Explain what the following statement means:
Polynomials are closed under the operations of addition and subtraction.
Provide one addition example and one subtraction example to demonstrate.
a set is closed under certain operation if the operation performed on two elements of the set gives an element of the same set
addition,subtractio sa well as multiplication of polynomials result into another polynomial.Therefore,the set of polynomials is closed under addition,subtraction and multiplication.
division of a polynomial need not be a polynomial (sometimes it is ,but not always).Therefore,the set of polynomials is not closed under division.see the example in the box beside.
Sample Response: If you add two polynomials, the sum is always a polynomial. Example: (2x2 + 3x) + (8x2 - 4x) = 10x2 - x If you subtract two polynomials, the difference is always a polynomial. Example: (2x2 + 3x) - (8x2 - 4x) = -6x2 + 7x
Compare your response to the sample response above. Did your response …

… explain what closure means for addition and give an example?

… explain what closure means for subtraction and give an example?

Answers

Answer 1

Polynomials are the algebraic expressions that consist of variables and coefficients.

How to explain the polynomial?

The Closure property of addition states that in a defined set, for example, the set of all positive numbers is closed with respect to addition since the sum obtained adding any 2 positive numbers is also a positive number which is a part of the same set.

Closure property of subtraction states that if any two real numbers a and b are subtracted from each other, the difference or result will be a real number as well. For example, 9 - 4 = 5.

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Related Questions

Please help with this as soon as possible. Assignment due tomorrow!!

Answers

1 - transversal is RS , angle is CORRESPONDING
2 - transversal is BA , angle is ALTERNATE INTERIOR
3 - transversal is RS , angle is CORRESPONDING
4 - transversal is TU , angle is ALTERNATE EXTERIOR
5 - transversal is TU , angle is ALTERNATE INTERIOR
6 - transversal is CD , angle is ALTERNATE EXTERIOR
7 - transversal is TU , angle is ALTERNATE EXTERIOR
8 - transversal is TU , angle is CORRESPONDING
9 - transversal is AB , angle is ALTERNATE INTERIOR
10 - transversal is CD , angle is ALTERNATE INTERIOR
11 - transversal is RS , angle is CORRESPONDING
12 - transversal is TU , angle is CORRESPONDING

.A cylindrical tank full of water has a
diameter of 10 feet and a height of 14 feet.
If 250 cubic feet is drained from the tank,
how much water remains?

Answers

Answer:

849

Step-by-step explanation:

Question 3 of 10
The minimum monthly payment for Janet's credit card is 2% of her balance or
$10, whichever is higher. If Janet's balance at the end of her last billing cycle
was $760, what is her minimum monthly payment?
A. $10.00
O B. $5.20
C. $25.20
OD. $15.20

Answers

The correct answer is: Option 15.20

Explanation:
At the end of her last billing the amount = $760

The minimum monthly payment of Janet's card is 2%.

To find the monthly payment, we need to find the 2% of $760.

Therefore,
$760 * 2 / 100 = $15.20 > $10

please help picture below

Answers

Answer:

720

Step-by-step explanation:

height is 22

right triangle sides are

5 12 and 13

Answer:

B) 720 cm²

Explanation:

Area of triangular prism = Base × Height + Length × (perimeter of base)

Here given:

Base: 12 cmHeight: 5 cmLength: 22 cmPerimeter of Base: (5 + 12 + 13) = 30 cm

=======================================

Solve for area: 12 × 5 + 22 × (30) = 720 cm²

A circle has a radius of 16 m. What is its circumference?
Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
16 m

Answers

Answer:

C=100.53 CM²

Step-by-step explanation:

Formula to the circumference of a circle is 2π·r

2π=6.28

6.28·16=100.53 CM²

Evaluate the expression when y=4.

y² + 6y +8

Answers

Answer:

48

Step-by-step explanation:

substitute y = 4 into the expression

y² + 6y + 8

= 4² + 6(4) + 8

= 16 + 24 + 8

= 48

What is the AREA of the figure below?

Answers

Answer: 12

Step-by-step explanation:

height x width

3 x 4 = 12

Evaluate f(-2): f(x)=3/2x-4​

Answers

Answer:

f(- 2) = - 7

Step-by-step explanation:

substitute x = - 2 into f(x)

f(- 2) = [tex]\frac{3}{2}[/tex] × - 2 - 4 = - 3 - 4 = - 7

Drag the tiles to the correct boxes to complete the pairs.
Match each division expression to its quotient.
16 divided by (-8). -2 2/5 divided by 4/5. 33/7 divided by 1 1/7. -12.2 divided by (-6.1)

Answers

Answer:

check explanation for answer

Step-by-step explanation:

16 ÷ -8 = -2

- 2 \frac{2}{5} ÷  \frac{4}{5} = -3

3 \frac{3}{7} ÷ \frac{1}{7} = 3

-12.2 ÷ -6.1 = 2

If 35 boxes equals to 21 dollars in total, how much does each box cost?

