Step-by-step explanation:
1) let the number=x
six times a number=6x
Condition:
6x+4=22
2) eleven times a number=11x
Condition:
11x-5=50
3) 9 times a number=9x
Condition:
9x-7=-16
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Answer:
Tank which is capable of holding 1 can fill each one of the tanks an exact number of time.
Step-by-step explanation:
Three tanks are capable of holding
To find which tank can be used to fill each one of them an exact number of time, find ![HCF(361,841,901)](https://tex.z-dn.net/?f=HCF%28361%2C841%2C901%29)
![361=19^2\\841=29^2\\901=17(53)](https://tex.z-dn.net/?f=361%3D19%5E2%5C%5C841%3D29%5E2%5C%5C901%3D17%2853%29)
Therefore,
![HCF(361,841,901)=1](https://tex.z-dn.net/?f=HCF%28361%2C841%2C901%29%3D1)
So, tank which is capable of holding 1 can fill each one of the tanks an exact number of time.
Simplify:
5(a + 5) + -3 = 3(2 + -1a)
Reorder the terms:
5(5 + a) + -3 = 3(2 + -1a)
(5 * 5 + a * 5) + -3 = 3(2 + -1a)
(25 + 5a) + -3 = 3(2 + -1a)
Reorder the terms again:
25 + -3 + 5a = 3(2 + -1a)
Combine like terms:
]25 + -3 = 22
22 + 5a = 3(2 + -1a)
22 + 5a = (2 * 3 + -1a * 3)
22 + 5a = (6 + -3a)
Solve:
22 + 5a = 6 + -3a
To solve for variable 'a':
You have to move all terms containing A to the left, all other terms to the right.
Then add '3a' to each side of the equation:
22 + 5a + 3a = 6 + -3a + 3a
Combine like terms:
5a + 3a = 8a
22 + 8a = 6 + -3a + 3a
Combine like terms again:
-3a + 3a = 0
22 + 8a = 6 + 0
22 + 8a = 6
Add '-22' to each side of the equation.:
22 + -22 + 8a = 6 + -22
Combine like terms:
22 + -22 = 0
0 + 8a = 6 + -22
8a = 6 + -22
Combine like terms once more:
6 + -22 = -16
8a = -16
Divide each side by '8'.
a = -2
Simplify:
a = -2
Answer: a=-2
Hope I could help! :)
Answer:
Step-by-step explanation:
Area of a sphere is ![4\pi d^{2}](https://tex.z-dn.net/?f=4%5Cpi%20d%5E%7B2%7D)
let d be the diameter of the moon and D be the diameter of the earth
d = 1/4 D
Area of Earth = ![4\pi D^{2} = 4\pi (\frac{d}{4} )^{2} = 4\pi \frac{d^{2} }{16} = \pi \frac{d^{2} }{4}](https://tex.z-dn.net/?f=4%5Cpi%20D%5E%7B2%7D%20%3D%204%5Cpi%20%28%5Cfrac%7Bd%7D%7B4%7D%20%29%5E%7B2%7D%20%3D%204%5Cpi%20%5Cfrac%7Bd%5E%7B2%7D%20%7D%7B16%7D%20%3D%20%5Cpi%20%5Cfrac%7Bd%5E%7B2%7D%20%7D%7B4%7D)
Area of moon = ![4\pi d^{2}](https://tex.z-dn.net/?f=4%5Cpi%20d%5E%7B2%7D)
![\frac{Area of moon}{Area of Earth} = \frac{1}{16}](https://tex.z-dn.net/?f=%5Cfrac%7BArea%20of%20moon%7D%7BArea%20of%20Earth%7D%20%3D%20%5Cfrac%7B1%7D%7B16%7D)
-8-5y= 12-9y
⇒ 9y -5y= 12+8
⇒ 4y= 20
⇒ y= 20/4
⇒ y= 5
Final answer: y=5~