Function under A) has range x>0 because we cant calculate square root of negative number (we can if we include imaginery numbers)
B) again x must be greater than 0
C) x + 5 > 0 which means that x > -5
-4 is withing range so C in correct
D) x - 5 > 0 which means x > 5
Answer is C because only function under C has domain such that it includes -4
Answer:
The Roman numerals CIX equals to 109.
Answer: b) they loaded 112356 lbs of cargo
Step-by-step explanation:
When a boat or an object floats in water, the volume of water that it displaces is equivalent to its weight.
When moving into the port, the cargo boat displaced 2200 ft³ of water. Since the density of water is 62.42 lb/ft³ and mass = density × volume, then the mass of the cargo boat on entering the port is
2200 × 62.42 = 137324 lbs
On leaving the port, it displaces 4000 ft³ of water. The mass of the cargo boat on leaving the port is
4000 × 62.42 = 249680 lbs
The difference in both masses is
249680 - 137324 = 112356 lbs
Therefore, they loaded 112356 lbs of cargo
3.14(3(2) + 3(4))
3.14( 6 + 12)
3.14(18)
=56.52
Answer:
Options (1), (2), (3) and (7)
Step-by-step explanation:
Given expression is ![\frac{\sqrt[3]{8^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B8%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D)
.
Now we will solve this expression with the help of law of exponents.
![\frac{\sqrt[3]{8^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}=\frac{\sqrt[3]{(2^3)^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B8%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B%282%5E3%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D)
![=\frac{\sqrt[3]{2\times 3} }{3\times2^{\frac{1}{9}}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B2%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D)
[Option 2]
![2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(\sqrt[9]{2})^2\times (\sqrt[3]{\frac{1}{3} } )^2](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B2%7D%7B9%7D%7D%5Ctimes%203%5E%7B-%5Cfrac%7B2%7D%7B3%7D%20%7D%3D%28%5Csqrt%5B9%5D%7B2%7D%29%5E2%5Ctimes%20%28%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%20%29%5E2)
[Option 1]
![=\sqrt[9]{4}\times \sqrt[3]{\frac{1}{9} }](https://tex.z-dn.net/?f=%3D%5Csqrt%5B9%5D%7B4%7D%5Ctimes%20%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B9%7D%20%7D)
[Option 3]
![=\sqrt[9]{2^2}\times \sqrt[3]{3^{-2}}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B9%5D%7B2%5E2%7D%5Ctimes%20%5Csqrt%5B3%5D%7B3%5E%7B-2%7D%7D)
[Option 7]
Therefore, Options (1), (2), (3) and (7) are the correct options.