Answers

let b be number of boxes

35b = 21
b = 0.6

each box cost -> $0.60
1 box = 21/35 = 0.60

So 1 box is basically $0.60 yeah

I don't get what I'm doing wrong,does anybody know this?The diameter of a great circle is 24 inched find the total surface area of the hemisphere don't forget to include the base in the total area.

Answers

since it's diameter is 24, its radius must be 12.

[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12 \end{cases}\implies SA=4\pi (12)^2\implies SA=576\pi[/tex]

now, that's for a sphere, for a hemisphere with the same radius it'd just be half that or 288π, now let's add the area of the circular base.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{hemisphere}{288\pi} ~~ + ~~\stackrel{circular~base}{\pi (12)^2}}\implies 288\pi ~~ + ~~144\pi \implies 432\pi[/tex]

The total surface area of the hemisphere is 288π. The area that include both surface area of hemisphere and the base of the total area is 432π.

What is hemisphere?

A hemisphere is "half the part of sphere".

According to the question,

The diameter of greater circle is 24 this implies radius of circle is 12.

Surface area of sphere = 4πr²

= 4×π × (12)²

= 576π.

Surface area of sphere is 576π

Surface area of Hemisphere is half of the surface area of sphere.

(576π)/2 = 288π

In order to include the base in the total area only if add surface area of hemisphere and area of circle.

surface area of hemisphere + rea of circle = 288π + π(r)²

= 288π + π(12)²

= 288π + 144π

= 432π

Hence, the total surface area of the hemisphere is 288π. The area that include both surface area of hemisphere and the base of the total area is 432π.

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(6ƒ² − 9ƒ + 10) − (− 2ƒ² − ƒ+3)

Answers

Answer:

Step-by-step explanation:

6f^2 - 9f + 10 + 2f^2 + f - 3

8f^2 - 8f + 7

Given ,
[tex] (6f^{2}-9f+10)-(-2f^{2}-f+3) [/tex]

=> [tex] 6f^{2}-9f+10+2f^{2}+f-3[/tex]

=> [tex] 8f^{2}-8f+7[/tex] is the answer

Which set only contains numbers that make the inequality true? x + 19 < 28 {10, 11, 12, 13} {10, 11, 12, 13} {3, 4, 5, 6} {3, 4, 5, 6} {12, 13, 14, 15} {12, 13, 14, 15} {7, 8, 9, 10}

Answers

Answer:

{3, 4, 5, 6} 

Step-by-step explanation:

Inequalities represent the value of a variable by comparing them to other values.

Inequality Signs

Before answering the question, make sure you understand the different inequality signs.

< - This sign represents less than. This means that the value on the left is less than the value on the right.> - This sign represents greater than. This means that the value on the left is greater than the value on the right.< - This sign means less than or equal to. So, the value on the left will be less than or the same as the value on the right.> - This sign means greater than or equal to. So, the value on the left will be greater than or the same as the value on the right.

Solving the Inequality

To make this question easier to answer, we can solve the inequality. Solving an inequality involves isolating the variable.

To do this subtract 19 from both sidesx < 9

Finding the Set

Now that we solved the inequality we can look for the correct set of numbers. Since we solved the inequality, we know that all of the correct values should be less than 9. However, because there was no equal to sign, 9 is not included in the set. The only set that has only correct solutions is {3, 4, 5, 6}.

A ball is thrown through the air, following a parabola: y= -x^2 + 4x + 4.

The land slopes upward: y = 0.5x + 2

1. Using the graph what is a solution to the system of equations?

( , )

2. What does the solution represent in this scenario?


a The point the ball reaches maximum height.

b The point where the ball meets the ground.

c The point where the ball is thrown.

Answers

The solution represents the point where the ball meets the ground

distance between points (-4,4) and (4,-2)

Answers

Answer:

10 units

Step-by-step explanation:

calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 4, 4 ) and (x₂, y₂ ) = (4, - 2 )

d = [tex]\sqrt{(4-(-4))^2+(-2-4)^2}[/tex]

   = [tex]\sqrt{(4+4)^2+(-6)^2}[/tex]

    = [tex]\sqrt{8^2+36}[/tex]

    = [tex]\sqrt{64+36}[/tex]

    = [tex]\sqrt{100}[/tex]

     = 10

what is the solution of y = 2/3x + 23/3?

Answers

Answer:X-Intercepts:([tex]-\frac{23}{2}[/tex] ,0),Y-Intercepts: (0, [tex]\frac{23}{3}[/tex]) slope[tex]\frac{2}{3}[/tex]Step-by-step explanation:[tex]\frac{2}{3}x[/tex]+[tex]\frac{23}{3}[/tex] = slope [tex]\frac{2}{3}[/tex]

HEy does anyone go to Purchase line High school in Pennsylvania? And is in 8th grade
please only answer if you are, please

Answers

No I’m not I got to los lunas middle school in New Mexico

What is the area of the polygon in square units?

