Part B

Find the sum of the squares of the roots of 3x^2 + 4x + 12 = 0

Contact [7]

Answer:

-56/9

Step-by-step explanation:

Let p and q be the roots of the equation.

So, here's how we're gonna work it out:

${p}^{2} + {q}^{2} = \\ {p}^{2} + {q}^{2} +2 pq - 2pq = \\ ( {p}^{2} +2pq + {q}^{2}) - 2pq = \\ {(p + q)}^{2} - 2pq$

Vieta's formulas give us the sum and the product of the roots of a quadratic equation. Using them we obtain:

p + q = -b / a = - 4 / 3
p × q = c / a = 12 / 3 = 4

${(p + q)}^{2} - 2pq = \\ {( - \frac{ 4}{3} )}^{2} - 2 \times 4 = \frac{16}{9 } - 8 = \\ \frac{16 - 72}{9} = - \frac{56}{9}$

4 0

3 years ago

What is -3(-6+8)^3-2(1-3)^3

marin [14]

Assignment: $\bold{Solve \ Equation: \ -3\left(-6+8\right)^3-2\left(1-3\right)^3}$

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Answer: $\boxed{\bold{-8}}$

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Explanation: $\downarrow\downarrow\downarrow$

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[ Step One ] Follow PEMDAS Order Of Operations; Calculate Within Parenthesis

Note: $\bold{PEMDAS: \ Parenthesis, \ Exponents, \ Multiply, \ Divide, \ Add, \ Subtract}$

$\bold{-6+8: \ 2}$

[ Step Two ] Rewrite Equation

$\bold{-3\cdot \:2^3-2\left(1-3\right)^3}$

[ Step Three ] Calculate Within Parenthesis

$\bold{1-3: \ -2}$

[ Step Four ] Rewrite Equation

$\bold{-3\cdot \:2^3-2\left(-2\right)^3}$

[ Step Five ] Calculate Exponents

$\bold{2^3: \ 8}$

[ Step Six ] Rewrite Equation

$\bold{-3\cdot \:8-2\left(-8\right)}$

[ Step Seven ] Multiply

$\bold{2\left(-8\right): \ -16}$

[ Step Eight ] Rewrite Equation

$\bold{-24-\left(-16\right)}$

[ Step Nine ] Subtract

$\bold{-24-\left(-16\right): \ -8}$

[ Step Ten ] Rewrite Equation

$\bold{-8}$

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$\bold{\rightarrow Mordancy \leftarrow}$

8 0

3 years ago

The number of motor vehicles registered in millions in the US has grown as follows:

zysi [14]

Answer:

a) Figure attached

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

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.819)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

Step-by-step explanation:

Previous concepts

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.

Solution to the problem

Part a

Year (x): 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985

Vehicles (Y): 32.4, 31.0, 49.2, 62.7, 73.9, 90.4, 108.4, 132.9, 155.8, 171.7

After apply natural log for the two variables and create the scatterplot in excel we got the following result on the figure attached.

Part b

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

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

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.81948)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

4 0

3 years ago

Maggie needs to spend at least six hours each week practicing the piano. She has already practiced 3

grandymaker [24]

Answer:

t ≥ 1.5

Step-by-step explanation:

Lets take time for practicing the piano to be t

The number of hours to practice per week should be at least 6 hours

This is written as t ≥ 6

She already practiced 3 hours this week, thus the remaining hours to practice should be

t ≥ 3

The minimum remaining hours to practice for the remaining 2 days should be

t=3

If these hours are evenly divided, then in a single day she should practice

for t ≥ 1.5

8 0

3 years ago

How do I solve for X Y Z

Verizon [17]

Answer:

(4,1,3)

Step-by-step explanation:

3 0

3 years ago