In a given proportion, the extremes are the first term of the first ratio and the second term of the second ratio. Here is the given proportion:
[tex]\[
\frac{4}{7} = \frac{12}{x}
\][/tex]
To identify the extremes:
1. The first ratio is [tex]\( \frac{4}{7} \)[/tex]. The first term here is [tex]\( 4 \)[/tex].
2. The second ratio is [tex]\( \frac{12}{x} \)[/tex]. The second term here is [tex]\( 12 \)[/tex].
Therefore, the extremes of the proportion [tex]\( \frac{4}{7} = \frac{12}{x} \)[/tex] are [tex]\( 4 \)[/tex] and [tex]\( 12 \)[/tex].
From the provided options:
A. [tex]\( 4, 7 \)[/tex] - This is not correct, as [tex]\( 7 \)[/tex] is the second term of the first ratio, not an extreme.
B. [tex]\( 7, 12 \)[/tex] - This is not correct, as [tex]\( 7 \)[/tex] is not an extreme.
C. [tex]\( 12, x \)[/tex] - This is not correct, as we need the first term of the first ratio and the second term of the second ratio, and [tex]\( x \)[/tex] is not an extreme.
D. [tex]\( 4, x \)[/tex] - This is not correct, as [tex]\( x \)[/tex] is not an extreme.
The correct answer is not listed based on my solution; however, based on the details given:
The extremes of this proportion are [tex]\( 4 \)[/tex] and [tex]\( 12 \)[/tex]. Therefore, the answer reflecting these extremes, though not listed, would ideally be:
Correct answer: [tex]\( 4, 12 \)[/tex].
