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3 years ago

If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is _.

1 answer:

defon3 years ago

8 0

Answer: If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is <u>its conjugate 7-i5</u>.

Step-by-step explanation:

We know that when a complex number $z=a+ib$ is a root of a polynomial with degree 'n' , then the conjugate of the complex number ( $\overline{z}=a-ib$ ) is also a root of the same polynomial.

Given: 7+5i is a zero of a polynomial function of degree 5 with coefficients

Here, 7+5i is a complex number.

So, it conjugate ( $\overline{7+5i}=7-5i$ ) is also a zero of a polynomial function.

Hence, if 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is <u>its conjugate 7-i5</u>.

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2 years ago

Read 2 more answers

42. Which matrix represents the image of the triangle with vertices at (-2,0), (1,5), and (4,-8) when dilated by a scale factor

jasenka [17]

The second matrix $\left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right]$ represents the triangle dilated by a scale factor of 3.

Step-by-step explanation:

Step 1:

To calculate the scale factor for any dilation, we divide the coordinates after dilation by the same coordinated before dilation.

The coordinates of a vertice are represented in the column of the matrix. Since there are three vertices, there are 2 rows with 3 columns. The order of the matrices is 2 × 3.

Step 2:

If we form a matrix with the vertices (-2,0), (1,5), and (4,-8), we get

$\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right]$

The scale factor is 3, so if we multiply the above matrix with 3 throughout, we will get the matrix that represents the vertices of the triangle after dilation.

Step 3:

The matrix that represents the triangle after dilation is given by

$3\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right] = \left[\begin{array}{ccc}3(-2)&3(1)&3(4)\\3(0)&3(5)&3(-8)\end{array}\right] = \left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right]$

This is the second option.

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2 years ago

3 times the first of three consecutive odd integers is 3 more than twice the third? what is the third integer

fenix001 [56]

Answer:

Step-by-step explanation:

The difference between consecutive integers is 1.

The difference between consecutive odd integers is 2.

Let the smallest odd integer be x.

Then the next greater one is x + 2. The greatest one is x + 4.

"3 times the first" is 3x

"twice the third" is 2(x + 4)

"3 times the first of three consecutive odd integers is 3 more than twice the third"

3x = 2(x + 4) + 3

3x = 2x + 8 + 3

x = 11

The smallest integer is 11.

x + 4 = 11 + 4 = 15

The greatest one is 15.

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2 years ago

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Answer:

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago