Answer: 20 ;)
Step-by-step explanation:
7.) the equation of the circle is
(x - 3)^2 + (y - 4)^2 = 25
If you substitute the point in you get
(6-3)^2 + (8-4)^2 = 25
3^2 + 4^2 = 25
9 + 16 = 25
25 = 25
Both sides of the equation are the same so it proves it lies on the circle
8.) you add the x coordinates together and divide by 2
7 + 4 = 11
11/2 = 5.5
You use +7 because you need to find the midpoint.
You then add 5.5 to - 7 or - 5.5 from 4
-7 + 5.5 = - 1.5
You do the same for y coordinates
6+5 = 11
11/2 = 5.5
6-5.5 = 0.5
So the coordinates of Rachel's house are
(-1.5, 0.5)
Diameter of the semicircle = 10 km.
Explanation: perimeter of semicircle = 1 2
the circumference + diameter Given: perimeter of semicircle = 25.7 k
m
Circumference of circle with radius r
= 2
π
r where 2
r
= diameter ⇒
25.7
=
22
π
r
+
2
r
⇒
25.7
=
π
r
+
2
r
=
r
(
π
+
2
) ⇒
25.7
=
r
(
3.14
+
2
)
=
r
(
5.14
) ⇒
r
=
=5m
⇒d
i
a
m
e
t
e
r
=
2
r
=
10
k
m
For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
Where:
m: It's the slope
b: It is the cut-off point with the y axis
In this case we have the following equation of the line:
Where:
By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will have an equation of the form:
Substitute the given point
to find "b":
Finally, the equation of the requested line is:
Answer:
