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aleksley [76]
3 years ago
15

Which of the following sets are closed under division? Select all that apply.

Mathematics
2 answers:
worty [1.4K]3 years ago
8 0

Answer:

None of the Above

Step-by-step explanation:

<u>Integers:</u>

Take a=1,b=2

Here, \frac{a}{b}=\frac{1}{2}

Since \frac{1}{2} is not an integer , integers are not closed under division .

<u>Irrational Numbers: </u>

Take a=\sqrt{3},b=\sqrt{27}

Here,\frac{a}{b}=\frac{\sqrt{3} }{\sqrt{27} }=\frac{1}{\sqrt{9} }=\frac{1}{3}

Since \frac{1}{3} is not an irrational number , irrational numbers are not closed under division.

<u>Whole Numbers:</u>

Take a=2,b=3

Here, \frac{a}{b} =\frac{2}{3}

Since \frac{2}{3} is not a whole number, whole numbers are not closed under division.

<u>Polynomials:</u>

Take two polynomials as 2x+3 , 0

Here, \frac{2x+3}{0} is not defined.

Since \frac{2x+3}{0} is not a polynomial, polynomials are not closed under division .

So, the correct option is none of the above

Lilit [14]3 years ago
6 0
The appropriate choice is probably
  none of the above


While the inverse of any irrational number is irrational, their ratio my not be, for example (√8)/(√2) is rational.
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Given the Arithmetic series A 1 + A 2 + A 3 + A 4 A1+A2+A3+A4 14 + 18 + 22 + 26 + . . . + 86 What is the value of sum?
postnew [5]

Answer:

950

Step-by-step explanation:

The common difference is 4, so the general term can be written:

... an = 14 + 4(n -1)

The value of n for the last term is ...

... 86 = 14 + 4(n -1) . . . . . the computation for the last term, 86

... 72 = 4(n -1) . . . . . . . . . subtract 14

... 18 = n -1 . . . . . . . . . . . divide by 4

... 19 = n . . . . . . . . . . . . . add 1

Your series has 19 terms. The first term is 14 and the last is 86, so the average term is (14+86)/2 = 50. Since there are 19 terms, the sum of them is ...

... 19×50 = 950

7 0
3 years ago
Lydia writes the equation below with a missing value.
Alex73 [517]

If she puts 0 in the box she would have a direct variation.

Lydia writes the equation y = 5x - __ with a missing value.

She puts a value in the box and says that the equation represents a direct variation.

We have to choose the correct option from the given options that explain that the equation could represent a direct variation.

When two variables are such that one is a constant multiple of the other, we said they are in Direct variation.

<h3>What is the direct variation?</h3>

In form of y = ax, where y and x are in direct variation.

Consider the given equation y = 5x  - __

For the equation to be in direct variation the value of the missing term has to be 0.

then the equation becomes,

y = 5x

Thus, If she puts 0 in the box she would have a direct variation.

Option (a) is correct.

To learn more about the direct variation visit:

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3 0
2 years ago
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A company manufactures running shoes and basketball shoes. The total revenue (in thousands of dollars) from x1 units of running
Alborosie

Answer:

x_1 =2 , x_2=7

Step-by-step explanation:

Consider the revenue function given by R(x_1,x_2) = -5x_1^2-8x_2^2 -2x_1x_2+34x_1+116x_2. We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).

\frac{dR}{dx_1} = -10x_1-2x_2+34 =0

\frac{dR}{dx_2} = -16x_2-2x_1+116 =0

From the first equation, we get, x_2 = \frac{-10x_1+34}{2}.If we replace that in the second equation, we get

-16\frac{-10x_1+34}{2} -2x_1+116=0= 80x_1-2x_1+116-272= 78x_1-156

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x_2 = \frac{-10\cdot 2 +34}{2}=\frac{14}{2} = 7

So, the critical point is (x_1,x_2) = (2,7). We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives  and check if the criteria is fulfilled in order for it to be a maximum. We get that

\frac{d^2R}{dx_1dx_2}= -2 = \frac{d^2R}{dx_2dx_1}

\frac{d^2R}{dx_{1}^2}=-10, \frac{d^2R}{dx_{2}^2}=-16

We have the following matrix,  

\left[\begin{matrix} -10 & -2 \\ -2 & -16\end{matrix}\right].

Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is (-10)\cdot (-16) - (-2)(-2) = 156>0 and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum

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snow_tiger [21]

Answer:

The solution to the equation is

x = -4

Step-by-step explanation:

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First, add -(1/2)x + 1/8 to both sides of the equation.

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[1/4 - 1/2]x = 7/8 + 1/8

x(1 - 2)/4 = (7 + 1)/8

-(1/4)x = 8/8

-(1/4)x = 1

Multiply both sides by -4

x = -4

3 0
3 years ago
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Answer:

25in

Step-by-step explanation:

6 0
3 years ago
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