ANSWER
EXPLANATION
Given the points P(2,-1) and Q(-9,-6),the coordinates of the point that partition the directed line segment PQ in the ratio 3:2 is given by
Where m=3 and n=2
The point is
Since the sequence is geometric, there is some constant
such that the sequence is recursively given by
By this definition, you can recursively substitute into the right hand side the definition for
to find an explicit formula for the
th term.
You know the second term, which means you can find
:
So, the 7th term of the sequence is
9x^2-16y^2=
(3x+4y)(3x-4y)
The regression equation which correctly models the data in this table is y = 1.49x - 107.5,
<h3>How to determine the regression equation?</h3>
From the table of data values, we have the following parameters:
∑x = 632
∑y = 404
∑x² = 80.142
∑xy = 51.448
Mathematically, the regression equation is represented by the following slope equation:
y = Bx + A
Next, we would determine A by using this expression:
A = (∑y·∑x² - ∑x·∑xy)/(n∑x² - (∑x)²)
A = (404×80,142 - 632×51,448)/(5×∑x² - (632)²)
A = (32,377,368 - 32,515136)/(5×80142 - 399,424)
A = -137,768/1286
A = 107.5
For B, we have:
B = (n∑xy· - ∑x·∑y)/(n∑x² - (∑x)²)
B = (5×51,448 - 632×404)/(5×∑x² - (632)²)
B = 1.49.
y = Bx + A
y = 1.49x - 107.5
Read more about regression equation here: brainly.com/question/28037520
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