Answer:
Let the weight of the leader dog = X
Then Darlene's dog weighs = 5X ( fives times as much)
Now add both together to equal 84 pounds:
5X + X = 84
Simplify:
6x = 84
Divide both sides by 6:
x = 84 / 6
x = 14
The leader dog weighs 14 pounds.
Darlene's dog weighs 70 pounds.
The radius of the incircle of the triangle with sides 25 cm, 51 cm, and 52
cm is <u>26 cm</u>.
<h3>How can the radius of the incircle of a triangle be found?</h3>
The area of the triangle is given as follows;
A = √(s·(s - a)·(s - b)·(s - c))
Where;
a = 25 cm
b = 51 cm
c = 52 cm
s = The semi perimeter of the triangle = (25 + 51 + 52) ÷ 2 = 64
A = √(64·(64 - 25)·(64 - 51)·(64 - 52)) = 624
The area of the triangle is the area of ΔABC + ΔAOC + ΔBOC + ΔAOB
Which gives;
![A = \mathbf{\dfrac{a \cdot r}{2} + \dfrac{b \cdot r}{2} + \dfrac{c \cdot r}{2}}](https://tex.z-dn.net/?f=A%20%3D%20%5Cmathbf%7B%5Cdfrac%7Ba%20%5Ccdot%20r%7D%7B2%7D%20%2B%20%5Cdfrac%7Bb%20%5Ccdot%20r%7D%7B2%7D%20%2B%20%5Cdfrac%7Bc%20%5Ccdot%20r%7D%7B2%7D%7D)
Therefore;
![A = r \cdot \left(\dfrac{a + b + c }{2} \right) = \mathbf{r \cdot s}](https://tex.z-dn.net/?f=A%20%3D%20r%20%5Ccdot%20%5Cleft%28%5Cdfrac%7Ba%20%2B%20b%20%2B%20c%20%7D%7B2%7D%20%5Cright%29%20%3D%20%5Cmathbf%7Br%20%5Ccdot%20s%7D)
![r = \dfrac{A}{s}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7BA%7D%7Bs%7D)
Therefore;
![r = \dfrac{624}{64} = 26](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7B624%7D%7B64%7D%20%3D%2026)
The radius of the incircle of the triangle is <u>26 cm</u>
Learn more about the incircle of a triangle here:
brainly.com/question/6558867
Answer:
1150 km/hr
Step-by-step explanation:
Formula for Average Speed is given as = Distance in Kilometers/ Time in Hours
In the question we are given the following parameters.
The length of a planet's orbit around a star = Distance = 17,650,000 km.
Time taken to complete a full orbit = 640 Earth days
Step 1
We need to convert the time in days to hours
1 Earth day = 24 hours
640 Earth days =
We cross multiply
640 Earth days × 24 hours
= 15360 hours.
Step 2
Average Speed = Distance in Kilometers/ Time in Hours
Average Speed = 17,650,000 km. /15360 hours
Average Speed = 1149.0885417 km/hr
Approximately to 3 significant figures=
1150 km/hr
Therefore, the planets average speed in kmh-1 to 3sf is 1150 km/hr
Ummm is this a full question?