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Misha Larkins [42]
3 years ago
13

Use the given zero to find the remaining complex zeros of the polynomial function and write the polynomial as a product of linea

r factors.
f(x)=x^3+8x^2+6x-52; zero:2
Mathematics
1 answer:
lidiya [134]3 years ago
5 0

Answer:

(x - 2)(x - 5 + 2i)(x - 5 - 2i)

Step-by-step explanation:

If one zero is 2, then one factor is (x - 2).

Use synthetic division here.  Taking the coefficients 1, 8, 6 and -52, divide 2 into them:

2    /  1      8      6     -52

                2     20     52

      -----------------------------

          1     10     26     0

Because the remainder is zero, we know that 2 is a root and (x - 2) is a factor, and that the coefficients of the quadratic quotient are 1, 10 and 26.

The discriminant is thus b^2 - 4ac, or 10^2 - 4(1)(26), or  100 - 104, or -4.

Because the discriminant is negative, we know that there will be two factors which themselves are complex conjugates.  One such factor is

      10 ± √-4         10 ± 2i

x = --------------- = ---------------

             2                   2

The complex zeros are thus x = 5 ± 2i.

The corresponding factors are (x - 5 + 2i) and (x - 5 - 2i)

and so the polynomial is

(x - 2)(x - 5 + 2i)(x - 5 - 2i)

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What is the greatest common factor of 4k, 18k4, and 12?
Setler [38]

Answer:  The greatest common factor is 2.

Step-by-step explanation:  We are given to find the greatest common factor of the following expressions:

E_1=4k,~~E_2=18k^4,~~E_3=12.

<u>Greatest Common Factor:</u>  The GCF of two or more numbers (expressions)  is the greatest factor that divides all the numbers or expressions.

We have

E_1=4k=2\times 2\times k,\\\\E_2=18k^4=2\times 3\times 3\times k\times k\times k\times k,\\\\E_3=12=2\times 2\times 3.

Therefore, the greatest common factor will be

G.C.F.=2.

Thus, the required greatest common factor is 2.

6 0
3 years ago
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Look closely at the model.
Maslowich

Answer:

Perimeter: 2(x+3) + 2(x+2)

Step-by-step explanation:

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3 years ago
If postage costs $.54 for the first ounce and $.22 for the each additional ounce, calculate the cost of mailing a 10- ounce enve
sweet-ann [11.9K]

Answer:

Hence, the total cost of mailing 10 ounces is:

$ 2.52

Step-by-step explanation:

If postage costs $.54 for the first ounce and $.22 for the each additional ounce.

i.e. cost of first ounce=$ 0.54.

Now let x denote the number of ounces after the first ounce,

Hence, the cost of x ounces=$ (0.22×x)=$ 0.22 x

Hence, the cost of mailing (x+1) ounces is: $ (0.54+0.22 x)

Now, we have to find the cost of  mailing a 10- ounce envelope.

i.e. after the first ounce we need 9 more ounces.

Hence, the total cost of mailing is calculated as:

=$ (0.54+0.22\times 9)\\\\=$ (0.54+1.98)\\\\=$ 2.52\\

Hence, cost of mailing 10 ounces is:

$ 2.52

8 0
3 years ago
Read 2 more answers
Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 270 em
allsm [11]

Answer:

The number of empty seats each of these three airlines carried on its flight are as follows:

United Continental = 150 empty seats

American = 50 empty seats

Southwest = 70 empty seats

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf for the complete question.

The explanation of the answers is now provided as follows:

Let U, A and W represents number of empty seats of United Continental, American, and Southwest respectively. Therefore, we have:

U + A + W = 270 ………………………. (1)

Since United Continental had three times as many empty seats as American, this implies that:

U = 3A ………………………………… (2)

Substituting U = 3A into equation (1), we have:

3A +A + W = 270

4A + W = 270

W = 270 - 4A ………………………….. (3)

For the cost, we have:

3,000[((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100)] = $114,990

((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = $114,990 / 3,000

((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = 38.33

0.447A + 0.146A + 0124W = 38.33

0.593A + 0.124W = 38.33 ………………… (4)

Substituting W = 270 - 4A from equation (3) into (4) and solve for A, we have:

0.593A + 0.124(270 - 4A) = 38.33

0.593A + 33.48 - 0.496A = 38.33

0.593A - 0.496A = 38.33 - 33.48

0.097A = 4.84

A = 4.84 / 0.097

A = 49.8969072164948

Rounding to a whole number, we have:

A = 50

Substituting A = 50 into each of equations (2) and (3), we have:

U = 3 * 50 = 150

W = 270 - (4 * 50) = 70

Therefore, the number of empty seats each of these three airlines carried on its flight are as follows:

United Continental = 150 empty seats

American = 50 empty seats

Southwest = 70 empty seats

Download pdf
6 0
3 years ago
Sorry for bad quality. First to answer gets brainliest
Maksim231197 [3]

Answer:a

Step-by-step explanation:

☺️

8 0
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