Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the
2 answers:
Answer: The answers are
(i) The slope of segments DE and AC is not 0.
(ii) The coordinates of D and E were found using the Midpoint Formula.
Step-by-step explanation: We can easily see in the proof that the co-ordinates of D and E were found using the mid-point formula, not distance between two points formula. So, this is the first flaw in the Gina's proof.
Also, we see that the slope of line DE and AC, both are same, not equal to 0 but is equal to
which is 0 only if
So, this is the second mistake.
Thus, the statements that corrects the flaw in Gina's proof are
(i) The slope of segments DE and AC is not 0.
(ii) The coordinates of D and E were found using the Midpoint Formula.
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Answer:
The center of the circle is .
Step-by-step explanation:
The center of the circle is the midpoint of the segment between the endpoints. We can determine the location of the center by this vectorial expression:
(1)
Where:
- Center.
,
- Location of the endpoints.
If we know that and
, then the location of the center of the circle is:
The center of the circle is .
Answer:
The minimum possible initial amount of fish:
Step-by-step explanation:
Let's start by saying that
= is the initial number of fishes
John:
When John arrives:
- he throws away one fish from the bunch
- divides the remaining fish into three.
- takes a third for himself.
the remaining fish are expressed by the above expression. Let's call it John
and simplify it!
When Joe arrives:
- he throws away one fish from the remaining bunch
- divides the remaining fish into three
- takes a third for himself.
the remaining fish are expressed by the above expression. Let's call it Joe
and simiplify it
since we've already expressed John in terms of x, we express the above expression in terms of x as well.
When James arrives:
We're gonna do this one quickly, since its the same process all over again
This is the last remaining pile of fish.
We know that no fish was divided, so the remaining number cannot be a decimal number. <u>We also know that this last pile was a multiple of 3 before a third was taken away by James</u>.
Whatever the last remaining pile was (let's say ), a third is taken away by James. the remaining bunch would be
hence we've expressed the last pile in terms of n as well. Since the above 'James' equation and this 'n' equation represent the same thing, we can equate them:
L.H.S must be a Whole Number value and this can be found through trial and error. (Just check at which value of n does 2n/3 give a non-decimal value) (We've also established from before that n is a multiple a of 3, so only use values that are in the table of 3, e.g 3,6,9,12,..
at n = 21, we'll see that 2n/3 is a whole number = 14. (and since this is the value of n to give a whole number answer of 2n/3 we can safely say this is the least possible amount remaining in the pile)
by solving this equation we'll have the value of x, which as we established at the start is the number of initial amount of fish!
This is minimum possible amount of fish before John threw out the first fish