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Answer :
Certainly! In this problem, we know that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex], meaning there's a direct relationship between them. This can be written as:
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
### Step 1: Find the Constant of Proportionality
We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. We can use this to find the value of [tex]\( k \)[/tex]:
[tex]\[ 7 = k \times 28 \][/tex]
To find [tex]\( k \)[/tex], divide both sides by 28:
[tex]\[ k = \frac{7}{28} \][/tex]
So, [tex]\( k = 0.25 \)[/tex].
### Step 2: Find [tex]\( x \)[/tex] When [tex]\( y = 3 \)[/tex]
Now we need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]. We will use the same proportional relationship:
[tex]\[ 3 = 0.25 \times x \][/tex]
To find [tex]\( x \)[/tex], divide both sides by 0.25:
[tex]\[ x = \frac{3}{0.25} \][/tex]
Calculating this gives:
[tex]\[ x = 12 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\( 12 \)[/tex].
The correct answer is:
c. 12
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
### Step 1: Find the Constant of Proportionality
We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. We can use this to find the value of [tex]\( k \)[/tex]:
[tex]\[ 7 = k \times 28 \][/tex]
To find [tex]\( k \)[/tex], divide both sides by 28:
[tex]\[ k = \frac{7}{28} \][/tex]
So, [tex]\( k = 0.25 \)[/tex].
### Step 2: Find [tex]\( x \)[/tex] When [tex]\( y = 3 \)[/tex]
Now we need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]. We will use the same proportional relationship:
[tex]\[ 3 = 0.25 \times x \][/tex]
To find [tex]\( x \)[/tex], divide both sides by 0.25:
[tex]\[ x = \frac{3}{0.25} \][/tex]
Calculating this gives:
[tex]\[ x = 12 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\( 12 \)[/tex].
The correct answer is:
c. 12
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