Answer:
17
Step-by-step explanation:
3(4)+5
12+5
17
Answer:
Step-by-step explanation:
We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point (8,1) and a slope from the equation y=-23x+5. We will chose point-slope since we have a point and slope.
Point slope:
in our new equation because it us perpendicular to it. This means we will need to change it into its negative reciprocal which is .
We will substitute and .
.
This is the equation of the line perpendicular to y=-23x+5 that crosses through (8,1).
The answer is d. Thank you
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
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