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romanna [79]
1 year ago
9

Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 . Assume the leading co

efficient is 1.
Mathematics
1 answer:
oksano4ka [1.4K]1 year ago
4 0

f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x) are − 3 , 4 , − 3 assuming that the leading coefficient is 1. This can be obtained by formula of polynomial function.

<h3>Find the required equation:</h3>
  • The zeroes or roots of a polynomial function are x values for which          f(x) = 0
  • If the zeroes or roots are r₁, r₂, r₃,... then possible polynomial function is

⇒ f(x) =  a(x - r₁)(x - r₂)(x - r₃)

where a is the leading coefficient

Here in the question it is given that,

  • Polynomial should be with degree 3
  • zeros of f(x) are − 3 , 4 , − 3

By using the formula of polynomial function we get,

⇒ f(x) =  a(x - r₁)(x - r₂)(x - r₃)

⇒ f(x) = 1(x - (-3))(x - (4))(x - (-3))

⇒ f(x) = 1(x + 3)(x - 4)(x + 3)

⇒ f(x) = (x + 3)(x² - x - 12)

⇒ f(x) = x³ - x² - 12x + 3x² - 3x - 36

⇒ f(x) = x³ + 2x² - 15x - 36

Hence f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 assuming that the leading coefficient is 1.

 

Learn more about polynomial function here:

brainly.com/question/12976257

#SPJ1

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KATRIN_1 [288]

Answer:

See Below.

Step-by-step explanation:

We want to verify:

\cos(x-y)-\cos(x+y)=2\sin(x)\sin(y)

We will utilize the following identities:

\cos(x-y)=\cos(x)\cos(y)+\sin(x)\sin(y)

And:

\cos(x+y)=\cos(x)\cos(y)-\sin(x)\sin(y)

So, by substitution, we acquire:

(\cos(x)\cos(y)+\sin(x)\sin(y))-(\cos(x)\cos(y)-\sin(x)\sin(y))=2\sin(x)\sin(y)

Distribute:

\cos(x)\cos(y)+\sin(x)\sin(y)-\cos(x)\cos(y)+\sin(x)\sin(y)=2\sin(x)\sin(y)

The first and third term will cancel:

\sin(x)\sin(y)+\sin(x)\sin(y)=2\sin(x)\sin(y)

Combine like terms:

2\sin(x)\sin(y)\stackrel{\checkmark}{=}2\sin(x)\sin(y)

5 0
3 years ago
Read 2 more answers
The main floor of Kinsey's home is 1,425 square feet. The upper level is 875 square feet with one unfinished bedroom that measur
kvv77 [185]

The reportable square footage for Kinsey's home = 2150square feet.

The main floor of Kinsey's home is 1,425 square feet.

The upper level is 875 square feet with one unfinished bedroom that measures 150 square feet.

The finished basement is 1,425 square feet with 7.5-foot ceilings.

That means the square footage of the upper floor plus the main floor (minus the unfinished laundry area).

Kinsey should report square feet (1425+875- 150)

= 2150square feet.

Hence, The reportable square footage for Kinsey's home = 2150square feet.

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3 0
1 year ago
A cone has a diameter of 6 cm and a height that is 3 times the diameter. Using 3.14 for pi, which of the following can be used t
Zinaida [17]

Option A: 1/3(3.14)(3cm)^2(18cm) is the correct answer

Step-by-step explanation:

Given

Diameter of Cone = d = 6 cm

Radius will be:

r = d/2 = 6/2 = 3 cm

Height of cone = h = 3d = 18 cm

The volume of cone is given by:

V = \frac{1}{3}\pi r^2h

Putting the values

V = \frac{1}{3} (3.14)(3)^2(18)

Hence,

Option A: 1/3(3.14)(3cm)^2(18cm) is the correct answer

Keywords: Volume, cone

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4 0
3 years ago
Convert 2 mi. 3,241 ft. to ft.
lesya [120]
2 miles = 10560 ft.
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7 0
3 years ago
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A financial talk show host claims to have a 55.3 % success rate in his investment recommendations. You collect some data over th
baherus [9]

Answer:

There is a 25.52% probability of observating 4 our fewer succesful recommendations.

Step-by-step explanation:

For each recommendation, there are only two possible outcomes. Either it was a success, or it was a failure. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

p = 0.553, n = 10

If the claim is correct and the performance of recommendations is independent, what is the probability that you would have observed 4 or fewer successful:

This is

P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.553)^{0}.(0.447)^{10} = 0.0003

P(X = 1) = C_{10,1}.(0.553)^{1}.(0.447)^{9} = 0.0039

P(X = 2) = C_{10,2}.(0.553)^{2}.(0.447)^{8} = 0.0219

P(X = 3) = C_{10,3}.(0.553)^{3}.(0.447)^{7} = 0.0724

P(X = 4) = C_{10,4}.(0.553)^{4}.(0.447)^{6} = 0.1567

P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0003 + 0.0039 + 0.0219 + 0.0724 + 0.1567 = 0.2552

There is a 25.52% probability of observating 4 our fewer succesful recommendations.

3 0
3 years ago
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