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3 years ago

Which one of the following is not closed under the operation being performed

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

4 0

Remember that polynomials are closed under addition, subtraction, and multiplication, but they are not closed under division. The only division you have there is B; therefore the correct answer is B.

A. $(14x-2)3(x-2)=14 x^{2} -90x+10$ . The result is still a polynomial; therefore, answer A is incorrect.

B. $\frac{(14x-2)}{3(x-2)} = \frac{14}{3}$ with a remainder of 26. The result is not a polynomial anymore; therefore, B is the correct answer.

C. $(14x-2)+3(x+2)=17x+4$ . The result is still a polynomial; therefore, answer C is incorrect.

D. $(14x-2)+3(x+2)=17x+4$ . The result is still a polynomial; therefore, answer D is incorrect.

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Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into

Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = $(\frac{60\pi }{\pi+4}) in$

b)the length of the wire for the square = $(\frac{240}{\pi+4}) in$

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

b= $\frac{y}{4}$

Area of the square which is L² can now be said to be;

$A_S=(\frac{y}{4})^2 = \frac{y^2}{16}$

On the otherhand; let the radius (r) of the circle be;

2πr = 60-y

$r = \frac{60-y}{2\pi }$

Area of the circle which is πr² can now be;

$A_C= \pi (\frac{60-y}{2\pi } )^2$

$=( \frac{60-y}{4\pi } )^2$

Total Area (A);

A = $A_S+A_C$

= $\frac{y^2}{16} +(\frac{60-y}{4\pi } )^2$

For the smallest possible area; $\frac{dA}{dy}=0$

∴ $\frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0$

If we divide through with (2) and each entity move to the opposite side; we have:

$\frac{y}{18}=\frac{(60-y)}{2\pi}$

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

$y= \frac{240}{\pi+4}$

∴ since $y= \frac{240}{\pi+4}$ , we can determine for the length of the circle ;

60-y can now be;

= $60-\frac{240}{\pi+4}$

= $\frac{(\pi+4)*60-240}{\pi+40}$

= $\frac{60\pi+240-240}{\pi+4}$

= $(\frac{60\pi}{\pi+4})in$

also, the length of wire for the square (y) ; $y= (\frac{240}{\pi+4})in$

The smallest possible area (A) = $\frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})$

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0

3 years ago

Approximately how many inches are in 6 meters? A) 72 inches B) 144 inches C) 216 inches D) 234 inches

Blababa [14]

The answer would be D

8 0

3 years ago

What is 119 over 8 in its simplest form?

ivolga24 [154]

119/8 is already in simplest form. However, if you attempt to change it to a mixed number the correct answer would be 14 7/8 (7 over 8).

Hope I helped!

3 0

3 years ago

Ill give you a brainliest if you get it right

lesantik [10]

A&d i think.. but basically the equation needs to be modeled where the answer will be a 14° difference

3 0

2 years ago

Read 2 more answers

Which of the following are roots of the polynomial function? Check all that apply.

lutik1710 [3]

You know 1 is not a root because the sum of the coeffcients of the equation is 14, not zero.

It is fairly easy to try 3 by synthetic division (see attachment), which tells you that 3 is a root and the remaining quadratic factor is x²-3x-5. The quadratic formula tells you the roots of that factor are

... x = (-b±√(b²-4ac))/(2a) = (3±√29)/2

The appropriate choices are

... C. (3-√29)/2

... D. (3+√29)/2

... F. 3

_____

The quadratic formula tells you the solution to

... ax²+bx+c=0

is x = (-b±√(b²-4ac))/(2a)

We have a=1, b=-3, c=-5.

8 0

3 years ago