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4vir4ik [10]
2 years ago
9

Which polynomial function has a leading coefficient of 1 and roots (7 i) and (5 – i) with multiplicity 1? f(x) = (x 7)(x – i)(x

5)(x i) f(x) = (x – 7)(x – i)(x – 5)(x i) f(x) = (x – (7 – i))(x – (5 i))(x – (7 i))(x – (5 – i)) f(x) = (x (7 – i))(x (5 i))(x (7 i))(x (5 – i))
Mathematics
1 answer:
Nuetrik [128]2 years ago
5 0

It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.

The simplest polynomial with these characteristics would be

f(x) = (x - (7 + i)) (x - (5 - i))

but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with

f(x) = (x - (7 + i)) (x - (7 - i)) (x - (5 - i)) (x - (5 + i))

which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:

f(x) = (x^2 - (7^2 - i^2)) (x^2 - (5^2 - i^2)) = (x^2 - 8) (x^2 - 6) = x^4 - 14x^2 + 48

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Consider the triangle below.
Pepsi [2]

The measure of angle P is 29 degrees

The sum of an interior angle of a triangle is 180 degrees. Given the following parameters:

  • m<M = 15x + 5
  • m<N = 3x + 2
  • m<P = 5x - 11

Taking the sum and equating to 180 degrees:

m<M + m<N + m<P = 180 degrees

15x + 5 + 3x + 2 + 5x - 11 = 180

23x - 4 = 180

23x = 184

x = 184/23

x = 8

Get the measure of m<P

m<P = 5x - 11

m<P = 5(8) - 11

m<P = 40 - 11

m<P = 29 degrees

Hence the measure of angle P is 29 degrees

Learn more on angles here: brainly.com/question/25770607

7 0
2 years ago
Figure I and Figure II are similar figures,
ELEN [110]

The ratio of corresponding sides is same for all the sides for similar polygon. the correct proportion is,

\frac{ST}{EF}=\frac{WR}{CD}

Thus the option H is the correct option.

To find the correct proportion we need to know about the properties of slimier polygon.

<h3>What are the properties of similar polygon?</h3>

Two polygons are said to be similar or congruent pentagon-

The corresponding angle of two pentagons are congruent.

The ratio of corresponding sides is same for all the sides.

The figure given in the problem of similar two polygons with six sides.

Rearrange the second figure as shown in figure.

As for the similar polygons, the ratio of corresponding sides is same for all the sides.

Thus the sides shown in the two rearranged figure must be same. Therefore,

\frac{ST}{EF}=\frac{WR}{CD}

Hence the correct proportion is,

\frac{ST}{EF}=\frac{WR}{CD}

Thus the option H is the correct option.

Learn more about the similar polygon here;

brainly.com/question/771807

8 0
2 years ago
C = 4+0. 10t what is the charge to rent a paddle boat for 20 minutes?
Blababa [14]
The charge should be $6. I believe I set this up correctly; let me know if there are any errors. Hope this is helpful & accurate.

5 0
2 years ago
Which of the following sets does not contain any irrational numbers?
dusya [7]

Answer:

{ 9/2 , square root of 100, 5.123}

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
How do I find the volume?​
kotykmax [81]

Answer:

14ft

First get the cones volume formula v=(3.14*r^2*h)/3

Second find the radius which is 1/2 the diameter.

Third plug in given and solve 366= (3.14*5^2*h)/3

366*3=3*(3.14*25*h)/3

1098=78.5h

1098/78.5=78.5h/78.5

13.987=h

5 0
3 years ago
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