Question
Which of the following is equal to 81 - 1/2
A. 1/ ^81
B. -^81
C. ^81
D. - 1/^81
A. 1/ ^81
B. -^81
C. ^81
D. - 1/^81
Answers
GPT-4o mini
To evaluate \( 81 - \frac{1}{2} \), we can rewrite \( 81 \) as a fraction:
\[
81 = \frac{162}{2}
\]
Now subtract \( \frac{1}{2} \):
\[
\frac{162}{2} - \frac{1}{2} = \frac{162 - 1}{2} = \frac{161}{2}
\]
Next, we need to check which of the answer choices corresponds to \( \frac{161}{2} \).
The options provided are:
A. \( \frac{1}{\sqrt{81}} \)
B. \( -\sqrt{81} \)
C. \( \sqrt{81} \)
D. \( -\frac{1}{\sqrt{81}} \)
Calculating \( \sqrt{81} \):
\[
\sqrt{81} = 9
\]
Now, let's evaluate the options:
A. \( \frac{1}{\sqrt{81}} = \frac{1}{9} \)
B. \( -\sqrt{81} = -9 \)
C. \( \sqrt{81} = 9 \)
D. \( -\frac{1}{\sqrt{81}} = -\frac{1}{9} \)
None of these options equate to \( \frac{161}{2} \), so the answer does not match any of the given choices. As it stands, the equality \( 81 - \frac{1}{2} = \frac{161}{2} \) is not represented in the given options.
\[
81 = \frac{162}{2}
\]
Now subtract \( \frac{1}{2} \):
\[
\frac{162}{2} - \frac{1}{2} = \frac{162 - 1}{2} = \frac{161}{2}
\]
Next, we need to check which of the answer choices corresponds to \( \frac{161}{2} \).
The options provided are:
A. \( \frac{1}{\sqrt{81}} \)
B. \( -\sqrt{81} \)
C. \( \sqrt{81} \)
D. \( -\frac{1}{\sqrt{81}} \)
Calculating \( \sqrt{81} \):
\[
\sqrt{81} = 9
\]
Now, let's evaluate the options:
A. \( \frac{1}{\sqrt{81}} = \frac{1}{9} \)
B. \( -\sqrt{81} = -9 \)
C. \( \sqrt{81} = 9 \)
D. \( -\frac{1}{\sqrt{81}} = -\frac{1}{9} \)
None of these options equate to \( \frac{161}{2} \), so the answer does not match any of the given choices. As it stands, the equality \( 81 - \frac{1}{2} = \frac{161}{2} \) is not represented in the given options.