(2+3) (54) Multiply the complex numbers
2 answers:
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Answer:
The perimeter of the base of the birdhouse is 36 units
Step-by-step explanation:
<u><em>The complete question is</em></u>
Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the measure of the exterior angle and the length of a diagonal that passes through the center is 12. What is the perimeter of the base of the birdhouse?
step 1
Find the measure of the interior angle
Let
x ---> the measure of the interior angle
y ---> the measure of the exterior angle
Remember that
the sum of the interior and exterior angle in any polygon is equal to 180 degrees
so
----> equation A
we have that
the measure of the interior angle is twice the measure of the exterior angle
so
----> equation B
substitute equation B in equation A
so
That means-----> The figure is a regular hexagon
step 2
Remember that
The length of the diagonal that passes through the center of the hexagon is equal to two times the length of the regular hexagon
Let
b ----> the length side of the hexagon
so
The perimeter of the hexagon is given by the formula
substitute
Hi there!
There are 3 parts to this equation:
f(x)
f(x+1)
4f(x)
We must first determine these three parts separately.
<u>1) f(x)</u>
We're given that :
⇒ :
<u>2) f(x+1)</u>
Now, we must find f(x+1). To do so, add 1 to x in the original function :
⇒
<u>3) 4f(x)</u>
To find 4f(x), multiply the original function by 4:
:
<u>4) Put it all together</u>
Now, plug each of the three parts into the equation :
Factor the left side
Divide both sides by 3^x
Because this equation is true, is therefore true.
I hope this helps!