Describe in words where the square root of 45 minus 9 would be plotted on a number line.
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
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.
Describe in words where the square root of 45 minus 9 would be plotted on a number line.
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
To find the square root of 45 minus 9, we first calculate the square root of 45 which is approximately 6.71. Then, we subtract 9 which gives us -2.29.
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.
Compare the square root of one hundred sixty and one hundred sixteen ninths using <, >, or =.
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
To compare the square root of one hundred sixty and one hundred sixteen ninths, we can simplify one hundred sixteen ninths to 12.89, which is the same numerical value.
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.
Choose the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed.
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
To solve this problem, we can simplify each term as follows:
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.