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Anvisha [2.4K]
3 years ago
5

We’ve seen that natural numbers are closed under addition. Determine the closure of natural numbers under the other three operat

ions, and give examples to support your answers.

Mathematics
1 answer:
nevsk [136]3 years ago
7 0

Natural numbers are not closed under subtraction. In fact, any operation x-y,\quad y>x has no solution using natural numbers.


Natural numbers are closed under multiplication. In fact, any operation x\cdot y means to sum x by itself y times, and we already know that natural numbers are closed under sum.


Natural numbers are not closed under division. In fact, if y doesn't divide x, any operation \frac{x}{y} has no solution using natural numbers.

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A manufacturing company with 450 employees begins a new product line and must increase their numbers of employees by 18%. How ma
pogonyaev

You are adding 18%, which makes it 118% of original employees

Times 450 by 1.18 = 531

6 0
3 years ago
Which statements are true
AnnyKZ [126]

Answer:

A, B and C (close examination)

Step-by-step explanation:

A. 15m3 - 6m = 3m(5m2 - 6m)

  • m = 0 or m = 1/3

B. 40m6-4=4(10m6-1)

  • 0 = 0
  • All real numbers are solutions

C. 6m2+18m=6m2(1+3m)

  • m = 0 or m = 1 or m = -1

D. 32m4+12m3(8m+3)

  • 128m4 + 36m3

This is tough one but I will explain this problem by close examination:

The problem is looking for an equation that have the variable m by itself

D is out of the picture because the equations does not have m by itself

Equation B's answer is that all numbers are solutions meaning any m value you put will become the same. (Similar to Infinite Solutions)

By close examination, The answer are A, B, and C.

5 0
3 years ago
Find the slope of the line whose equation is y=2/3x-3. <br> Please explain :)
Vladimir [108]

Answer:

m=2/3.

Step-by-step explanation:

the equation for slope is y=mx+b, where m is slope. So, 2/3 is your slope.

5 0
3 years ago
Let w = x2 + y2 + z2, x = uv, y = u cos(v), z = u sin(v). use the chain rule to find ∂w ∂u when (u, v) = (9, 0).
jasenka [17]
By the chain rule,

\dfrac{\partial w}{\partial u}=\dfrac{\partial w}{\partial x}\cdot\dfrac{\partial x}{\partial u}+\dfrac{\partial w}{\partial y}\cdot\dfrac{\partial y}{\partial u}+\dfrac{\partial w}{\partial z}\cdot\dfrac{\partial z}{\partial u}
\dfrac{\partial w}{\partial u}=2xv+2y\cos v+2z\sin v

We also have x(9,0)=0, y(9,0)=9, and z(9,0)=0, so at this point we get

\dfrac{\partial w}{\partial u}(9,0)=2\cdot9\cdot\cos0=18
7 0
3 years ago
The length and width of a rectangle are shown below.
natulia [17]

Answer:

-2x² + 90x + 500

Step-by-step explanation:

Use FOIL method

Area of rectangle = length * width

                             = (50 - x)(2x + 10)

                             = 50*(2x) + 50*10 + (-x)*2x + (-x)*10

                             = 100x + 500 - 2x² - 10x

                             = -2x² + 10<u>0x - 10x </u>+ 500  {Combine like terms}

                            = -2x² + 90x + 500

7 0
3 years ago
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