Answer:
Mr. Johnson can arrange 18 students in each row, that is 4 rows of boys and 5 rows of girls.
Step-by-step explanation:
Given:
Number of boys = 72
number of girls = 90
We need to arrange students in rows with equal number of only boys and only girls.
To find the maximum number (x) of boys or girls in each row, we will find the GCF (Greatest Common Factor) of the numbers 72 and 90, such that 'x' divides both numbers evenly without a remainder.
Now to find GCF we will factorize both numbers.
from above we can say that;
GCF = 
Hence Mr. Johnson can arrange 18 students in each row, that is 4 rows of boys and 5 rows of girls.
Answer: No
Step-by-step explanation: It does not pass the vertical line test
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:
Step-by-step explanation:
