Answer:
See the proof below.
Step-by-step explanation:
For this case we need to proof the following indentity:
So we need to begin with the definition of tangent, we know that 
and we can do this:
(1)
We also have the following identities:
Now we can apply those identities into equation (1) like this:
(2)
We can divide numerator and denominator from expression (2) by 
we got this:
And simplifying we got:
And that complete the proof.
Answer:
85% off $51 is $43.35 which equals to $7.65
Amanda paid only $7.65 for the 85% off the original price.
Step-by-step explanation:
Answer:
Explained below :)
(I tried my best, sorry if it doesn't make sense.)
Step-by-step explanation:
Example: 1/4 - 1/8= ?
1: Find the common denominator (bottom number)
2: If the common denominator is 8 then you multiply 1/4 by 2/2 to get the denominator of 8. If you needed then you can multiply the other fraction to get the same denominator.
3: Once you get multiply that then you get 2/8 -1/8.
4: Subtract the numerator (top number) 1
5: Keep the numerator (8)
6: Your answer would be 1/8
Answer:
Volume = 12 *6 *8 , Surface area = 2 ( 12 *6 + 8 *12 + 6* 8 )
Step-by-step explanation:
Given : Cuboid with length 12 , width 6 and height 8 units.
To find : Drag each expression to show whether it can be used to find the volume, surface area, or neither.
Solution : We have given Cuboid with
Length = 12 units ,
Width = 6 units
Height = 8 units.
Volume of cuboid = length * width * height .
Volume = 12 *6 *8.
Surface area = 2 ( l *w + h *+w *h)
Surface area = 2 ( 12 *6 + 8 *12 + 6* 8 ).
None = 12 +6 +8.
Therefore, Volume = 12 *6 *8 , Surface area = 2 ( 12 *6 + 8 *12 + 6* 8 ) .
Answer: The flagpole is about 22.3 feet tall.
This is roughly the size of a two story building, assuming each floor is 10 feet or so.
Since this height is under 25 ft, this flagpole is in compliance with the regulation.
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Work Shown:
The horizontal leg of the triangle is 36 ft. This is the adjacent leg to the reference angle 25 degrees.
The vertical leg of the triangle is x-5.5, and this leg is the opposite side to the reference angle 25 degrees.
Use the tangent rule to connect the opposite and adjacent sides.
Solve for x.
tan(angle) = opposite/adjacent
tan(25) = (x-5.5)/36
36*tan(25) = x-5.5
x-5.5 = 36*tan(25)
x = 36*tan(25)+5.5
x = 22.28707569358
x = 22.3 ft is the approximate height of the flagpole
Make sure your calculator is in degree mode.
The height is not over 25 ft, so this flagpole meets the requirements.
