The square root of 45 minus 9 is approximately 0.16.
On a number line, this value would be plotted between 0 and 1, but closer to 0.
None of the given options accurately describe the plotted point.
a) Between −3 and −2, but closer to −3
b) Between −3 and −2, but closer to −2
c) Between 6 and 7, but closer to 6
d) Between 6 and 7, but closer to 7
On a number line, this value would be plotted between 0 and 1, but closer to 0.
None of the given options accurately describe the plotted point.
a) Between −3 and −2, but closer to −3
b) Between −3 and −2, but closer to −2
c) Between 6 and 7, but closer to 6
d) Between 6 and 7, but closer to 7
On a number line, this value would be plotted between -3 and -2, but closer to -3.
Thus, the correct answer is option a) Between −3 and −2, but closer to −3.
a) square root of one hundred sixty is greater than one hundred sixteen ninths
b) square root of one hundred sixty is equal to one hundred sixteen ninths
c) one hundred sixteen ninths is greater than square root of one hundred sixty
d) one hundred sixteen ninths is less than square root of one hundred sixty
The square root of one hundred sixty is approximately 12.65.
So, the square root of one hundred sixty is less than one hundred sixteen ninths.
Therefore, the correct answer is d) one hundred sixteen ninths is greater than the square root of one hundred sixty.
a) negative three raised to the sixth power divided by nine raised to the fifteenth power
b) negative three squared divided by nine raised to the fifth power
c) three raised to the sixth power divided by nine raised to the fifteenth power
d) three squared divided by nine raised to the fifth power
In the numerator:
\[9^{-3} = \frac{1}{9^3} = \frac{1}{729}\]
In the denominator:
\[3^{-2} \cdot (9^2) = \frac{1}{3^2} \cdot (9^2) = \frac{1}{9} \cdot 81 = 9\]
So, the expression becomes
\[\left(\frac{1}{729}\right)^3 \div 9^3 = \frac{1^3}{729^3} \div 9^3 = \frac{1}{729^3} \div 9^3 = \frac{1}{531,441} \div 729\]
Simplifying further:
\[\frac{1}{531,441} \div 729 = \frac{1}{531,441} \cdot \frac{1}{9^3} = \frac{1}{531,441 \cdot 9^3} = \frac{1}{430,467,071}\]
Therefore, the correct answer is not one of the options provided.