Question

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Jakita examines the ordered pairs ( 3/4, 2/3), (1/4, 2), (1, 1/2) and (1/2, 1), and determines the points form a direct variation with a k value of 1/2.

Which statements about Jakita's conclusion are true? Select two options.
A.) The points actually represent an inverse variation.
B.) The k value of the direct variation is actually 2.
C.) The ordered pairs can be represented by the function y = x/2
D.) The ordered pairs can be represented by the function y = 1/2x
E.) As one quantity increases, the other also increases.​

Answer 1

Answer: A and D

Explanation:

Cause edg2020

Answer 2

A and D

Explanation:

We are given that

(3/4,2/3),(1/4,1),(1,1/2) and (1/2,1)

`x_1=(3)/(4)`

`y_1=(2)/(3)`

`x_2=(1)/(4),y_2=1`

`x_3=1,y_3=(1)/(2)`

`x_4=(1)/(2),y_4=1`

k=
`(1)/(2)`

Direct proportion:

`(x)/(y)=k`

Inverse proportion:
`xy=k`

`(x_1)/(y_1)=(3)/(4)* (3)/(2)=(9)/(8)\\eq (1)/(2)`

Therefore, it is not in direct proportion.

`(1)/(4* 2)=(1)/(8)\\eq(1)/(2)`

`(1)/((1)/(2))=2\\eq (1)/(2)`

`x_1y_1=(3)/(4)* (2)/(3)=(1)/(2)`

`x_2y_2=(1)/(4)* 2=(1)/(2)`

`x_3y_3=1* (1)/(2)=(1)/(2)`

`x_4y_4=(1)/(2)* 1=(1)/(2)`

Therefore,
`xy=k=(1)/(2)`

Hence, the given points form an inverse variation .

`xy=(1)/(2)`

`y=(1)/(2x)`

Option A and D is true.