Answer:
6.31 mi
Step-by-step explanation:
The diagram below explains the solution better.
From the diagram,
C = starting point of the race.
A = end of the first part of the race.
B = end of the race.
Using Cosine rule, we can find the straight-line distance between the starting point and the end of the race.
Cosine rule states that:
![a^2 = b^2 + c^2 - 2bc[cos(A)]](https://tex.z-dn.net/?f=a%5E2%20%3D%20b%5E2%20%2B%20c%5E2%20-%202bc%5Bcos%28A%29%5D)
where A = angle A = <A
Given that
b = 5.2 miles
c = 2.0 miles
<A = 115° (from the diagram)
Hence,
![a^2 = 5.2^2 + 2.0^2 - 2*5.2*2.0[cos(115)]\\\\a^2 = 27.04 + 4 - 20.8[cos(115)]\\\\a^2 = 31.04 + 8.79\\\\a^2 = 39.83\\\\a = \sqrt{39.83}\\ \\a = 6.31 mi](https://tex.z-dn.net/?f=a%5E2%20%3D%205.2%5E2%20%2B%202.0%5E2%20-%202%2A5.2%2A2.0%5Bcos%28115%29%5D%5C%5C%5C%5Ca%5E2%20%3D%2027.04%20%2B%204%20-%2020.8%5Bcos%28115%29%5D%5C%5C%5C%5Ca%5E2%20%3D%2031.04%20%2B%208.79%5C%5C%5C%5Ca%5E2%20%3D%2039.83%5C%5C%5C%5Ca%20%3D%20%5Csqrt%7B39.83%7D%5C%5C%20%5C%5Ca%20%3D%206.31%20mi)
The straight-line distance between the starting point and the end of the race is 6.31 mi
You can revise: the sum of the two adjacent angles is 180°
and the sum of the measurements of the three corners in a triangle is also 180°
<1= 180°-57°=123°
As <2=52°, so we have <3= 180°-(28°+71°+52°)= 180°-151°=29°
have fun
Answer:
b=84
Step-by-step explanation:
from your equation, subtract 3969 from each side
you are left with b^2=7056
sqrt b^2 = sqrt 7056
b=84
Answer:
Step-by-step explanation:
Explanation:
Start by writing out your starting expression
x
2
−
5
x
2
+
5
x
−
14
−
x
+
3
x
+
7
Next, factor the denominator of the first fraction
x
2
+
5
x
−
14
x
2
+
7
x
−
2
x
−
14
x
(
x
−
2
)
+
7
(
x
−
2
)
(
x
−
2
)
(
x
+
7
)
Your expression is thus equivalent to
x
2
−
5
(
x
−
2
)
⋅
(
x
+
7
)
−
x
+
3
x
+
7
Since you have to subtract two fractions, you need to find the commonon denominator first. To do that, multiply the second fraction by
x
−
2
x
−
2
x
2
−
5
(
x
−
2
)
⋅
(
x
+
7
)
−
(
x
+
3
)
⋅
(
x
−
2
)
(
x
−
2
)
⋅
(
x
+
7
)
This will get you
x
2
−
5
−
(
x
+
3
)
(
x
−
2
)
(
x
−
2
)
(
x
+
7
)
x
2
−
5
−
x
2
−
x
+
6
(
x
−
2
)
(
x
+
7
)
=
1
−
x
(
x
−
2
)
(
x
+
7
)
Answer:
can u get a pic of the diagram
Step-by-step explanation:
