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3 years ago

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Point AAA is at {(-6,-5)}(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and point CCC is at {(4,0)}(4,0)l

eft parenthesis, 4, comma, 0, right parenthesis. Find the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that the ratio of ABABA, B to BCBCB, C is 2:32:32, colon, 3.

2 answers:

mario62 [17]3 years ago

4 0

Answer:

(3,0)

Step-by-step explanation:

above.

lozanna [386]3 years ago

3 0

Answer:

B(-2,-3).

Step-by-step explanation:

The given points are A(-6,-5) and C(4,0).

We need to find the coordinates of point B on segment AC such that AB:BC=2:3.

It means point B divides the line segment AC in the ratio of 2:3.

Section formula: If a point divide a line segment in m:n, then

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Using section formula, the coordinates of point B are

$B=\left(\dfrac{2(4)+3(-6)}{2+3},\dfrac{2(0)+3(-5)}{2+3}\right)$

$B=\left(\dfrac{8-18}{5},\dfrac{0-15}{5}\right)$

$B=\left(\dfrac{-10}{5},\dfrac{-15}{5}\right)$

$B=\left(-2,-3\right)$

Therefore, the coordinates of point B are (-2,-3).

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Aleksandr [31]

Answer:

$y=3.529 x +37.91$

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

$y(8) = 3.529*8 + 37.91= 66.142$

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

$y(11) = 3.529*11 + 37.91= 76.729$

Step-by-step explanation:

For this case we have the following data:

Miles Traveled x: 2,3,10,7,8,15,3,1,11

Sales y :31,33,78,62,65,61,48,55,120

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:

$\sum_{i=1}^n x_i =60$

$\sum_{i=1}^n y_i =553$

$\sum_{i=1}^n x^2_i =582$

$\sum_{i=1}^n y^2_i =39653$

$\sum_{i=1}^n x_i y_i =4329$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=582-\frac{60^2}{9}=182$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=4329-\frac{60*553}{9}=642.33$

And the slope would be:

$m=\frac{642.33}{182}=3.529$

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

$\bar x= \frac{\sum x_i}{n}=\frac{60}{9}=6.67$

$\bar y= \frac{\sum y_i}{n}=\frac{553}{9}=61.44$

And we can find the intercept using this:

$b=\bar y -m \bar x=61.44-(3.529*6.67)=37.91$

So the line would be given by:

$y=3.529 x +37.91$

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

$y(8) = 3.529*8 + 37.91= 66.142$

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

$y(11) = 3.529*11 + 37.91= 76.729$

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