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Bond [772]
2 years ago
9

Which gives the line of best fit?

Mathematics
1 answer:
BartSMP [9]2 years ago
7 0

Answer:

B

Step-by-step explanation:

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Apply The Remainder Theorem, Fundamental Theorem, Rational Root Theorem, Descartes Rule, and Factor Theorem to find the remainde
Over [174]

9514 1404 393

Answer:

  possible rational roots: ±{1/3, 2/3, 1, 4/3, 2, 3, 4, 6, 12}

  actual roots: -1, (2 ±4i√2)/3

  no turning points; no local extrema

  end behavior is same-sign as x-value end-behavior

Step-by-step explanation:

The Fundamental Theorem tells us this 3rd-degree polynomial will have 3 roots.

The Rational Root Theorem tells us any rational roots will be of the form ...

  ±{factor of 12}/{factor of 3} = ±{1, 2, 3, 4, 6, 12}/{1, 3}

  = ±{1/3, 2/3, 1, 4/3, 2, 3, 4, 6, 12} . . . possible rational roots

Descartes' Rule of Signs tells us the two sign changes mean there will be 0 or 2 positive real roots. Changing signs on the odd-degree terms makes the sign-change count go to 1, so we know there is one negative real root.

The y-intercept is 12. The sum of all coefficients is 22, so f(1) > f(0) and there are no positive real roots in the interval [0, 1]. Synthetic division by x-1 shows the remainder is 22 (which we knew) and all the quotient coefficients are all positive. This means x=0 is an upper bound on the real roots.

The sum of odd-degree coefficients is 3+8=11, equal to the sum of even-degree coefficients, -1+12=11. This means that -1 is a real root. Synthetic division by x+1 shows the remainder is zero (which we knew) and the quotient coefficients alternate signs. This means x=-1 is a lower bound on real roots. The quotient of 3x^2 -4x +12 is a quadratic factor of f(x):

  f(x) = (x +1)(3x^2 -4x +12)

The complex roots of the quadratic can be found using the quadratic formula:

  x = (-(-4) ±√((-4)^2 -4(3)(12)))/(2(3)) = (4 ± √-128)/6

  x = (2 ± 4i√2)/3 . . . . complex roots

__

The graph in the third attachment (red) shows there are no turning points, hence no relative extrema. The end behavior, as for any odd-degree polynomial with a positive leading coefficient, is down to the left and up to the right.

4 0
2 years ago
Which polynomial is represented by the algebra tiles? 2x2 – 4x – 6 2x2 4x 6 –2x2 – 4x – 6 –2x2 4x 6.
natta225 [31]

Polynomials consist of both indeterminates and coefficients. The polynomial that is been represented by the algebra tiles is 2x²-4x -6.

<h3>What are polynomials?</h3>

A polynomial consists of both indeterminates and coefficients and involves mathematical operations such as addition, subtraction, multiplication, and division.

In order to find the polynomial that is been represented by the tiles, we will simply, calculate the number of tiles for each variable,

As we can see in the image,

Number of tiles labeled as x² = 2

Number of tiles labeled as -x = 4

Number of tiles labeled '-' = 6

therefore, the polynomial can be written as 2x²-4x -6.

Hence, the polynomial that is been represented by the algebra tiles is 2x²-4x -6.

Learn more about Polynomials:

brainly.com/question/17822016

4 0
2 years ago
With an interest rate of 3.25% over 4 years, how much money was originally deposited if
padilas [110]
Interest = Principle(Rate)(Time)
$84.50 = P(0.0325)(4)
$84.50 = P(0.13)
$84.50/0.13 = P
P = 650

$650 was originally deposited.
6 0
3 years ago
Read 2 more answers
12 - (-3) =<br> what does it equal
erik [133]

Answer:15

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Please help . I don't know fractions really well. please and thanks
Lerok [7]
I can help you with #20. For example, lets say 3/5, this fraction would be made up of 5 parts and 3 are covered, which doesn't make it full, if it was 5/5 it would be full. When you do something with a reciprocal you turn it over, so 3/5 would be turned over to 5/3, thus making it a whole number
3 0
3 years ago
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