Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric progression is
• 
= a₁ 
where a₁ is the first term and r the common ratio
given a₄ = 24, then
a₁
= 24 → (1)
Given a₈ = 
, then
a₁
= → (2)
Divide (2) by (1)
= 
= 
Hence r = ![\sqrt[4]{\frac{1}{81} }](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cfrac%7B1%7D%7B81%7D%20%7D)
= 
Substitute this value into (1)
a₁ × ( )³ = 24
a₁ × 
= 24, hence
a₁ = 24 × 27 = 648
Answer:
Step-by-step explanation:
By the triangle sum theorem, the sum of angles in a triangle is equal to 180°. Therefore, m∠A + m∠B + m∠C = 180°. Using the Substitution property
(6x)° + 90° + (x+6)° = 180°
To solve for x, first combine the terms to get (7x + 96) = 180°
Using the Subtraction property of equality,
7x = 84.
Then using the division property of equality x = 12.
To find the measure of angle A,
Use the subtraction property to get m∠A = 6(12)°.
Finally simplifying the expression gets m∠A = 72°.
a) ABD and CBD are Supplementary angles and need to equal 180 degrees
Subtract 117 from 180 for CBD:
CBD = 180 - 117 = 63 degrees
b) In triangles the the shortest side would be opposite the shortest angle.
Since angle D is 56 degrees ( the smallest inside angle) then side BC would be the shortest side.
c) The side opposite the largest angle would be the longest.
Angle B is 63 degrees ( the largest) so side CD is the longest.
Answer:
DM should equal 20 inches
