Which simplified fraction is equal to 0.53 (the 3 is repeating)
2 answers:
<h3>Answer: Choice B. 8/15</h3>
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Explanation:
x = 0.53333333... the 3's go on forever
10x = 5.3333333..... we have infinitely many 3's here as well
100x = 53.333333..... same story
Each time we multiply both sides by 10, we move the decimal point over 1 spot to the right.
Focus on this system of equations
Note how the decimal points line up so we can see both right sides have the same 33333... pattern
If we subtract those equations straight down, the left hand side turns into 90x because 100x-10x = 90x
The right hand side terms subtract to 48. The infinite number of 3's after the decimal will cancel out when we subtract. So we basically have 53-5 = 48.
After those subtractions, we now have the new equation 90x = 48
Divide both sides by 90 and reduce
90x = 48
90x/90 = 48/90
x = 48/90
x = (6*8)/(6*15)
x = 8/15
8/15 = 0.53333333....
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I've attached an image showing the coordinates of Ship A and Ship B.
Answer:
distressed vessel is located at (1, 1.5)
Step-by-step explanation:
From the image attached, we can see that;
Coordinate of ship A is (3, 4)
Coordinate of ship B is (1, 1)
Now, we are told that Ship A receives a distress signal from the southwest, and ship B receives a distress from the same vessel from the north.
This means that the distressed ship is somewhere in between ship A & B.
To solve this, we will extend the arrow line from Ship A in that same SW direction and we will do the same for ship B in the same North direction. Their point of intersection is where the distressed ship is located.
Now, if we do that, we will see that they will intersect at the point; (1, 1.5)
Thus,distressed vessel is located at (1, 1.5)
