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.
The correct answer is 24
You have to apply factorials here and formulas. You have 4 letters which means that your n=4, and you have 3 objects at a time which, means that you have 4 different groups of combinations with 6 permutations in each due to the 3! factorial. 6 x 4 is 24.
5n = 25
divide both sides by 5
n = 5
Y= 150
Start by using substitution.
Change x+y=375 to x=375-y
Substitute this into 1.25x+0.75y=393.75
1.25(375-y)+0.75y=393.75
Distribute the 1.25
468.75-1.25y+0.75=393.75
Add like terms (y)
468.75-0.5y=393.75
Subtract 468.75 to the right
-0.5y=-75
Divide by -0.5
y=150