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2 years ago

Determine whether the three points are collinear. (0, - 10). (-3,- 13), (2,-8)

Mathematics

1 answer:

LUCKY_DIMON [66]2 years ago

5 0

Answer:

<h2>YES. These points are collinear.</h2>

Step-by-step explanation:

If three points are collinear, then the slopes are the same.

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

For (0, -10) and (-3, -13):

$m=\dfrac{-13-(-10)}{-3-0}=\dfrac{-13+10}{-3}=\dfrac{-3}{-3}=1$

For (-3, -13) and (2, -8):

$m=\dfrac{-8-(-13)}{2-(-3)}=\dfrac{-8+13}{2+3}=\dfrac{5}{5}=1$

We can check the last pair (0, -10) and (2, -8):

$m=\dfrac{-8-(-10)}{2-0}=\dfrac{-8+10}{2}=\dfrac{2}{2}=1$

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Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, -5). Write the equati

amid [387]

In this we know all three zeros and one point from which the graph pass.
So we will let specific cubic polynomial function of the form
$f(x) = a(x - x_1)(x-x_2)(x-x_3)$

As we know zeros are that point where we will get value of function equal to zero. So it is basically in form $(x_n , 0)$

SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say $x_1 = 2 , x_2 = 3 , x_3 = 5$

So required equation is
$f(x) = a (x-2)(x-3)(x-5)$
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              $= a(x^3 - 5x^2 + 6x- 5x^2 + 25x - 30)$
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Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
$-5= a (0-0+0 - 30)$
$-5 = -30a$
$a = \frac{-5}{-30} = \frac{1}{6}$
So required equation of cubic polynomial is
$f(x) = \frac{1}{6}(x^3 -10x^2+31x-30)$

For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.

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Read 2 more answers

Are these answers right Or wrong

uysha [10]

They are right except for 12. i think it is C but i could be wrong.

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topjm [15]

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lara [203]

Yes you have a good example.

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-------------

a more numeric example may be this

Lets say you bought 12 cookies, so x = 12

This means it costs 2*x = 2*12 = 24 dollars total if the discount doesnt apply

However, the 3 dollar discount is there, so the grand total is 24-3 = 21 dollars.

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