Evan bought 6 batteries at $10 apiece and 6 batteries at $4 apiece. the total cost was the same as he would have spent buying 6

Answer:

Part A) The straight-line distance between the school and the Fire Station is

Part B) The straight-line distance between the school and the hospital is

Step-by-step explanation:

The full question can be found in the attached image.

Let

The positive x-coordinates represent the East

The positive y-coordinates represent the North

The negative x-coordinates indicate the West

The negative y-coordinates indicate the South

Treat point A (0,0) as the Middle School (reference point).

Part A) The Town Hall is situated 4.3 miles directly east of the Middle School,

thus the coordinates for Town Hall are B(4.3,0).

The Fire Station is positioned 1.7 miles directly north of Town Hall, therefore

the coordinates for the Fire Station are C(4.3,1.7).

What is the straight-line distance between the school and the Fire Station?

Keep in mind that

the distance formula between two points is indicated as

We have

A(0,0) and C(4.3,1.7).

Now substitute

Part B) Now considering

The hospital is 3.1 miles west of the fire station.

The coordinates for the hospital are D(4.3-3.1,1.7).

D(1.2,1.7)

What is the straight-line distance between the school and the hospital?

Remember that

the distance formula applies here as well,

with points A(0,0) and D(1.2,1.7).

Substituting the values gives us

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.

Response:c

Detailed explanation: