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Andrews [41]
3 years ago
12

Find the sum of the infinite geometric series -27, -9, -3, … The ratio is /3 and u1 is -27

Mathematics
1 answer:
Strike441 [17]3 years ago
8 0
<h3>Answer: C) -81/2</h3>

===================================================

Work Shown:

a = -27 = first term

r = 1/3 = common ratio, note how this is between -1 and 1

We start with -27 and multiply by 1/3 each time to get the next term

S = infinite sum

S = a/(1-r), which only works because -1 < r < 1 is true

S = -27/(1-1/3)

S = -27/(2/3)

S = (-27/1) divided by (2/3)

S = (-27/1) times (3/2)

S = (-27*3)/(1*2)

S = -81/2

As you generate and add up the terms of the sequence, the infinite sum slowly starts to approach -81/2 = -40.5; we'll never actually achieve this sum exactly. Think of it as approaching an asymptote.

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In the diagram of PARALLELOGRAM ABCD, segment BE is perpendicular to segment CED, segment DF is perpendicular to BFC and segment
tiny-mole [99]

Answer:

In parallelogram ABCD

FD is perpendicular to BC

BE is perpendicular to CD

Consider triangle BEC and triangle DFC

FC = EC (Given)

Angle BEC = Angle DFC (=90°)

Angle BCE = Angle DCF (common)

Therefore triangle BEC is congruent to triangle DFC (AAS congruency)

DF = BE (CPCT)

Since the altitudes are equal their bases will also be equal

Therefore BC = DC

Therefore BC = DC = AD = AB

Therefore ABCD is a rhombus

Hope this helps!

Mark me as brainliest

3 0
3 years ago
A library is open til' 5:00 P.M. On Wednesdays, the library closes 2 hours early. How many hours for a month is the library open
svet-max [94.6K]
So
if you assume that the month has 30 days and that the library opens at midnight, then
24 hours in a day
5 pm=12+5=17 hours
on wednessday=17-2=15 hours
wednessday=1/7 of week
so we find 1/7 of 30 which is 30/7=4 and 2/7
then subtract that from 30
30-4 and 2/7=25 and 5/7

ok so then we have
25 and 5/7 days is 17 hours and
4 and 2/7 days is 15 hours
so just multipy them and add

25 and 5/7 times 17=437.143 hours
4 and 2/7 days times 15 =64.2857
add

437.143+64.2856=501.429
so aprox 501.429

the real equation is  [(\frac{1}{7})(n)(15)]+[ (\frac{6}{7}) (n)(17)]=hours where n represents the number of days in the month

apros 501.429
8 0
3 years ago
If Susan earn 1,800 per month and her rent is 504 per month, what percent of her income is spent on rent?
svetoff [14.1K]
504÷1800=0.28
28% of her income goes to her rent
4 0
3 years ago
16 square meters is equivalent o how many square yards
Marat540 [252]

Answer: 19.13 yd²

Step-by-step explanation:

1. By definition,  you have that 1 square meter is equal to 1.19599 square yards. You can express it as following:

1 m²= 1.19599 yd²

2. Then, keeping the information above on mind, you can make the conversion from 16 m² to yd² as it is shown below:

(16m^2)(\frac{1.19599yd^2}{1m^2})=19.13yd^2

Therefore, you have that 16 m² is equivalent to 19.13 yd².

6 0
3 years ago
Solve for x by completing the square: x2 - 12x + 11 = 0
sineoko [7]

Answer:

B

Step-by-step explanation:

x² - 12x + 11 = 0 ( subtract 11 from both sides )

x² - 12x = - 11

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 6)x + 36 = - 11 + 36

(x - 6)² = 25 ( take square root of both sides )

x - 6 = ± \sqrt{25} = ± 5 ( add 6 to both sides )

x = 6 ± 5

Then

x = 6 - 5 = 1 ⇒ (1, 0 )

x = 6 + 5 = 11 ⇒ (11, 0 )

6 0
2 years ago
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