Answer:
Given a triangle ABC, Pythagoras' Theorem shows that:

Thus,

The distance formula, gives an equivalent expression based on two points at the end of the hypotenuse for a triangle.


Therefore when given the hypotenuse with endpoints at

We know that the third point of the right triangle will be at

and that the two side lengths will be defined by the absolute values of:


Answer:
The amount becomes $6964.53 after 3 years .
Step-by-step explanation:
Formula

Where P is the principle , r is the rate of interest in the decimal form and t is the time in the years .
As given
Earl invested 6,000 in a money market account that pays 5% interest quarterly for 3 years .
P = $6000
5% is written in the decimal form.

= 0.05
r = 0.05
t = 3 years
Putting all the values in the formula




Therefore the amount becomes $6964.53 after 3 years .
Answer:
20 quarts.
Step-by-step explanation:
Because there are 20 quarts in 5 gallons.
<h3><em><u>The equation to find the number of hours for which the total cost will be the same for the two services is:</u></em></h3><h3>12 + 5h = 18 + 3h</h3>
<em><u>Solution:</u></em>
Let "h" be the number of hours
Given that,
<em><u>Derrick's Dog Sitting charges $12 plus $5 per hour</u></em>
Cost : 12 + 5(number of hours )
Cost : 12 + 5h ---------- eqn 1
<em><u>Darlene's Dog Sitting charges $18 plus $3 per hour</u></em>
Cost: 18 + 3(number of hours)
Cost: 18 + 3h ---------- eqn 1
<em><u>For eqn 1 = eqn 2, the number of hours for the total cost will be the same for the two services</u></em>
Therefore,
12 + 5h = 18 + 3h
Thus option A is correct