Answer:
Step-by-step explanation:
1.The prime factorization of 54 is: 2 x 3 x 3 x 3.
2.The prime factorization of 24 is: 2 x 2 x 2 x 3.
3.The prime factors and multiplicities 54 and 24 have in common are: 2 x 3.
4.2 x 3 is the GCF of 54 and 24.
Answer: GCF(54,24) = 6.
Focus on the top line angles for now.
Those two angles combine to the straight angle ABC, which is 180 degrees.
(angleABY) + (angleYBC) = angle ABC
(x+25)+(2x+50) = 180
(x+2x) + (25+50) = 180
3x+75 = 180
3x = 180-75
3x = 105
x = 105/3
x = 35
We'll use this x value to find that:
- angle YBC = 2x+50 = 2*35+50 = 70+50 = 120 degrees
- angle BEF = 5x-55 = 5*35-55 = 175-55 = 120 degrees
Angles YBC and BEF are corresponding angles (they are both in the northeast corner of their respective four-corner angle configuration). They are both 120 degrees. Since we have congruent corresponding angles, we have effectively proven that AC is parallel to DF. Refer to the converse of the corresponding angles theorem.
The regular version of the "corresponding angles theorem" says that if two lines are parallel, then the corresponding angles are congruent. The converse reverses the logic of the conditional statement. Meaning that if the corresponding angles are congruent, then the lines are parallel.
Answer:
a = -5
Step-by-step explanation:
(5 - 3)/(5 - a)
2/(5 - a)
perpendicular of 2/(5 - a) = -(5 - a)/2
(a - 0)/(1 - 0) = -(5 - a)/2
a/1 = -(5 - a)/2
2a = -5 + a
a = -5
Given:
The given equation is
To find:
The vertex, focus, and directrix.
Solution:
The equation of a parabola is
...(i)
where, (h,k) is vertex, 
and directrix is 
We have,
It can be written as
...(ii)
On comparing (i) and (ii), we get
Vertex of the parabola is (2,3).
Therefore, the focus of the parabola is 
.
Directrix of the parabola is
Therefore, the directrix of the parabola is .
