Write the function in the form f(x) = (x − k)q(x) + r for the given value of k. F(x) = x3 − x2 − 18x + 19, k = 4 f(x) = Demonstrate that f(k) = r. F(4) =

Answers

Answer 1

Solution :

Given :

[tex]$f(x)=x^3-x^2-18x+19$[/tex]

By using the remainder theorem, if f(x) is divided by (x-k) and the remainder is 'r', then

[tex]$f(x)=(x-k)q(x)+r$[/tex]

Here, k = 4

Therefore, divide the f(x) with (x - 4) to find the q(x) and r.

           __________________

[tex]$x-4$[/tex]    |    [tex]$x^3-x^2-18x+19$[/tex]         |      [tex]$x^2+3x-6$[/tex]

            [tex]$x^3-4x^2$[/tex]

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

                    [tex]$3x^2-18x$[/tex]

                    [tex]$3x^2-12x$[/tex]

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

                          [tex]$-6x+19$[/tex]

                          [tex]$-6x+24$[/tex]

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

                                  [tex]$-5$[/tex]

Therefore,

q(x) =  [tex]$x^2+3x-6$[/tex]

  r = -5

[tex]$f(x)=(x-4)(x^2+3x-6)-5$[/tex]

[tex]$f(4)=(4-4)(4^2+3 \times 4-6)-5$[/tex]

       [tex]$=-5$[/tex]


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Just put the opposite coordinates on the other side of the segment and thats your answer!

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Step-by-step explanation:

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Answer

[tex] \sf{}b_{1} = - 72 \: \: \: or \: \: \: b_{2} = 72[/tex]

Explain

.

[tex] \sf{65}^{2} + {b}^{2} = {97}^{2} [/tex]

[tex] \sf{}4.225 + {b}^{2} = 9.409[/tex]

[tex] \sf {b}^{2} = 9.409 - 4.225[/tex]

[tex] \sf {b}^{2} = 5.184[/tex]

[tex] \sf{}b_{1.2} = ±\sqrt{5.184} [/tex]

[tex] \sf{}b_{1.2} = ±72[/tex]

[tex] \sf{}b_{1} = - 72 \: \: \: or \: \: \: b_{2} = 72[/tex]

.

.

#LearnWithBrainly

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Answer:

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Answers

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Answer:

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Answers

Answer:

a₇₅ = - 430

Step-by-step explanation:

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What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

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Given data ,

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Substituting the values in the equation , we get

T₇₅ = 88 + ( 75 - 1 ) ( -7 )

     = 88 + 74 ( -7 )

     = 88 - 518

     = -430

Therefore , the value of T₇₅  is  -430

Hence , The 75th term of the arithmetic progression is -430

To learn more about arithmetic progression click :

https://brainly.com/question/1522572

#SPJ2

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