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Masja [62]
3 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]3 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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In ΔABC, ∠B measures 35° and the values of a and b are 19 and 11, respectively. Find the remaining measurements of the triangle,
Alexxx [7]

Answer:

(A)∠A = 82.2°,∠C = 62.8°, c = 17.1

Step-by-step explanation:

In Triangle ABC

∠B=35°

a=19

b=11

Using Law of SInes

\dfrac{a}{\sin A} =\dfrac{b}{\sin B} \\\dfrac{19}{\sin A} =\dfrac{11}{\sin 35^\circ} \\11*\sin A=19*\sin 35^\circ\\\sin A=(19*\sin 35^\circ) \div 11\\A= \arcsin [(19*\sin 35^\circ) \div 11]\\A=82.2^\circ

Now:

\angle A+\angle B+\angle C=180^\circ\\35^\circ+82.2^\circ+\angle C=180^\circ\\\angle C=180^\circ-[35^\circ+82.2^\circ]\\\angle C=62.8^\circ

Using Law of Sines

\dfrac{c}{\sin C} =\dfrac{a}{\sin A} \\\dfrac{c}{\sin 62.8^\circ} =\dfrac{19}{\sin 82.2^\circ}\\c=\dfrac{19}{\sin 82.2^\circ}*\sin 62.8^\circ\\\\c=17.1

Therefore:

∠A = 82.2°,∠C = 62.8°, c = 17.1

The correct option is A.

3 0
3 years ago
Assssssssssssssssssssssssssssssssss
uysha [10]

Answer:

15, 9, 3n

Step-by-step explanation:

Just multiply the number of red balls by 3 to get total number, and divide the total number by three to get the number of red balls

7 0
3 years ago
At your summer job with a research company, you must get a random sample of people from your town to answer a question about spe
frez [133]
1) local shopping mall

This is most relevant to spending habits. This would be where people would be spending money on a lot of different things and where their spending habits would show. It'd make the most sense to survey people there.

3 0
4 years ago
Read 2 more answers
Question 9 (3 points)
Mila [183]

From the dot plot, we have that 90.91% of the students have 5 or more vowels in their first and last  names.

---------------------

The dot plot states that:

  • 2 students have 4 vowels in their first and last name.
  • 3 students have 5 vowels.
  • 8 students have 6 vowels.
  • 9 students have 7 vowels.

Then:

  • Total of 2 + 3 + 8 + 9 = 22 students.
  • 3 + 8 + 9 = 20 have or more vowels.

p = \frac{20}{22} \times 100\% = 90.91\%

90.91% of the students have 5 or more vowels in their first and last  names.

A similar problem is given at brainly.com/question/14354536

5 0
3 years ago
Natalle is a softball coach. She has a pitching private lesson with Kasey. Kasey's mom pays Natalle $11 per hour plus a $6 tip.
kirill [66]
11t\text{ + 6 = 39}

where t is the number of hours worked by Natalle

Here, we want to write an equation that will represent the given scenario

Let the number of hours for which she earned the pay be t

From the question, she earns $11 per hour

So for t hours, the amount earned excluding the tip will be;

(11\times t)\text{ = \$11t}

Now, let us add the tip and equate to the total amount earned

We have this as;

11t\text{ + 6 = 39}

3 0
1 year ago
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