Answer:
It is sufficient to prove that 
Step-by-step explanation:
The propositions 
being equivalent means they should always have the same truth value. If one of them is true, then all of them must be true. And if one of them is false, then all of them must be false.
Suppose we've proven that (call these first, second and third implications).
If 
was true, then by the first implication that we proved, it would follow that 
is also true. And then by the second implication that we prove it would follow then that 
is also true. Therefore the three of them would be true. Notice the reasoning would have been the same if we had started assuming that the one that was true was either 
. So one of them being true makes all of them be true.
On the other hand, if was false, then by the third implication that we proved, it would follow that 
has to be false (otherwise would have to be true, which would be a contradiction). And then, since is false, by the second implication that we proved it would follow that 
is false (otherwise 
would have to be true, which would be a contradiction). Therefore the three of them would be false. Notice the reasoning would have been the same if we had started assuming that the one that was false was either . So one of them being false makes all of them be false.
So, the three propositions always have the same truth value, and so they're all equivalent.
Answer:
9 inches
Step-by-step explanation:
base is rectangular in shape
Side of base of square pyramid is X inches
height of square pyramid is 1/9 X
Volume of any pyramid is 1/3 *(area of base* height of pyramid)
area of base of square pyramid = Side of base * Side of base
as area of square is equal to side * side
area of base of square pyramid = x* x square inches = 
Volume of pyramid = 1/3 *(area of base* height of pyramid)
substituting given value of of volume of pyramid , height of pyramid and area of base calculated above we have
![27 = 1/3(x^2)*(1/9 x)\\\\27*3*9 = x^3\\729 = x^3\\x = \sqrt[3]{729} \\x = 9](https://tex.z-dn.net/?f=27%20%3D%201%2F3%28x%5E2%29%2A%281%2F9%20x%29%5C%5C%5C%5C27%2A3%2A9%20%3D%20x%5E3%5C%5C729%20%3D%20x%5E3%5C%5Cx%20%3D%20%5Csqrt%5B3%5D%7B729%7D%20%5C%5Cx%20%3D%209)
Therefor value of x is 9 inches.
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Answer:
The bench costs 450
Step-by-step explanation:
Let t = cost of the table
b = cost of bench
t+b = 846
t = b-54
t+b =846
Substituting t = b-54 into the above equation
b-54 +b =846
Combine like terms
2b -54 = 846
Add 54 to each side
2b-54+54 = 846 +54
2b =900
Divide by 2
2b/2 = 900/2
b =450
The bench costs 450
Answer:
y=3x
Step-by-step explanation:
