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Nutka1998 [239]
3 years ago
8

The first term of an arithmetic sequence is -2. The eighth term of the sequence is 26. What is the common difference of the arit

hmetic sequence?
Mathematics
2 answers:
andreev551 [17]3 years ago
8 0

Answer:

d = 4

Step-by-step explanation:

The n th term of an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₁ = - 2 and a₈ = 26 , then

- 2 + 7d = 26 ( add 2 to both sides (

7d = 28 ( divide both sides by 7 )

d = 4

Dmitry_Shevchenko [17]3 years ago
7 0

Answer:

d = 4

Step-by-step explanation:

a₁ = -2

a₈ = aₙ = 26

n = 8

aₙ = a₁ + d(n-1)

d = aₙ - a₁ / (n-1)

d = 26 -(-2) / (8-1)

d = 26 + 2 / 7

d = 28 / 7

d = 4

-2

-2 + 4 = 2

2 + 4 = 6

6 + 4 = 10

10 + 4 = 14

14 + 4 = 18

18 + 4 = 22

22 + 4 = 26

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Step-by-step explanation:

the sum of the two interior angles equals that exterior angle

121+40=161

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3 years ago
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What is 0.464646... as a fraction
rewona [7]

This is what I get


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3 years ago
Crop researchers plant 15 plots with a new variety of corn. The yields in bushels per acre are: 138.0 139.1 113.0 132.5 140.7 10
son4ous [18]
There is a relationship between confidence interval and standard deviation:
\theta=\overline{x} \pm \frac{z\sigma}{\sqrt{n}}
Where \overline{x} is the mean, \sigma is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first: 
\sigma=\sqrt{\frac{\sum(x-\overline{x})^2}{n}
When we do all the calculations we find that:
\overline{x}=123.8\\ \sigma=11.84
Now we can find confidence intervals:
($90\%,z=1.645): \theta=123.8 \pm \frac{1.645\cdot 11.84}{\sqrt{15}}=123.8 \pm5.0\\($95\%,z=1.960): \theta=123.8 \pm \frac{1.960\cdot 11.84}{\sqrt{15}}=123.8 \pm 5.99\\ ($99\%,z=2.576): \theta=123.8 \pm \frac{2.576\cdot 11.84}{\sqrt{15}}=123.8 \pm 7.87\\
We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing
6 0
3 years ago
Write the equation with both x= 8 and x= -8 as solution
nlexa [21]

Answer:

y = x^2 - 64

Step-by-step explanation:

Hello!

We can use the factored form of a Quadratic to find an equation with 8 and -8 as our solution.

<h3>Factored Form: y = a(x - h)(x - k)</h3>

The value in each parenthesis should be 0. So 8 and -8 can be flipped and used for h and k.

  • y = a(x - h)(x - k)
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This will give roots 8 and -8 for x.

  • y = 1(x - 8)(x + 8)\\
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A possible equation is y = x^2 - 64.

5 0
1 year ago
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kotegsom [21]
5x+40 factors to 5(x+8). Notice how distributing the 5 back through to each term in the parenthesis gives
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Therefore, the factors are 5 and (x+8).
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We don't know the numeric value of (x+8) since we don't know the value of x, so we leave it as is. 
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