Whenever he visits Dayton, Quincy has to drive 12 miles due north from home. Whenever he
visits Belleville, he has to drive 16 miles due east from home. How far apart are Dayton and
Belleville, measured in a straight line?

20 miles

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:

x^2 = a^2 + b^2

Where x is the hypotenuse of the triangle (in this case the distance between Dayton and Belleville) and a and b are the other sides.

Replacing with the values given:

x^2 = 16^2 + 12^2

x^2 = 256+144

x^2 = 400

x = √400

x = 20 miles

Feel free to ask for more if needed or if you did not understand something.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

a natural event such as a flood, earthquake, or hurricane that causes great damage or loss of life.

step-by-step explanation: