Answer:
33
Step-by-step explanation:
Let the three gp be a, ar and ar^2
a + ar + ar^2 = 21 => a(1 + r + r^2) = 21 . . . (1)
a^2 + a^2r^2 + a^2r^4 = 189 => a^2(1 + r^2 + r^4) = 189 . . . (2)
squaring (1) gives
a^2(1 + r + r^2)^2 = 441 . . . (3)
(3) ÷ (2) => (1 + r + r^2)^2 / (1 + r^2 + r^4) = 441/189 = 7/3
3(1 + r + r^2)^2 = 7(1 + r^2 + r^4)
3(r^4 + 2r^3 + 3r^2 + 2r + 1) = 7(1 + r^2 + r^4)
3r^4 + 6r^3 + 9r^2 + 6r + 3 = 7 + 7r^2 + 7r^4
4r^4 - 6r^3 - 2r^2 - 6r + 4 = 0
r = 1/2 or r = 2
From (1), a = 21/(1 + r + r^2)
When r = 2:
a = 21/(1 + 2 + 4) = 21/7 = 3
Therefore, the numbers are 3, 6 and 12.
9514 1404 393
Answer:
C. 168°
Step-by-step explanation:
The exterior angle at any vertex of an n-gon will be ...
360°/n
So a 30-gon will have exterior angles of ...
360°/30 = 12°
The adjacent interior angle is supplementary to this, so is ...
180° -12° = 168°
_____
<em>Using the reasonableness test</em>
You know that the interior angles of a square are 90°, and that regular polygons with more sides have larger interior angles. The most any regular polygon's interior angle can be is 180°. The only answer choice between 90° and 180° is the correct choice: 168°.
Answer:
A (100)
Step-by-step explanation:
If 2 hours pass starting at 23:35 today, then tomorrow the time will be 1:35. The difference between 1:35 and 1:15 is 20 (minutes) Because there are 120 minutes in 2 hours (60 minutes per hour), This means we do 120 minutes minus 20 minutes. This gives us an answer is A, 100 :)
