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:
x=2 and y=5
Step-by-step explanation:
Steps:
I will solve your system by substitution.
x=y−3;2x+y=9
Step: Solve x = y − 3 for x:
Step: Substitute y − 3 for x in 2x + y = 9:
2x+y=9
2(y−3)+y=9
3y−6=9(Simplify both sides of the equation)
3y−6+6=9+6(Add 6 to both sides)
3y=15
3y/3=15/3 (Divide both sides by 3)
y=5
Step: Substitute 5 for y in x = y − 3 :
x=y−3
x=5−3
x=2(Simplify both sides of the equation)
Answer:
x=2 and y=5
Hopes this helps: i used a visual as well
The ratio of males to females is 1.4 : 1, so the fraction of the total that is made up of males is 1.4/(1.4 + 1) = 1.4/2.4 = 7/12.
There were (7/12)*475 ≈ 277 males at the party.
There were 475 - 277 = 198 females at the party.
Answer:
SA = 2πr² + 2πrh
Step-by-step explanation:
2πr² will provide the surface area of the top and bottom of the cylinder
2πrh will provide the surface area of the cylinder portion that connects the top and bottom
