<u>Given</u>:
Given that the regular decagon has sides that are 8 cm long.
We need to determine the area of the regular decagon.
<u>Area of the regular decagon:</u>
The area of the regular decagon can be determined using the formula,
where s is the length of the side and n is the number of sides.
Substituting s = 8 and n = 10, we get;
Simplifying, we get;
Rounding off to the nearest whole number, we get;
Thus, the area of the regular decagon is 642 cm²
Hence, Option B is the correct answer.
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Answer:
Step-by-step explanation:
You should use the distance formula:
√(2-(-6) squared + 0 - (-5) squared
8 squared + 5 squared = 64+25 = √89
The answer is approximately 9.433
Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
Answer: 34/25
Step-by-step explanation:
(136÷4)(100÷4) = 34/25 when reduced to the simplest form. As the numerator is greater than the denominator, we have an IMPROPER fraction,