19.899 as an approximation
2 sqrt (99) = 6sqrt (11) exactly
The leftmost line segment has a domain of -4 ≤ x < -1, or [-4, 1).
The central line segment has a domain of -1 ≤ x ≤ 2, or [-1, 2].
The rightmost line segment has a domain of 2 < x ≤ 5, or (2, 5].
Overall, this function has a domain of
[-4, 1) U [-1, 2] U (2, 5]
(where U means "union" in the set-theoretic notion)
But this also simplifies to the interval [-4, 5].
These correspond to the <u>first</u> and <u>last</u> choices.
It is 8 ft long on the unmeasured side length
ANSWER
The first three expressions will simplify to a rational answer.
EXPLANATION
Let us simplify the expressions then we can see which of them are rational.
A.
![7\sqrt{3} \times \sqrt{3}](https://tex.z-dn.net/?f=7%5Csqrt%7B3%7D%20%5Ctimes%20%5Csqrt%7B3%7D)
We multiply out the roots to get
![7\sqrt{3} \times \sqrt{3}=7 \times (\sqrt{3})^2](https://tex.z-dn.net/?f=7%5Csqrt%7B3%7D%20%5Ctimes%20%5Csqrt%7B3%7D%3D7%20%5Ctimes%20%28%5Csqrt%7B3%7D%29%5E2)
This simplifies to
![7\sqrt{3} \times \sqrt{3}=7 \times 3](https://tex.z-dn.net/?f=7%5Csqrt%7B3%7D%20%5Ctimes%20%5Csqrt%7B3%7D%3D7%20%5Ctimes%203)
![7\sqrt{3} \times \sqrt{3}=21](https://tex.z-dn.net/?f=7%5Csqrt%7B3%7D%20%5Ctimes%20%5Csqrt%7B3%7D%3D21)
This is a rational number hence the answer is rational.
B.
![\sqrt{5} \times \sqrt{5}=(\sqrt{5})^2](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D%20%5Ctimes%20%5Csqrt%7B5%7D%3D%28%5Csqrt%7B5%7D%29%5E2)
![\sqrt{5} \times \sqrt{5}=5](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D%20%5Ctimes%20%5Csqrt%7B5%7D%3D5)
This is also a rational solution.
C.
![2\sqrt{9} \times \sqrt{4}=2\times3\times2](https://tex.z-dn.net/?f=2%5Csqrt%7B9%7D%20%5Ctimes%20%5Csqrt%7B4%7D%3D2%5Ctimes3%5Ctimes2)
![2\sqrt{9} \times \sqrt{4}=12](https://tex.z-dn.net/?f=2%5Csqrt%7B9%7D%20%5Ctimes%20%5Csqrt%7B4%7D%3D12)
This one too is a rational solution.
D.
![\sqrt{3} \times \sqrt{16}=\sqrt{3}\times4](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%20%5Ctimes%20%5Csqrt%7B16%7D%3D%5Csqrt%7B3%7D%5Ctimes4)
![\sqrt{3} \times \sqrt{16}=4\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%20%5Ctimes%20%5Csqrt%7B16%7D%3D4%5Csqrt%7B3%7D)
This is an irrational answer because √3 is an irrational number and multiplying a rational number, 4 by an irrational number results in an irrational number.
Answer:
N=15
Step-by-step explanation:
Simplify 1/4 (2n-8)
2n-8/4+1/4n=1/2(n+6)
Factor out the common term 2.
2(n-4)/4+1/3n=1/2(n+6)
Simplify 2(n-4)/4 to n-4/2
n-4/2+n/3=1/2(n+6)
Simplify 1/3n to n/3
n-4/2+n/3=1/2(n+6)
Simplify 1/2(n+6) to n+6/2
n-4/2+n/3=n+6/2
Multiply both sides by 6 (the LCM of 2, 3,).
3(n−4)+2n=3(n+6)
7 Expand.
3n−12+2n=3n+18
Simplify 3n-12+2n to 5n-12
5n−12=3n+18
Add 12 to both sides.
5n=3n+18+12
Simplify 3n+18+12 to 3n+30
5n=3n+30
Subtract 3n from both sides.
5n-3n=30
Simplify 5n-3n to 2n.
2n=30
Divide both sides by 22
n= 30/2
Simplify 30/2 to 15.
n=15
n=15
Brainliest