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3 years ago

What is n^+8n+16 in factored form

Mathematics

1 answer:

maw [93]3 years ago

6 0

Answer:

factored form: (n + 4)²

Solving for n: n = -4

Step-by-step explanation:

n² + 8n + 16

To solve this, simplify. Note that the factors of n² & 16, when combined, must equal 8n. Find factors of 16:

Factors of 16:

1, 2, 4, 8, 16

Use the factor 4:

n² + 8n + 16

n 4

(n + 4)(n +4) = (n + 4)² is your factored form.

If you need to, solve for n. Take one of the parenthesis, and set it equal to 0:

(n + 4) = 0

Isolate the variable, n. Note the equal sign, what you do to one side, you do to the other. Subtract 4 from both sides:

n + 4 (-4) = 0 (-4)

n = 0 - 4

n = -4

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Answer:

a)Slope: $\hat \beta_1 =\frac{7625.9}{1248.9}=6.106$

Intercept: $\hat \beta_o = 157.955 -6.106 (69.686)=-267.548$

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And the determination coeffecient is $r^2 = 0.657^2 =0.432$

Step-by-step explanation:

Data given and definitions

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

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n=110, $\sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8$

$\sum Y_i =17375 , \sum X_i = 7665.5$

Part a

The slope is given by this formula:

$\hat \beta_1 =\frac{\sum (x-\bar x) (y-\bar y)}{\sum (x-\bar x )^2}$

If we replace we got:

$\hat \beta_1 =\frac{7625.9}{1248.9}=6.106$

We can find the intercept with the following formula

$\hat \beta_o = \bar y -\hat \beta_1 \bar x$

We can find the average for x and y like this:

$\bar X=7665.5/110 =69.686, \bar y= 17375/110=157.955$

And replacing we got:

$\hat \beta_o = 157.955 -6.106 (69.686)=-267.548$

Part b

In order to calculate the correlation coefficient we can use this formula:

$r=\frac{\sum (x-\bar x)(y-\bar y) }{\sqrt{[\sum (x-\bar x)^2][\sum(y-\bar y)^2]}}$

For our case we have this:

n=110, $\sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8$

So we can find the correlation coefficient replacing like this:

$r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657$

And the determination coeffecient is $r^2 = 0.657^2 =0.432$

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Answer:

in this problem we have

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Remember that

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convert to standard form

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therefore

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3 years ago

What is n^+8n+16 in factored form​

What is n^+8n+16 in factored form