Answer:
= 12
Step-by-step explanation:
The shape ABCDEF is an irregular polygon.
The sum of the interior angles of any regular or irregular polygon = (n - 2) x 180 (where n is the number of sides of the polygon).
Therefore, the sum of the interior angles of shape ABCDEF = (6 - 2) x 180 = 720°
So to find the value of , we need to add together all the interior angles and equal it to 720, then solve for .
Before we do that, we need to determine angle F.
From inspection, we can see that angle F and 52° are a linear pair. We know that a linear pair of angles add up to 180°, so F + 52 = 180 ⇒ F = 180 - 52 = 128°
Therefore:
A + B + C + D + E + F = 720
(10 - 5) + 108 + (8 - 3) + (14 - 25) + 133 + 128 = 720
Collect like terms:
10 + 8 + 14 - 5 + 108 - 3 - 25 + 133 + 128 = 720
Combine like terms:
32 + 336 = 720
Subtract 336 from both sides:
32 = 384
Divide both sides by 32:
= 12
Answer:
50.020 and 50.02
Step-by-step explanation:
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Answer:
1,800 ft
Step-by-step explanation:
Rebecca will walk in the pattern of a regular polygon with 'n' sides and internal angles of 160 degrees (180 at a straight line - 20 degrees from each turn).
The equation that describes the internal angle of a regular polygon is:
For A = 160 degrees:
If each side is 100 ft long, the total distance that Rebecca has walked is:
She walked 1,800 ft.
Answer:
5.78×10¹⁵
Step-by-step explanation:
The playlist has 12 songs, and he wants the same number of songs for each genre, so he must pick 4 songs per genre.
The number of ways he can choose 4 country songs (ignoring the order) is ₂₂C₄ = 7315.
The number of ways he can choose 4 reggae songs (ignoring the order) is ₁₁C₄ = 330.
The number of ways he can choose 4 pop songs (ignoring the order) is ₅C₄ = 5.
The total number of combinations is 7315 × 330 × 5 = 1.21×10⁷.
Once he has his 12 songs selected, the number of ways he can arrange them is ₁₂P₁₂ = 12! = 4.79×10⁸.
So the total number of possible playlists is:
(1.21×10⁷) × (4.79×10⁸) = 5.78×10¹⁵
