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igomit [66]
3 years ago
8

A polynomial has a leading coefficient of 1 and the

Mathematics
2 answers:
Hoochie [10]3 years ago
7 0

Answer:

(A)[x-(2+i)][x-(2-i)][x-\sqrt{2}][x+\sqrt{2}]

Step-by-step explanation:

A polynomial has a leading coefficient of 1 and the  following factors with multiplicity 1:

x-(2+i)\\x-\sqrt{2}

We apply the following to find the factored form of the polynomial.

  • If a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial.
  • If the polynomial has an irrational root a+\sqrt{b}, where a and b are rational and b is not a perfect square, then it has also a conjugate root a-\sqrt{b}.

\text{Complex conjugate of }x-(2+i)=x-(2-i)\\\\\text{Complex conjugate of }x-\sqrt{2}=x+\sqrt{2}

Therefore, the factored form of the polynomial is:

[x-(2+i)][x-(2-i)][x-\sqrt{2}][x+\sqrt{2}]

Nutka1998 [239]3 years ago
7 0

Answer:C

Step-by-step explanation:

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For all values of x
Yuliya22 [10]

Answer:

A.) gf(x) = 3x^2 + 12x + 9

B.) g'(x) = 2

Step-by-step explanation:

A.) The two given functions are:

f(x) = (x + 2)^2 and g(x) = 3(x - 1)

Open the bracket of the two functions

f(x) = (x + 2)^2

f(x) = x^2 + 2x + 2x + 4

f(x) = x^2 + 4x + 4

and

g(x) = 3(x - 1)

g(x) = 3x - 3

To find gf(x), substitute f(x) for x in g(x)

gf(x) = 3( x^2 + 4x + 4 ) - 3

gf(x) = 3x^2 + 12x + 12 - 3

gf(x) = 3x^2 + 12x + 9

Where

a = 3, b = 12, c = 9

B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)

To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula

Y = 3x + 3

X = 3y + 3

Make y the subject of formula

3y = x - 3

Y = x/3 - 3/3

Y = x/3 - 1

Therefore, g'(x) = x/3 - 1

For g'(12), substitute 12 for x in g' (x)

g'(x) = 12/4 - 1

g'(x) = 3 - 1

g'(x) = 2.

5 0
3 years ago
In the given figure, find m∠RST, if m∠RSU = 43º and m∠UST = 23º.
pickupchik [31]

Applying the angle addition postulate, the measure of angle RST is: 66°.

<h3>What is the Angle Addition Postulate?</h3>

If two angles share a common vertex and a common side, they are adjacent angles that form a larger angle. According to the angle addition postulate, the sum of these two adjacent angles will give a sum that is equal to the measure of the larger angle they both form.

We know the following:

Measure of angle RSU = 43º

Measure of angle UST = 23º

In the diagram given, angle RSU and angle UST are adjacent angles that form a larger angle, angle RST.

Therefore, based on the angle addition postulate, the measure of angle RST = sum of the measures of angles RSU and UST.

Therefore, we would have:

m∠RST = m∠RSU + m∠UST

Substitute

m∠RST = 43 + 23

m∠RST = 66°

Learn more about the angle addition postulate on:

brainly.com/question/24746945

#SPJ1

8 0
2 years ago
Determine whether each quadrilateral is a parallelogram. Justify your answer. Yes/No? Reason... opposite side congruent, opposit
Alex_Xolod [135]

Answer:

Yes! The given quadrilateral represents Parallelogram.

Reason: The given quadrilateral has opposite sides congruent.

Step-by-step explanation:

Given the quadrilateral with the four vertices.

  • Now in order to determine whether the given quadrilateral is a parallelogram or not, we need to check whether the opposite sides are congruent or not.

  • It is clear that the given quadrilateral has opposite sides congruent.

Therefore, the given quadrilateral represents Parallelogram.

Hence,

Yes! The given quadrilateral represents Parallelogram.

Reason: The given quadrilateral has opposite sides congruent.

7 0
3 years ago
Find m<br> i’ll give brainlest
soldier1979 [14.2K]

Answer:

its just a black picture

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What is the approximate value of this logarithmic expression?
mestny [16]

Answer:

log_8{24} = 1.53

Step-by-step explanation:

Given

log_8{24}

Required

Solve:

Apply the following law of logarithm:

log_a{b} = \frac{log\ b}{log\ a}

So, we have:

log_8{24} = \frac{log\ 24}{log\ 8}

Using calculator, we have:

log_8{24} = \frac{1.38021124171}{0.90308998699}

log_8{24} = 1.52832083358

Approximate

log_8{24} = 1.53

8 0
4 years ago
Read 2 more answers
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