A car traveling at a constant speed will travel farther in 3 hours than in 2 hours. which inequality shows this in function nota
1 answer:
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The given information are the coordinates of points H, Z and B. So, the first step to do is to plot these points on a Cartesian plane as shown in the attached picture. We can deduce visually that horse Z is closer to the barns than horse H. But, to further justify the answer, we have to provide the magnitude of the distance of horses H and Z to barn B. In this approach, we use the distance formula:
d = √(x₂ - x₁)² + (y₂ - y₁)²
Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165
Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012
Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters
Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.
d = √(x₂ - x₁)² + (y₂ - y₁)²
Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165
Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012
Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters
Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.
The total number of seats in the theater is 600 seats, if the students filled up 570 seats, which was 95% of the total number of seats in the theater.
Step-by-step explanation:
The given is,
Seats filled by students are 570 seats
Which is 95% of the total number of seats in the theater
Step: 1
Let, x - Total number of seats available in theater
Percentage of seats filled, y= 95%
Seats filled by students = 570
Formula to calculate total number of seats in theater,
95% of seats
570 =
x =
= 600
x = 600 seats
Step: 2
Check for solution,
5% of seats
= (0.05 × 600)
= 30 seats
Total no. of seats = 5% of seats + 95% of seats
= 30 + 570
600 = 600
Result:
The total number of seats in the theater is 600 seats.