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Masja [62]
2 years ago
7

The sum of three consecutive terms of an arithmetic sequence is 27, and the sum of their squares is 293. What is the absolute di

fference between the greatest and the least of these three numbers in the arithmetic sequence?
The answer is 10 but I don’t know how to get it
Mathematics
1 answer:
Ber [7]2 years ago
7 0

The absolute difference between the greatest and the least of these three numbers in the arithmetic sequence is 10.

The sequence is an arithmetic sequence. Therefore,

d = common difference

let

a = centre term

Therefore, the 3 consecutive term will be as follows

a - d,  a, a + d

a - d +  a + a + d = 27

3a = 27

a = 27 / 3

a = 9

Therefore,

(a-d)² + (a)² + (a + d)² = 293

(a²-2ad+d²) + 9² + (a² + 2ad + d²) = 293

(81 - 18d + d²) + 81 + (81 + 18d + d²) = 293

243 + 2d² = 293

2d² = 50

d² = 50 / 2

d = √25

d = 5

common difference = 5

Therefore, the 3 numbers are as follows

9 - 5 , 9, 9 + 5 = 4, 9, 14

The difference between the greatest and the least of these 3 numbers are as follows:

14 - 4 = 10

learn more on Arithmetic progression: brainly.com/question/25749583?referrer=searchResults

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4 fiction to 1 nonfiction
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Whats is the answer to 5/8 -1/10
LuckyWell [14K]

Answer:

Hello, Your answer will be 45

Step-by-step explanation:

5+8=5*+%=45 <em>Hope This Helps!</em>

5 0
3 years ago
Factor completely 4xy − 7x 20y − 35. (x 5)(4y − 7) (x − 5)(4y 7) (x − 5)(4y − 7) (x 5)(4y 7).
yuradex [85]

Answer:

A)

Step-by-step explanation:

Given expression:

To factor the given expression completely.

Solution:

In order to factor the expression, we will factor in pairs.

We will factor the G.C.F of the terms in the pairs.

G.C.F. of  and  can be given as:

Thus, G.C.F. =

G.C.F. of  and  can be given as:

Thus, G.C.F. =

The expression after factoring the G.C.F. pairs is given as:

Taking G.C.F. of the whole expression as  is a common term.

The expression is completely factored.

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
PLEASE HELP: The mass of a ball is 128 g. It has a density of 0.5 g/cm³. What is the volume of the ball? Show your work and plac
tiny-mole [99]

Answer:

Part 1) The volume of the ball is 256 cm³

Part 2) The radius of the ball is 3.94 cm

Step-by-step explanation:

Part 1) we know that

The density is equal to divide the mass by the volume

D=m/V

Solve for the volume

The volume is equal to divide the mass by the density

V=m/D

In this problem we have

m=128 g

D=0.5 g/cm³

substitute

V=128/0.5=256 cm³

Part 2) what is the radius of the ball?

we know that

The volume of the sphere (ball) is equal to

V=\frac{4}{3}\pi r^{3}

we have

V=256\ cm^{3}

assume

\pi =3.14

substitute and solve for r

256=\frac{4}{3}(3.14)r^{3}

768=(12.56)r^{3}

r^{3}=768/(12.56)

r=3.94\ cm

7 0
3 years ago
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