Question

If y varies inversely with x, and the constant of variation
is 4.5, what are the values missing in the table?

Answer 1

Answer:

A. 0.5

B. 4.5

C. 1.5

D. 0.5

Step-by-step explanation:

y varies inversely with x can be written as:

y = k/x

where k is constant of variation.

1. value of A

x=A, y = 9 and k = 4.5 (given)

y = k/x

9 = 4.5/A

=> A = 4.5/9

=> A=0.5

2. Value of B

x =1, y= B, k = 4.5

y = k/x

B = 4.5/1

B= 4.5

3. Value of C

x=C, y=3. k=4.5

y = k/x

3 = 4.5/C

3C = 4.5

C = 4.5/3

C = 1.5

4. Value of D

x= 9, y=D, k=4.5

y = k/x

D = 4.5/9

D = 0.5

Answer 2

Answer:

$A=0.5$

$B=4.5$

$C=1.5$

$D=0.5$

Step-by-step explanation:

The form an the equation of inverse variation is:

$y=\frac{k}{x}$

Being "k" the constant of variation.

Since we know "k" and we have the values given in the table, we can find the missing values:

To find A we need to substitute the $y=9$, the value of "k" and $x=A$ into the equation and solve for "A":

$9=\frac{4.5}{A}$

$A=\frac{4.5}{9}=0.5$

To find B we need to substitute the $x=1$, the value of "k" and $y=B$ into the equation:

$B=\frac{4.5}{1}=4.5$

To find C we need to substitute the $y=3$, the value of "k" and $x=C$ into the equation and solve for "C":

$3=\frac{4.5}{C}$

$C=\frac{4.5}{3}=1.5$

To find D we need to substitute the $x=9$, the value of "k" and $y=D$ into the equation:

$D=\frac{4.5}{9}=0.5$