which of the following equations demonstrate that the set of polynomials is not closed under the certain operations? A. Division: (x^2+2x) / (x+1) = x+ x/x+1 B. Multip.: (3x^4+x^3)(-2x^4+x^3)= -6x^6+ x^7+x^6 C. Addition: (3x^4+x^3)+(-2x^4+x^3)= x^4 + 2x^3 D. Multip.: (x^2+2x)(x+1)= x^3 +3x^2+2x

Answers

Answer 1

Answer: The correct answer is A) Division.

Explanation:
When we divide these two polynomials, we get an answer that is not a polynomial. This is due to the rational portion of the answer, x/(x+1).

We know from our definitions of polynomials and monomials that if there is a variable with a negative exponent, that means that we do not have a monomial and therefore not a polynomial. Having x+1 in the denominator means it would have a negative exponent, and is therefore not a polynomial.

Since we divided two polynomials and had a result that was not a polynomial, this means that the set of polynomials is not closed under division.

Answer 2

Answer:

Answer:

Division: (x^2+2x) / (x+1) = x+ x/x+1

Step-by-step explanation:

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A circle has a radius of 5 meter. What is the length of the arc that is captured by a central angle that measures 120 degrees? Round your answer to the nearest tenth.a) 3.33 meters
b) 31.42 meters
c) 10.47 meters
d) 2.09 meters

Answers

The length of the arc captured by a central angle of 120 degrees in a circle with a radius of 5 meters is approximately 10.47 meters. Hence, the correct answer is an option (c) 10.47 meters.

What is an arc?

Arc is the measure of the angle on the circumference of a circle.

Length of an Arc = θ × (π/180) × r

Here,
The length of an arc of a circle with radius r and central angle θ (in radians) is given by the formula:

Length of arc = r × θ

To use this formula, we need to convert the given central angle of 120 degrees to radians:

θ = (120/180) × π = 2/3 × π

Now, we can substitute the given values into the formula to get the length of the arc:

Length of arc = 5 × (2/3 × π) = (10/3) × π ≈ 10.47 meters

Therefore, the length of the arc captured by a central angle of 120 degrees in a circle with a radius of 5 meters is approximately 10.47 meters. Hence, the correct answer is an option (c) 10.47 meters.

Learn more about arcs here:

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Well, the formula for the length of an arc is;
n⁰ × 2πr
360
Where; n⁰ is the angle
π is pie, which is 22/7 or 3.143 approximately
and r is the radius

Anyway, according to the question;
n⁰ is 120⁰
and r is 5 meters. And as you know, the pie is 22/7. So that will be

120⁰/360 x 2 x 22/7 x 5
And that will give you 10.47metres. Which is approximately 11 metres. Hope i helped, have a nice day

Which statement is true about every rectangular pyramid?Each lateral face has an area less than the area of the base.
At least two of the lateral faces are congruent.
Each lateral face has the same height.
At least one of the faces has a whole number base or height.

Answers

Answer:

At least two of the lateral faces are congruent.

Step-by-step explanation:

Because the words "at least" are used this means that at a minimum 2 of the faces are congruent. Because the base is in the shape of a triangle, this will definitely be true.

hope this helps:)

Answer:

At least two of the lateral faces are congruent.

Step-by-step explanation:

Because the words "at least" are used this means that at a minimum 2 of the faces are congruent. Because the base is in the shape of a triangle, this will definitely be true.

hope this helps:)

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Answers

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Next, compare all your disbursements from your checkbook register to all the debits in your bank statement to determine the amount of disbursements not yet debited by the bank.

Also, you need to check for any bank charges already debited to your bank account but not yet recorded.

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