Answer:
Step-by-step explanation:
Given:
Fifth term of a geometric sequence = 
Common ratio (r) = ¼
Required:
Formula for the nth term of the geometric sequence
Solution:
Step 1: find the first term of the sequence
Formula for nth term of a geometric sequence = 
, where:
a = first term
r = common ratio = ¼
Thus, we are given the 5th term to be ¹/16, so n here = 5.
Input all these values into the formula to find a, the first term.
Cross multiply
Divide both sides by 16
Step 2: input the value of a and r to find the nth term formula of the sequence
nth term =
nth term = 
Answer:
27 degrees withI think angle sum postulate
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k )² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 8x + 8y + 23 = 0
collect the x and y terms together and subtract 23 from both sides
x² - 8x + y² + 8y = - 23
using the method of completing the square
add ( half the coefficient of the x / y terms )² to both sides
x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16
(x - 4)² + (y + 4)² = 9 ← in standard form
with centre = (4, - 4 ) and r = 
= 3
this is shown in graph b
3/16 as a decimal is 0.18
and 5/48 as a decimal is 0.10
SO
you have 0.10, 0.18, 0.75, and 0.5 so put that in order
<h3>
Answers:</h3>
angle FHG = 42 degrees
angle GHI = 100 degrees
=========================================================
Explanation:
FHI is the largest angle. It is split into two pieces FHG and GHI which have measures of (3x+6) and (9x-8) degrees respectively.
Put another way, those two smaller angles (FHG and GHI) combine to form the larger angle (FHI)
This is the angle addition postulate.
------------------
(angle FHG) + (angle GHI) = angle FHI
(3x+6) + (9x-8) = 142
3x+6+9x-8 = 142
(3x+9x) + (6-8) = 142
12x - 2 = 142
12x-2+2 = 142+2 ... adding 2 to both sides
12x = 144
12x/12 = 144/12 .... dividing both sides by 12
x = 12
------------------
Use that x value to find the angles we're after
angle FHG = 3x+6 = 3*12+6 = 36+6 = 42
angle GHI = 9x-8 = 9*12-8 = 108-8 = 100
Note how
(angle FHG) + (angle GHI) = 42 + 100 = 142
which is the measure of angle FHI. This confirms the answers.
