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alexandr1967 [171]
3 years ago
5

Using synthetic division, what is the quotient (3x3 + 4x − 32) ÷ (x − 2)?

Mathematics
2 answers:
Wewaii [24]3 years ago
5 0
The question is set up in the following way:

2] 3   0   4   -32

_____________

Here the 2 is from when x-2 is set equal to zero and then solved for x, the rest is from the the number being divided with zero taking the place of the x^2.

Then the following happens:

2] 3   0   4   -32   
         6  12   32
______________
    3   6  16   0

Here the following happens: 
1. We drop down the first coefficient, which is 3
2. We take this coefficient and multiply it by the two in the corner and get 6.
3. We place this six under the second coefficient (0) and add them together and get 6.
4. We take this 6 and multiply it by the two in the corner and get 12.
5. We take this 12 and put it under the third coefficient (4), add them together and get 16.
6. We take the 16 and multiply it by the two in the corner and get 32.
7. We take the 32 and place in under the forth coefficient and get zero.

This gives us the coefficients of the final answer in the order 3, 6 and 16 with no remaninders which gives us 3x^2+6x+16.<span />
Thepotemich [5.8K]3 years ago
3 0

Answer:

The quotient of given division is 3x^2+6x+16.

Step-by-step explanation:

The given expression is

\frac{3x^3+4x-32}{x-2}

The dividend  is

3x^3+0x^2+4x-32

The coefficients of dividend are 3, 0, 4 and -32.

The divisor is (x-2).

If the divisor in the form of (x-c), then we multiply the coefficients and resultant number are multiplied by c. So, the coefficients and resultant number are multiplies by 2.

The steps of synthetic division are:

1. Write the coefficients and 2 in the top row.

2. Write the first coefficient as it is, in bottom row.

3. Multiply the coefficient by 2 and write it in middle row. Now, add them. Apply the same process again.

The bottom row represent the coefficient of quotient and remainder.

The coefficient of quotient are 3,6 and 16. The remainder is 0.

The quotient of given division is 3x^2+6x+16.

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3 years ago
Find the circumference of a circle with a radius of 35 inches in terms of 7 and to the nearest tenth of an inch.​
Lera25 [3.4K]

Answer and Step-by-step explanation:

The circumference formula for a circle is:

C = 2\pi r

Plug 35 in for r (radius) and solve.

C = (35) 2\pi\\\\C = 70\pi\\\\C = 219.9

So, approximately 219.9 in^2 is the answer.

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4 0
2 years ago
Can you give me the answer by 11 pm
otez555 [7]
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6 0
2 years ago
1) A family consisting of three persons—A, B, and C—goes to a medical clinic that always has a doctor at each of stations 1, 2,
crimeas [40]

Answer:

Step-by-step explanation:

Let us record the station number 1, 2 or 3 for each family member A, B or C.

I am attaching a table containing total outcomes. Outcomes are presented along rows while the assigned station to each member is written along columns. For ease of understanding, 1 3 2 in the table should be interpreted as family member A being assigned to station 1, member B to station 3 and member C to station number 2, respectively.

From table it is clear that the total outcomes possible are 27.

We know that, probability can be defined as,

PROBABITILY = \frac{NUMBER\;OF\;DESIRED\;OUTCOMES}{TOTAL\;NUMBER\;OF\;OUTCOMES}

a) All Members Assigned to the Same Station.

Cases for all members being assigned to same station are as follows:

[1 1 1], [2 2 2], [3 3 3] (outcome number 1, 14 and 27 in the table).

Therefore,

PROBABILITY\;(Case\;a) = \frac{3}{27}\\\\PROBABILITY\;(Case\;a) = 0.111

b) At Most Two Members Assigned to the Same Station.

It means that maximum of 2 members can have the same station. Cases for this situation are as follows:

[1 1 2], [1 1 3], [1 2 1], [1 2 2], [1 3 1], [1 3 3], [2 1 1], [2 1 2], [2 2 1], [2 2 3], [2 3 2],

[2 3 3], [3 1 1], [3 1 3], [3 2 2], [3 2 3], [3 3 1], [3 3 2]

(outcome number 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 17, 18, 19, 21, 23, 24, 25 and 26 in the table).

Therefore,

PROBABILITY\;(Case\;b) = \frac{18}{27}\\\\PROBABILITY\;(Case\;b) = 0.666

c) All Members Assigned to a Different Station.

For this scenario, we have the following results:

[1 2 3], [1 3 2], [2 1 3], [2 3 1], [3 1 2], [3 2 1] (outcome number 6, 8, 12, 16, 20 and 22 in the table).

Therefore,

PROBABILITY\;(Case\;c) = \frac{6}{27}\\\\PROBABILITY\;(Case\;c) = 0.222

3 0
3 years ago
Solve 12|x|−7=8. Does anyone know how to do this?<br>​
Travka [436]

Answer:

8+8=16/12

x=16/12, 4/3

4 0
3 years ago
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