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cupoosta [38]
4 years ago
8

Simplify completely the quantity x squared plus x minus 12 over quantity x squared minus x minus 20 divided by the quantity 3 x

squared minus 24 x plus 45 over quantity 12 x squared minus 48 x minus 60.
Mathematics
1 answer:
posledela4 years ago
4 0
X² + x - 12 / x² - x - 20  ÷ 3x² - 24x + 45 / 12x² - 48x - 60

x² + x - 12 / x² - x - 20 * 12x² - 48x - 60 / 3x² - 24x + 45

<u>(x² + x - 12)(12x² - 48x - 60)</u>
(x² - x - 20)(3x² - 24x + 45)

<span><u>12x^4 - 48x³ - 60x² + 12x³ - 48x² - 60x - 144x² + 576x + 720</u>
</span>3x^4 - 24x³ + 45x² - 3x³ + 24x² - 45x - 60x² + 480x - 900
<span>
<u>12x^4 - 48x³ + 12x³ - 60x² - 48x² - 144x² - 60x + 576x + 720</u></span>
3x^4 - 24x³ - 3x³ + 45x² + 24x² - 60x² - 45x + 480x - 900

<u>12x^4 - 36x³ - 252x² + 516x + 720</u>
3x^4 - 27x³ + 9x² + 435x - 900

<u>12(x^4 - 3x³ - 21x² + 43x + 60)  </u>
  3(x^4 - 9x³ + 3x² + 145x + 300)

<u>4(</u><span><u>x^4 - 3x³ - 21x² + 43x + 60)  </u>
</span><span>  (x^4 - 9x³ + 3x² + 145x + 300)</span>
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It’s 60 feet away from the cliff because it has a height of 70 feet tall
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What is the equation of the line of best fit for the following data? Round the
Svet_ta [14]

Answer:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=438-\frac{44^2}{5}=50.8

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=415-\frac{44*42}{5}=45.4

And the slope would be:

m=\frac{45.4}{50.8}=0.8937 \approx 0.894

Now we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{44}{5}=8.8

\bar y= \frac{\sum y_i}{n}=\frac{42}{5}=8.4

And we can find the intercept using this:

b=\bar y -m \bar x=8.4-(0.894*8.8)=0.535

So the line would be given by:

y=0.894 x +0.535

And the best option is:

A. y = 0.894x + 0.535

Step-by-step explanation:

We have the following dataset given

x: 5,6,9,10,14

y: 4,6,9,11,12

We want to find the least-squares line appropriate for this data given by this general expresion:

y = mx +b

Where m is the slope and b the intercept

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i = 44

\sum_{i=1}^n y_i =42

\sum_{i=1}^n x^2_i =438

\sum_{i=1}^n y^2_i =398

\sum_{i=1}^n x_i y_i =415

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=438-\frac{44^2}{5}=50.8

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=415-\frac{44*42}{5}=45.4

And the slope would be:

m=\frac{45.4}{50.8}=0.8937 \approx 0.894

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{44}{5}=8.8

\bar y= \frac{\sum y_i}{n}=\frac{42}{5}=8.4

And we can find the intercept using this:

b=\bar y -m \bar x=8.4-(0.894*8.8)=0.535

So the line would be given by:

y=0.894 x +0.535

And the best option is:

A. y = 0.894x + 0.535

4 0
4 years ago
Which are the solutions of x2 = –5x + 8? SOLUTIONs ok not a single answer i need to know its opposite
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Answer:

I think it is -5+root-7/2 & -5-root-7/2

Step-by-step explanation:


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Answer:

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Step-by-step explanation:

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The length is 1.7 m

The width is .8 m

A = 1.7 x .8

A = 1.36

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3 years ago
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