9514 1404 393
Answer:
"and"
Step-by-step explanation:
Properly written, the word "and" separates the integer portion from the fractional portion of the number. If there is no "and", then there is no integer portion, so the number is a fraction less than 1.
<u>Examples</u>:
one <em>and</em> three tenths = 1 3/10
thirty-one thousandths = 31/1000
Answer:
268.40
Step-by-step explanation:
We can write a ratio to solve
2.5 meters 22 meters
----------------- = --------------
30.5 dollars x dollars
Using cross products
2.5 * x = 30.5 * 22
2.5x =671
Divide each side by 2.5
2.5x / 2.5 = 671/2.5
x =268.4
Let the numbers be x and y.
x*y=HCF*LCM=6*60=360
thus
y=360/x
next we find the list of combinations of x and y and test if they satisfy the conditions above:
(6,60),(12,30),(18,20),(24,15)
out of the above, only (6,60) and (12,30) satisfy both conditions. Thus our answer is:
(6,60) or (12,30)
We want to find one-half of the reciprocal of 7/sqrt(98). Let's write down an expression for this:
![\dfrac{1}{2} \times \dfrac{\sqrt{98}}{7}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cdfrac%7B%5Csqrt%7B98%7D%7D%7B7%7D)
We can rewrite 98 into ![2 \times 49](https://tex.z-dn.net/?f=2%20%5Ctimes%2049)
![\dfrac{1}{2} \times \dfrac{\sqrt{2 \times 49}}{7}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cdfrac%7B%5Csqrt%7B2%20%5Ctimes%2049%7D%7D%7B7%7D)
![=\dfrac{1}{2} \times \dfrac{\sqrt{2} \times \sqrt{49}}{7}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cdfrac%7B%5Csqrt%7B2%7D%20%5Ctimes%20%5Csqrt%7B49%7D%7D%7B7%7D)
The square root of 49 is 7
![=\dfrac{1}{2} \times \dfrac{\sqrt{2} \times 7}{7}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cdfrac%7B%5Csqrt%7B2%7D%20%5Ctimes%207%7D%7B7%7D)
![=\dfrac{1}{2} \times\sqrt{2}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%5Csqrt%7B2%7D)
![=\dfrac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
This should be your answer. Let me know if you need any clarifications, thanks!