To prove the QRST is a parallelogram.
Step 1: Given and
Step 2: are alternate interior angles.
Definition of alternate interior angles
Step 3: Alternate interior angle theorem:
If two parallel lines cut by a transversal then the alternate interior angles are congruence.
QR and TS are parallel lines cut by QS.
Therefore,
Step 4: Reflexive property of congruence:
Any geometric figure is congruence to itself.
Therefore,
Step 5: By the above steps
(Angle), (Angle) and (Side)
Hence (by ASA congruence theorem)
Step 6: Corresponding parts of congruence triangles are congruent.
Step 7: Property of parallelogram:
If one pair of opposite sides are both parallel and congruent, then the quadrilateral is a parallelogram.
Hence Quadrilateral QRST is a parallelogram.
Answer:
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Step-by-step explanation:
1.Assuming the same sample size and considering the same value for the errors ( not taking into consideration the type of music, the volume of the sound and cow familiar the runner is with that type of stimuli, age group, time of the day/ number of days, running conditions like wether and equipment, distance) one can state:
A. Music has no influence over the running speed ( when jogging) in Washington DC
B.When listening to music, people ( in Washington DC) run faster while jogging
The mean running speed is a simple, ponderate or other type of mean ( that takes into consideration the variations of speed at the beginning and by the end of the race?
-5x + y = 5 . . . . . (1)
-4x + 2y = 2 . . . . (2)
(1) x 2 => -10x + 2y = 10 . . . (3)
(2) - (1) => 6x = -10 => x = -8/6 = -4/3
From (1), -5(-4/3) + y = 5 => y = 5 - 20/3 = -5/3
Therefore, x = -4/3; y = -5/3