Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the
third side: Given: ΔABC Prove: The midsegment between sides Line segment AB and Line segment BC is parallel to side Line segment AC. Draw ΔABC on the coordinate plane with point A at the origin (0, 0). Let point B have the ordered pair (x1, y1) and locate point C on the x-axis at (x2, 0). Point D is the midpoint of Line segment AB with coordinates at Ordered pair the quantity 0 plus x sub 1, divided by 2. The quantity 0 plus y sub 1, divided by 2 by the Midpoint Formula. Point E is the midpoint of Line segment BC with coordinates of Ordered pair the quantity x sub 1 plus x sub 2, divided by 2. The quantity 0 plus y sub 1, divided by 2 by the Midpoint Formula. The slope of Line segment DE is found to be 0 through the application of the slope formula: The difference of y sub 2 and y sub 1, divided by the difference of x sub 2 and x sub 1 is equal to the difference of the quantity 0 plus y sub 1, divided by 2, and the quantity 0 plus y sub 1, divided by 2, divided by the difference of the quantity x sub 1 plus x sub 2, divided by 2 and the quantity 0 plus x sub 1, divided by 2 is equal to 0 divided by the quantity x sub 2 divided by 2 is equal to 0 When the slope formula is applied to Line segment AC the difference between y sub 2 and y sub 1, divided by the difference of x sub 2 and x sub 1 is equal to the difference of 0 and 0, divided by the difference of x sub 2 and 0 is equal to 0 divided by x sub 2 is equal to 0, its slope is also 0. Since the slope of Line segment DE and Line segment AC are identical, Line segment DE and Line segment AC are parallel by the Parallel Postulate. Which statement corrects the flaw in Gina's proof? The coordinates of D and E were found using the slope formula. Segments DE and AC are parallel by definition of parallel lines. The coordinates of D and E were found using the Distance between Two Points Postulate The slope of segments DE and AC is not 0.
2 answers:
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The Researcher will find 69 viruses, because 231 viruses are decayed in 7 hours, if a virus with a decay rate of 19% per hour and they start with 300 viruses.
Step-by-step explanation:
The given is,
A new virus with a decay rate of 19% per hour
They start with 300 viruses
Step:1
Formula to calculate the viruses at decay rate,
............................(1)
Where, y - No of viruses after given time
A - Viruses at initial stage
r - Decay rate
t - No. of hours
From the given,
A = 300
r = 19% per hour
t = 7 hours
Equation (1) becomes,
Viruses of 7 hours ≅ 69 viruses
( or )
Step:1
For 1st hour,
= (No.of viruses in hour) - (No,of viruses in last hour × Decay rate )
= (300)-(300 × 0.19)
= 300 - 57
= 243
For 2nd hour,
= (243)-(243 × 0.19)
= 243 - 46.17
= 196.83
For 3rd hour,
= (196.83)-(196.83 × 0.19)
= 196.83 - 37.39
= 159.4323
For 4th hour,
= (159.4323)-(159.4323 × 0.19)
= 159.4323 - 30.2921
= 129.1402
For 5th hour,
= (129.1402)-(129.1402 × 0.19)
= 129.1402 - 24.5366
= 104.6035
For 6th hour,
= ( 104.6035)-( 104.6035 × 0.19)
= 104.6035 - 19.8747
= 84.7288
For 7th hour,
= (84.7288)-(84.7288 × 0.19)
= 84.7288 - 16.0984
= 68.63 viruses
Result:
The Researcher will find 69 viruses, because 231 viruses are decayed in 7 hours, if a virus with a decay rate of 19% per hour and they start with 300 viruses.