Answer:
= 18 ( 3 + 2(\sqrt{3} + \sqrt{2} ))
Step-by-step explanation:
![6(\sqrt{36} +\sqrt{27}) + 6(\sqrt{27} +\sqrt{18}) + 6(\sqrt{18} + \sqrt{9} )\\= 6( {6} +\sqrt{9*3}) + 6( \sqrt{9*3} +\sqrt{9*2}) + 6(\sqrt{9*2} + 3 )\\= 6( {6} +3\sqrt{3}) + 6(3\sqrt{3} +3\sqrt{2}) + 6(3\sqrt{2} + 3 )\\=36 + 18\sqrt{3} + 18\sqrt{3} + 18\sqrt{2}+ 18\sqrt{2} + 18\\= 36+18 +18( \sqrt{3}+ \sqrt{3} +\sqrt{2} + \sqrt{2})\\= 54 + 18 (2\sqrt{3} +2\sqrt{2})\\=54 + 36\sqrt{3} + 36\sqrt{2}\\= 18 ( 3 + 2(\sqrt{3} + \sqrt{2} ))](https://tex.z-dn.net/?f=6%28%5Csqrt%7B36%7D%20%2B%5Csqrt%7B27%7D%29%20%2B%206%28%5Csqrt%7B27%7D%20%2B%5Csqrt%7B18%7D%29%20%2B%206%28%5Csqrt%7B18%7D%20%2B%20%5Csqrt%7B9%7D%20%29%5C%5C%3D%206%28%20%7B6%7D%20%2B%5Csqrt%7B9%2A3%7D%29%20%2B%206%28%20%5Csqrt%7B9%2A3%7D%20%20%2B%5Csqrt%7B9%2A2%7D%29%20%2B%206%28%5Csqrt%7B9%2A2%7D%20%2B%203%20%29%5C%5C%3D%206%28%20%7B6%7D%20%2B3%5Csqrt%7B3%7D%29%20%2B%206%283%5Csqrt%7B3%7D%20%2B3%5Csqrt%7B2%7D%29%20%2B%206%283%5Csqrt%7B2%7D%20%2B%203%20%29%5C%5C%3D36%20%2B%2018%5Csqrt%7B3%7D%20%2B%2018%5Csqrt%7B3%7D%20%2B%2018%5Csqrt%7B2%7D%2B%2018%5Csqrt%7B2%7D%20%2B%2018%5C%5C%3D%2036%2B18%20%20%2B18%28%20%5Csqrt%7B3%7D%2B%20%5Csqrt%7B3%7D%20%2B%5Csqrt%7B2%7D%20%2B%20%5Csqrt%7B2%7D%29%5C%5C%3D%2054%20%2B%2018%20%282%5Csqrt%7B3%7D%20%2B2%5Csqrt%7B2%7D%29%5C%5C%3D54%20%2B%2036%5Csqrt%7B3%7D%20%20%2B%2036%5Csqrt%7B2%7D%5C%5C%3D%2018%20%28%203%20%2B%202%28%5Csqrt%7B3%7D%20%20%2B%20%5Csqrt%7B2%7D%20%29%29)
This is a ratio problem; the ratio of the length to width is constant (and therefore equal):
4 /6 = 15 / x
Now, with a ratio, we may do any allowable algebra operation: cross-multiply, invert both sides, multiply or divide both sides by the same amount, etc.
Let's cross-multiply:
4x = (15)(6)
x = 90/4
x = 22.5 in.
Given:
Jeffery babysits for 4 dollars per hour and works as a math tutor for 7 dollars per hour.
He is only allowed to work 13 hours total per week.
He wants to make at least 65 dollars.
To find:
The system of inequalities to represent this situation.
Solution:
Let x be the number of hours he babysits per week and y be the number of hours h works as a math tutor.
He is only allowed to work 13 hours total per week. It means sum of x and y must be less than or equal to 13.
![x+y\leq 13](https://tex.z-dn.net/?f=x%2By%5Cleq%2013)
He wants to make at least 65 dollars. It means total earnings must be greater than or equal to 65.
![4x+7y\geq 65](https://tex.z-dn.net/?f=4x%2B7y%5Cgeq%2065)
Number of hours can not be negative.
.
Therefore, the required system of inequalities contains some equations,
and
.
The answer is A because 75 + 15 is 90
Answer:
y = -1
Step-by-step explanation: