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Rearrange the equation to isolate X .A=CDX X= If C=5.00 , D=9.00 , and A=3.00 , what is the value of X ?X= If A is halved while C and D remain constant, what happens to the value of X ?

A. The value of X is doubled.
B. The value of X is tripled.
C. The value of X does not change.
D. The value of X is halved.

Respuesta :

JeanaShupp

Answer: [tex]X=\dfrac{A}{CD}[/tex]

If C=5.00 , D=9.00 , and A=3.00 ,  , then the value of x = [tex]\dfrac{1}{15}[/tex].

If A is halved while C and D remain constant,

D. The value of X is halved.

Step-by-step explanation:

The given equation : [tex]A=CDX[/tex]

Divide both sides by (CD) , we get

[tex]\dfrac{A}{CD}=X[/tex]

Or  [tex]X=\dfrac{A}{CD}[/tex]                     (i)

If C=5.00 , D=9.00 , and A=3.00 , then

[tex]X=\dfrac{3}{5\times9}=\dfrac{1}{15}[/tex]

i.e. The value of x = [tex]\dfrac{1}{15}[/tex].

If A is halved while C and D remain constant.

Let [tex]A'=\dfrac{A}{2}[/tex]

Then ,

[tex]X'=\dfrac{A'}{CD}=\dfrac{(\dfrac{A}{2})}{CD}\\\\=\dfrac{A}{2CD}[/tex]

i.e. [tex]X'=(\dfrac{1}{2})(\dfrac{A}{CD})=\dfrac{1}{2}(X)[/tex]     [From  (i)]

Thus , If A is halved while C and D remain constant, then the value of X is halved.

Option (D) will be the correct option.

    Given equation in the question,

  • A = CDX

If A = 3, C = 5 and D = 9,

By substituting these values in the equation given,

3 = 5 × 9 × X

X = [tex]\frac{3}{45}[/tex]

X = [tex]\frac{1}{15}[/tex]

If A is halved while C and D remains constant,

[tex]\frac{3}{2}=5\times 9\times X[/tex]

[tex]X=\frac{3}{2\times 5\times 9}[/tex]

[tex]X=\frac{1}{30}[/tex]

[tex]X=\frac{1}{15}\times \frac{1}{2}[/tex]

 Therefore, value of X will be halved. Option (D) will be the answer.

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