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aliya0001 [1]
3 years ago
15

The sum of the first n terms of an arithmetic sequence is n/2(4n + 20).

Mathematics
1 answer:
lesantik [10]3 years ago
8 0

Answer:

(a).

S_{n} =  \frac{n}{2} (4n + 20) \\  \\S _{n - 1} =  \frac{(n - 1)}{2} (4n - 4 + 20) \\  \\ S _{n - 1} =  \frac{(n - 1)}{2} (4n + 16) \\  \\S _{n - 1} = \frac{(n - 1)(4n + 16)}{2}  \\   \\  { \boxed{S _{n - 1} =  {2 {n}^{2} + 6n - 8}}} \\

(b).

from general equation:

S _{n - 1} =  \frac{(n - 1)}{2} (4n + 16)

first term is 4n

common difference:

16 =  \{(n - 1) - 1 \}d \\ 16 = (n - 2)d \\ d =  \frac{16}{n - 2}

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A cone with diameter 20 cm and a height of 20 cm. Find the volume of the cone rounded to the nearest tenth.
zhuklara [117]

Answer:

2094.4 cm³

Step-by-step explanation:

The volume of a cone =πr²h/3

Where

r = radius = Diameter/2

Diameter = 20cm, radius = 20cm/2 = 10cm

Height = 20cm

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Volume of a cone = 2094.3951 cm³

Approximately to the nearest tenth = 2094.4 cm³

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8 0
3 years ago
What would be the answer to x + 22 - 13x greater than or equal to 118
Fynjy0 [20]

Answer:.

x greater than or equal to -8

Step-by-step explanation:

x+22-13x≥118

Collect like terms

x-13x≥118-22

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The answer is x greater than or equal to -8

4 0
3 years ago
Read 2 more answers
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Nina [5.8K]

Answer:

(2x+1)(x+3)

2x(x+3)+1(x+3)

2x2+6x+x+3

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if you want you can also multiply 2x+3 by x+3

like this:

(2x+1)(x+3)

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2x2+x+6x+3

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They will both give you the same answer.

5 0
3 years ago
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Answer:Write 9/20 as a percent. Use equivalent fractions: 9/20 = 45/100 = 45%.

Step-by-step explanation:

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vlada-n [284]

Answer:

10 units

Step-by-step explanation:

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6^2 + 8^2 = d^2, where d is that distance:

36 + 64 = 100 = d^2, and so d = 10.  The distance in question is 10 units.

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3 years ago
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