So 476/14 = miles per gallon or M/G
so if we want to find gallons in 578 miles we multiply 578/x by 14/476
you get 8092/476x you get 17 for x or 17 gallons in 578 miles
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.
The cell phone tower provides 5 square miles of coverage.
You find the x coordinates using x = -b/2a = -6/2(-1) = 3
Substitute 3 in the equation and find y
y = -(3^2) + 6(3) - 12 = -9 + 18 - 12 = -3
Vertex (3,-3)
Answer:
36
Step-by-step explanation:
Hello,
If
it becomes
![X^3-289X^2-X+289=(X^2-1)(X-289)](https://tex.z-dn.net/?f=X%5E3-289X%5E2-X%2B289%3D%28X%5E2-1%29%28X-289%29)
and ![289=17^2](https://tex.z-dn.net/?f=289%3D17%5E2)
![X^2-1=(X-1)(X+1)=(x^2-1)(x^2+1)=(x+1)(x-1)(x^2+1) \\\\x^2-289=x^2-17^2=(x-17)(x+17)](https://tex.z-dn.net/?f=X%5E2-1%3D%28X-1%29%28X%2B1%29%3D%28x%5E2-1%29%28x%5E2%2B1%29%3D%28x%2B1%29%28x-1%29%28x%5E2%2B1%29%20%5C%5C%5C%5Cx%5E2-289%3Dx%5E2-17%5E2%3D%28x-17%29%28x%2B17%29)
So,
![x^6-289x^4-x^2+289=(x^2-1)(x^2+1)(x^2-289)=(x-1)(x+1)(x+17)(x-17)(x^2+1)](https://tex.z-dn.net/?f=x%5E6-289x%5E4-x%5E2%2B289%3D%28x%5E2-1%29%28x%5E2%2B1%29%28x%5E2-289%29%3D%28x-1%29%28x%2B1%29%28x%2B17%29%28x-17%29%28x%5E2%2B1%29)
a = 1
b = 1
c = 17
d = 17
e = 0
Then a + b + c + d + e = 36
Thanks