/2 x 15

We can write the expression as -

{x} = 1/2 x 15

{x} = 15/2

{x} = 7.5 x 2/2

{x} = 7.5

Therefore, the equivalent value of the expression (1/2 x 15) is 7.5.

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Answer:

7.5

Step-by-step explanation:

it's basically just 15 divided by 2