Step-by-step explanation:
If the tickets given to employees = 40
Then tickets given to listeners = 2 x no of employees tickets
= 2 x40 = 80
Total tickets = 40+ 80 = 120
∠MJK = 90 (It is a rectangle, so all its corners are right angles)
∠MJL = 90 - 27 = 63 (Complementary angles)
∠JLK = 180 - 90 = 27 = 63 (Sum of all angles in a triangle is 180)
∠KML = 27 (Isosceles triangle)
∠MNL = 180 - 27 - 27 - 126 (Sum of all angles in a triangle is 180)
We can see values of angles in degrees first
= 150°
Similarly
= 300°
Now reference angle means positive acute angle they will have
As we can see in attachment 150° lies in second quadrant so its reference angle will be 180°-150° = 30° from x axis line as shown.
Where as angle 300° lies in fourth quadrant so its reference angle will be 360° - 300° = 60° from x axis as shown. So clearly both reference angles are different . So 1st choice " angles donot have same reference angle" best explains it
Choice (2) and (3) are incorrect as tan is positive only in first and third quadrants and angle 300° is in fourth quadrant.
since angle 150° is in second quadrant and 300° is in fourth quadrant so both will have same negative sign so choice (4) is not correct.
So final ansewr is choice (1) "the angles donot have same reference angle"
Answer:
(x,y)=(5-2y,y), y belongs to all real numbers
Step-by-step explanation:
x=5-2y
3x=15-6y
3(5-2y)=15-6y
15-6y=15-6y
y∈All Real Numbers
(x,y)=(5-2y,y), y∈All Real Numbers
Step-by-step explanation:
the general vertex form is
y = a(x - h)² + k
with (h, k) being the vertex of the curve.
after doing all the multiplications we get
y = a(x² - 2hx + h²) + k = ax² - 2ahx + ah² + k
now we have
y = x² + 24x + 124
and we can compare
ax² = x²
a = 1
-2ahx = -2hx = 24x
-2h = 24
h = 24/-2 = -12
ah² + k = 124
(-12)² + k = 124
144 + k = 124
k = -20
so, the vertex form is
y = (x + 12)² - 20