A four-quadrant graph with an irregular polygon with vertices at negative four comma eight, five comma eight, five comma two, nine comma two, twelve comma negative six, and negative four comma negative six.

Answers

The area of the Area  of the polygon is known to be 9 units². Find more about polygon below

What is the Area of a Polygon?

The area of a polygon is one that is defined as the measurement of the given area that is known to be covered by it.

Note that to calculate the area, it will be

Area = 1/2 (5 + 1) x 3 = 9 units²

Thus the answer of 9 units is correct.

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PLEASE HELP!!

Oakdale Farms grew two different varieties of tomatoes last summer. When
the tomatoes were fully grown, they took a sample of each variety and
compared their weights.

Answers

Answer:

D

Step-by-step explanation:

it's because of simple logic

Find the value of x. Round your answer to the nearest tenth

Answers

Answer:

Your answer would be 24 but then if you  round it to the nearest tenth the you would have 20

Step-by-step explanation:

i hope this helps

Which of the following conditions must be met in order to make a statistical inference about a population based on a
sample if the sample does not come from a normally distributed population?

Answers

The correct answer is C. n is greater than or equal to 30

The slope of the line that passes through the points [6,9[ and [11,2] is

Answers

Answer:

-7/5

Step-by-step explanation:

m = slope = (y1-y2) / (x1-x2)  =  7/-5 = - 7/5

help need to pass class and iready

Answers

Answer:

[tex]\Large\boxed{\sf{y > 32}}[/tex]

Step-by-step explanation:

To get the final answer, isolate the variable y on one side of the equation.

1/4y≥8

First, multiply by 4 from both sides.

[tex]\Longrightarrow: \sf{4*\dfrac{1}{4}y\geq 8*4 }[/tex]

Solve.

8*4=32

[tex]\boxed{\sf{y\geq 32}}[/tex]

Therefore, the correct answer is D.

I hope this helps, let me know if you have any questions.

help please

Based on a your normal distribution curve, 68% of a sample pack of M&M's would have
at LEAST how many orange M&M's out of a pack of 56 total M&M's

Answers

Based on your normal distribution curve, 68% of the sample pack of M&M's will have 38 orange M&M's

Data obtained from the questionTotal pack = 56Percentage = 68%Amount of M&M's =?

How to determine the amount of M&M's

The amount of M&M's that will be obtained from the pack of 56 can be obtained as follow:

Amount = percentage × total

Amount of M&M's = 68% × 56

Amount of M&M's = 0.68 × 56

Amount of M&M's = 38

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please help me with this problem i will give brainliest please :) <3

Answers

Answer:

I believe it would be 3,000,000 by the end of 12 years since nothing is being taken out or deposited but instead, she put a compound interest so the numbers would go up from what i gather

Step-by-step explanation:

You can help me please ?

Answers

Answer:

B = 48

Step-by-step explanation:

8 x 6 = 48

hope this helps!

3 to the third power minus 4 to the second power

Answers

Answer:

3^3-4^2=11

Step-by-step explanation:

3^3=27

4^2=16

27-16=11

Can someone help me please

Answers

Answer:

∠A≅∠Y          AB≅YZ

∠B≅∠Z          AC≅YX

∠C≅∠X          BC≅ZX

ΔABC≅ΔYXZ

Step-by-step explanation:

congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle

Find the length of the straight lines joining the following pairs of points (-1,3)and(5,2)

Answers

Answer:

es lo que es

Step-by-step explanation:

step by step =step mom

Choose the function that represents the data in the table.
х
0
-3
1
-1
2
5
3
15
4
29
5
47
y
Oy - 3
0 y= 2* – 3
O y = 2x - 3
O y = 2x2 – 3

Answers

Answer:

Option (D): f(x) = 2x^2 – 3

Step-by-step explanation:

Math.

The function that represents the data in the table is y=2x²-3

What is a function?

A relation is a function if it has only One y-value for each x-value.

Let us check the function of the given data by plugging any ordered pair in the given functions

Let us take a point (1, -1) to check each function

(a) y=x/2-3

-1= 1/2-3

-1=-5/2

So y=x/2-3 is not the function

(b) y=2ˣ-3

-1=2-3

-1=-1

Now let us check for other point

5=4-3

5=1

This function is not satisfied for all points

(c) y=2x-3

-1=-1

For point (2, 5)

5=-1

This function is not satisfied for all points

(d) y=2x²-3

-1=2-3

-1=-1

Now 5=8-3

5=5

Hence, the function that represents the data in the table is y=2x²-3

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