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Hatshy [7]
3 years ago
14

Complete the synthetic division problem below.

Mathematics
2 answers:
leva [86]3 years ago
8 0

Answer:

B

Step-by-step explanation:

This was originally a third degree polynomial:

2x^3+4x^2-4x+6, to be exact.

When you divide by -3, you are basically trying to determine if x + 3 is a zero of that third degree polynomial.  The quotient is always one degree lesser than the polynomial you started with, and if there is no remainder, then x + 3 is a zero of the polynomial and you could go on to factor the second degree polynoial completely to get all 3 solutions.  To perform the synthetic division, you always first bring down the number in the first position, in our case a 2.  Then multiply that 2 by -3 to get -6.

-3|  2   4   -4   6

          -6

    2    -2

So far this is what we have done.  Now we multiply the -3 by the -2 and put that up under the -4 and add:

-3|  2   4   -4   6

          -6   6

    2    -2   2

Now we multiply the -3 by the 2 to get -6 and put that up under the 6 and add:

-3|   2   4   -4   6

           -6    6  -6

      2    -2   2   0

That last row gives us the depressed polynomial, which as stated earlier here, is one degree less than what you started with:

2x^2-2x+2

kotegsom [21]3 years ago
6 0

Answer: OPTION B

Step-by-step explanation:

You need to follow these steps:

- Carry the number 2 down and multiply it by the the number -3.

- Place the product obtained above the horizontal line, below the number 4 and add them.

- Put the sum below the horizontal line.

- Multiply this sum by the number -3.

- Place the product obtained above the horizontal line, below the number -4 and add them.

- Put the sum below the horizontal line.

- Multiply this sum by the number -3.

- Place the product obtained above the horizontal line, below the number 6 and add them.

Then:

-3\ |\ 2\ \ \ \ \ 4\ \ -4\ \ \ \ \ \ 6\\\.\ \ \ \ \ |\ \ \ \ -6\ \ \ \ \ 6\ \ \ -6

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

.\ \ \ \ \ \ 2\ \ \ -2\ \ \ \ 2\ \ \ \ \ 0

 Therefore, the quotient in polynomial form is:

2x^2-2x+2

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The average number of traffic tickets issued in a city on any given day
Anton [14]

Answer:

The most tickets were written on Saturday .On Saturday 325 tickets were issued

Step-by-step explanation:

The average number of traffic tickets issued in a city on any given day  Sunday-Saturday  can be approximated by

T(x) = -6x^2 + 84x + 37

Where  x represents the number of days after Sunday

T(x) represents the number of traffic tickets issued.

Sunday = x=0

Monday = x=1

Tuesday = x=2

Wednesday = x=3

Thursday = x =4

Friday = x=5

Saturday = x=6

Substitute  x= 0

T(x) = -6x^2 + 84x + 37\\T(x) = -6(0)^2 + 84(0) + 37\\T(x)=37

On Sunday 37 tickets were issued

Substitute  x= 1

T(x) = -6x^2 + 84x + 37\\T(x) = -6(1)^2 + 84(1) + 37\\T(x)=115

On Monday 115 tickets were issued

Substitute  x= 2

T(x) = -6x^2 + 84x + 37\\T(x) = -6(2)^2 + 84(2) + 37\\T(x)=181

On Tuesday 181 tickets were issued

Substitute  x= 3

T(x) = -6x^2 + 84x + 37\\T(x) = -6(3)^2 + 84(3) + 37\\T(x)=235

On Wednesday 235 tickets were issued

Substitute  x= 4

T(x) = -6x^2 + 84x + 37\\T(x) = -6(4)^2 + 84(4) + 37\\T(x)=277

On Thursday 277 tickets were issued

Substitute  x= 5

T(x) = -6x^2 + 84x + 37\\T(x) = -6(5)^2 + 84(5) + 37\\T(x)=307

On Friday 307 tickets were issued

Substitute  x= 6

T(x) = -6x^2 + 84x + 37\\T(x) = -6(6)^2 + 84(6) + 37\\T(x)=325

On Saturday 325 tickets were issued

Hence the most tickets were written on Saturday .On Saturday 325 tickets were issued

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3 years ago
Explain how to determine if the number is a solution to the equation. n + 6 = 33 for n = 27
stepan [7]
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8 0
3 years ago
Read 2 more answers
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The first one is distributive property.
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If f(x) = -(1/x^3) and x takes on successive values from -10 to 0.1 ,
prohojiy [21]
Alright, this one is a little interesting... Let's perform some tests to figure out what is happening:
f(-10) = -(1/(-10)^3) = -(1/-1000) = 1/1000  (positive)
f(-5) = -(1/(-5)^3) = -(1/-125) = 1/125 (positive, bigger than the last one)
f(-1) = -(1/(-1)^3) = -(1/-1) = 1 (positive, bigger than the last one)
f(-0.1) = -(1/(-0.1)^3) = -(1/-0.001) = 1/0.001 = 1000 (positive, bigger than the last one)
f(0) = -(1/0^3) = undefined!
f(0.1) = -(1/(0.1)^3) = -(1/0.001) = -1/0.001 = -1000 (negative)
f(1) = -(1/1^3) = -(1/1) = -1 (negative, but bigger than last one)

It's a little confusing with the undefined part at x = 0. What I can say is this, it is increasing from -10 up to 0, something weird happens at 0 and it resets, and starts increasing from 0 up to 0.1. 

I guess A would be the best answer?

3 0
3 years ago
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