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umka21 [38]
3 years ago
7

What is the complete factorization of the polynomial below? X3-4x^2+x-4

Mathematics
1 answer:
OLga [1]3 years ago
3 0

Answer:  (x - 4)(x - (i))(x + (i))

Step-by-step explanation:

This factoring job lends itself well to synthetic division.  Looking at the constant term, -4, I came up with several possible roots based upon -4:  {±1, ±2, ±4}.  I chose +4 as my first trial root.  Sure enough, there was a zero remainder, which indicated that 4 is a root of this polynomial and (x - 4) is a factor.  The coefficients of the trinomial quotients are 1   0   1, which indicates a quotient of x^2 + 1, which has the following roots:  x = +(i) and x = -(i)

So the complete factorization of the polynomial is (x - 4)(x - (i))(x + (i)).

4   )   1    -4    1    -4

    ----------------------

Answer:

      1

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A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 419 gram setting. It is
Dahasolnce [82]

Answer:

The calculated t- value = 1.09 > 3.19 at 0.025 level of significance

Null hypothesis is rejected

There is sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

Given the mean of the Population(μ)  = 419 grams

The sample size 'n' =19

Given mean of the sample x⁻ = 412

Given variance of the sample S² = 784

                                                 S = √784 = 28

<u><em>Step(ii)</em></u>:-

<u><em>Null hypothesis: H₀</em></u>: There is no sufficient evidence to support the claim that the bags are underfilled.

<u><em>Alternative hypothesis: H₁:</em></u>

There is sufficient evidence to support the claim that the bags are underfilled.

Test statistic

                     t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }

                    t = \frac{412 -419}{\frac{28}{\sqrt{19} } }

                   t = -1.09

                 |t| = |-1.09|

<em>Degrees of freedom   ν = n-1 = 19-1 =18</em>

<em>t₀.₀₂₅ =  3.19</em>

<u><em>Final answer:</em></u><em>-</em>

The calculated t- value = 1.09 > 3.19 at 0.025 level of significance

Null hypothesis is rejected

There is sufficient evidence to support the claim that the bags are underfilled

                   

8 0
3 years ago
<img src="https://tex.z-dn.net/?f=%284%20%2B%206i%29%20%7B%7D%5E%7B2%7D%20" id="TexFormula1" title="(4 + 6i) {}^{2} " alt="(4 +
34kurt

Answer:

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Step-by-step explanation:

(4+6i)^{2} is essentially (4+6i)(4+6i) (you are squaring (4+6i), so multiplying it by itself), so to simplify, you would need to distribute.

A good way to go about this is using the F.O.I.L. method, multiplying the First numbers in the parentheses, then the Outers, then Inners, and finally, Lasts.

(4+6i)(4+6i) >> (4+6i)(4+6i) >> (4+6i)(4+6i) >> (4+6i)(4+6i)

((4*4)+(4*6i)+(6i*4)(6i*6i))

After doing so, you would end up with 16+24i+24i+36i^{2}, and after combining like terms, 16+48i+36i^{2}.

To write the expression in standard form, though, just order the terms from highest to lowest power!

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