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ella [17]
1 year ago
9

the data in the table below represents a linear relationship . what is the missing piece of data table and answer choices will b

e in chatA) -6 B) -2 C) 2 D) 6

Mathematics
1 answer:
Gennadij [26K]1 year ago
3 0

C) 2

1) Given the table, let's find out that missing data picking 2 points (2,-10) and (6,-4)

Since we have the slope, let's work on finding the linear coefficient

plugging point (2,-10) into that:

y= mx +b

-10 =3/2(2) +b

-10 =6/2 +b

-10= 3 +b

-10-3 =b

b= -13

2) So the rule of that function is y= 3/2x -13

Plugging x= 10 we have

y= 3/2(10) -13

y=2

3) So the missing y-coordinate is 2.

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The question here asks us to find all the roots, or solutions, of the quartic equation x⁴ - 4x³ + x² + 12x - 12 = 0. We can start off by using the Rational Root Theorem, which calls for the constant over the leading coefficient, which for us would be 12 over 1. Since we need to list all the factors of 12, they all become + or -. 
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We can now factor the whole original equation to (x - 2)(x³ - 2x² -3x + 6) = 0. Now, we have to factor the expression x³ - 2x² -3x + 6, and grouping seems like the most appropriate way.
x³ - 2x² -3x + 6 = 0
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Next, use the Zero Product Property to get the values of x.
x² - 3 = 0
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Therefore, the roots of the equation x⁴ - 4x³ + x² + 12x - 12 = 0 are x = 2,x = 2 (repeated solution), x = 1.73, x = -1.73. Hope this helped and have a great day!

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