Answer:
ntersecting lines DA and CE.
To find:
Each pair of adjacent angles and vertical angles.
Solution:
Adjacent angles are in the same straight line.
Pair of adjacent angles:
(1) ∠EBD and ∠DBC
(2) ∠DBC and ∠CBA
(3) ∠CBA and ∠ABE
(4) ∠ABE and ∠EBD
Vertical angles are opposite angles in the same vertex.
Pair of vertical angles:
(1) ∠EBD and ∠CBA
(2) ∠DBC and ∠EBA
Answer:
The first term is 28.
Step-by-step explanation:
Given: 8th term of Geometric sequence , 
and 3rd term of Geometric Sequence, 
We have to find First term of given geometric Sequence.
Let a be the first term of geometric sequence.
We know that,

So,




So, 


Therefore, The first term is 28.
Answer:
2261,9 cm³
Step-by-step explanation:
First, you need to find the area of the base:

A=36
cm²
Now let's multiply it for the height:
36π cm² × 20 cm = 720π cm³
= 2261,9 cm³
Answer:
1/21
Step-by-step explanation:
14 = 2/3c ➡ 14×3c=2 ➡ 42c = 2➡ c = 1/21
Draw a diagram to illustrate the problem as shown in the figure below.
Euclid is placed at the origin at (0,0).
Apollonius is 12 m north and 9 m east of Euclid, so its coordinate is (9,12).
Pythagoras is at the arbitrary position (x,y) so that is is at distance d from Euclid and 2d from Apollonius.
From the distance formula, obtain
d² = x² + y² (1)
(2d)² = (x-9)² + (y-12)²
or
4d² = (x-9)² + (y-12)² (2)
Substitute (1) into (2).
4(x² + y²) = x² - 18x + 81 + y² - 24y + 144
3x² + 3y² + 18x + 24y = 225
Divide by 3.
x² + 6x + y² + 8y = 75
Create perfect squares.
(x+3)² - 9 + (y+4)² - 16 = 75
(x+3)² + (y+4)² = 10²
Answer:
The path of Pythagoras is a circle of radius 10 m, centered at (-3, -4).