Answer:
321.68feet
Step-by-step explanation:
Given the following
Top of the house above the sea level = 150feet = opposite
Angle of elevation = 25°
Required
Distance from the boat to the base of the house(adjacent)
Using the SOH CAH TOA identity
tan theta = opp/adj
tan 25 = 150/d
d = 150/tan25
d = 150/0.4663
d = 321.68
Hence the required distance is 321.68feet
Answer:
C is the answer
Step-by-step explanation:
35+1=36
35-------------36
Answer:
The lateral surface area is 84 cm^2
Step-by-step explanation:
The rectangular prism is a geometric figure that has rectangles at each of it's faces. The lateral surface is formed by four rectangles, the ones formed by the length and the height and the ones formed by the width and the height. So in order to calculate the area of this surface we need to calculate the area of these rectangles and sum it. We have:
A_lateral = 2*width*height + 2*length*height
A_lateral = 2*6*3 + 2*8*3 = 36 + 48 = 84 cm ^2
So the lateral surface area is 84 cm^2
Answer: Choice B
(-2, 5)
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Explanation:
The original system is
Multiply both sides of the second equation by 3. Doing so leads to this updated system of equations
Now add straight down
The x terms add to -4x+3x = -1x = -x
The y terms add to 3y+(-3y) = 0y = 0
The terms on the right hand sides add to 23+(-21) = 2
We end up with the equation -x = 2 which solves to x = -2
Now use this to find y. You can pick any equation with x,y in it
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-4x+3y = 23
-4(-2)+3y = 23
8+3y = 23
3y = 23-8
3y = 15
y = 15/3
y = 5
Or
x-y = -7
-2-y = -7
-y = -7+2
y = -5
y = 5
Either way, we get the same y value.
So that's why the solution is (x,y) = (-2, 5)
