Response:
D. The sidelines are parallel because they are perpendicular to a common line.
Justification:
According to the perpendicular transversal theorem, when a line is perpendicular to one of two parallel lines, it is also perpendicular to the other line. Furthermore, the converse of the theorem states that if two lines are perpendicular to the same line, they must be parallel. Therefore, the sidelines are indeed parallel and also perpendicular to this single line.
8.96 gallons of water
To solve this question, you multiply the ratio of the volumes of container b to container a by the volume of container a. As container b has a greater volume than container a, the ratio will be greater than 1. In this scenario, it is 112% since it includes a 12% increase: 100% + 12% = 112%. Consequently, the volume of container b is calculated as 112% x 8 gallons = 8.96 gallons.
Given that,
Julia completes a 20-mile bike ride in 1.2 hours.
The distance Julia covers is 20 miles and her time taken is 1.2 hours.
Therefore, Julia's speed = 
= 16.67 mph
Katie finishes the same 20-mile ride in 1.6 hours.
Katie’s distance is 20 miles and her time is 1.6 hours.
Hence, Katie's speed = 
= 12.5 mph
To determine how much faster Julia rides compared to Katie, subtract Katie’s speed from Julia’s speed.
Thus, 16.67 mph minus 12.5 mph equals 4.17 mph, approximately 4.2 mph.
Consequently, Julia cycles 4.2 mph faster than Katie.
Response:
Detailed breakdown:
Considering a rectangle measuring 3cm by 4cm with a circle of 1 cm diameter within it:
The area of the shaded section equals Area of Rectangle minus Area of Circle
The area of a rectangle is calculated as Length multiplied by Width
The area of the circle is
Area of shaded region = 12 - 3.142
Given:
There are 4/5 as many students who do not wear glasses as those who do.
60 students wear glasses.
Find the total number of students in the grade.
Calculate 60 * 4/5 = (60 * 4)/5 = 240 / 5 = 48 students who do not wear glasses.
Total students = 60 w/ glasses + 48 w/o glasses = 108 students.
