Answer:
C = (-5,12) E = (11,8)
Step-by-step explanation:
The difference between -5 and 3 is 8, so add 8 to the midpoint (3), and it's 11
The difference between 10 and 8 is 2, so add 2 to the midpoint (10), and it's 12
<span>mBCP = 86/2 = 43
answer is A. 43 first choice</span>
Answer:
Step-by-step explanation:
To find the value of , we are solving the exponential equation using logarithms.
Let's solve it step-by-step
Step 1. Divide both sides of the equation by -1 to get rid of the negative signs:
Step 2. Take natural logarithm to bot sides of the equation:
Step 3. Use the power rule for logarithms:
For our equation: and
Step 4. Divide both sides of the equation by
We can conclude that the value of x in our exponential equation is approximately 25.24.
Answer:
12.61 miles
Step-by-step explanation:
The distance of lighthouse B from lighthouse A, the distance from lighthouse A to the boat and the distance of lighthouse B from the boat all form a triangle. Since lighthouse B is west of lighthouse A, and at a distance of 9 miles form lighthouse A, light house A is at a bearing of North 90° East of lighthouse B. The distance from lighthouse A to the boat is 6 miles, and the bearing of the boat from lighthouse B is North 64° East.
So, the angle between the distance from lighthouse B to the boat and lighthouse B to lighthouse A is 90° - 64° = 26°
Since we have two sides and an angle, we use the sine rule
a/sinA = b/sinB where a = 6, A = 26°, b = 9, B = unknown
So, sinB = bsinA/a
= 9sin26/6
= 3(0.4384)/2
= 1.3151/2
= 0.6576
B = sin⁻¹(0.6576)
= 41.11°
≅ 41.1°
We now find the third angle in the triangle, C(the angle facing the distance from lighthouse B to the boat) from
26° + 41.1° + C = 180° (sum of angles in a triangle)
67.1° + C = 180°
C = 180° - 67.1° = 112.9°
Using the sine rule again to find the third side, c(the distance from lighthouse B to the boat), we have
a/sinA = c/sinC
c = asinC/sinA
= 6sin112.9°/sin26°
= 6(0.9212)/0.4384
= 5.5271/0.4384
= 12.61 miles
First, find c:
C is a supplementary angle, therefore, calculate x+113=180
180-113=x
X=67
Now, knowing that all of the angles of a triangle add up to 180, calculate for B.
72+b+67=180
139+b=180
B=180-139
B=41