How are polynomials like other number systems such as whole numbers and integers?

Answers

Answer 1
You can add, subtract, and multiply them. These three operations obey the rules for integers. There's a polynomial division algorithm that fills formally the same role as the usual division algorithm for integers. Polynomials added to, subtracted from, or multiplied by other polynomials yield only polynomials. Likewise, integers added to, subtracted from, or multiplied by other integers yield only integers.

Related Questions

HELP ME PLEASE NEED ANSWER NOWWWWWWWWWW solve the following system of equation. Round your answer to the nearest tenth. Your answer will be in the form (M,N). Find M+N, rounded to the nearest tenth.
5x+2y=21
-2x+6y=-34

Answers

 
(A) 5x+2y=21
(B) -2x+6y=-34

multiply (A) by - 3→ -15x - 6y = - 63 (C)

Now add (C) to (B):

-15x - 6y = - 63 (C)
-2x + 6y  =-34 (B)
 -----------    --------
-17x         = - 97       and x = 97/17

Now replace x value in any of the equation and you'll find y = - 64/17

1st Answer (97/17 , - 64/17)
2nd Answer : 97/17 + (-64/17) = 97/17 - 64/17 = 33/17 ≈ 2

If two cards are drawn without replacement, what is the probability of drawing at least one ace

Answers

It would be 50%. Since there are 2 cards and the maximum for percents are 100%, 100 divided by 2 would be 50.

Evaluate [(21 + 6) − 3squared] ÷ 9 ⋅ 2.
choices are

4
4.6
1
52

Answers

The answer is 4 hope this helps. Good Luck!

A rectangle is twice twice as long as it is wide and has the same perimeter as a square whose area is 9 square feet feet larger than that of the rectangle. what are the dimensions of both the rectangle and the​ square?

Answers

The dimension of rectangle : 6 and 12 units

                                  square= 9 units

What is Perimeter ?

Perimeter is the distance around the edge of a shape.

Given:

let the width of rectangle be x.

length= 2x

let the side of square is y units.

Perimeter of rectangle = Perimeter of square

and, Area of square= Area of rectangle + 9

First, Perimeter of square= 4* side

                                           = 4y units

Perimeter of rectangle,

=2(l+b)

=2(2x+x)

=6x units

Since, Perimeter of rectangle = Perimeter of square

6x=4y

3x=2y

Now, Area of square= Area of rectangle +9

                           y²= x*2x+9

                          y²= 2x²+9

                          y²= 2(2y/3)²+9

                          y²= 8y²/9+9

                         1/9 y²= 9

                             y²=81

                            y=±9

So, x=2y/3= 2*9/3

      x= 6

Hence, dimension of rectangle is 6 and 12.

            dimension of square is 9 units.

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The distance you travel while hiking is a function of how fast you hike and how long you hike at this rate. You usually maintain a speed of three miles per hour while hiking. Write a statement that describes how the distance that you travel is determined. Then identify the independent and dependent variables of this function.

Answers

If hours is represented as h, your distance is therefore 3*h (due to that for every hour, you walk 3 miles. For example, in one hour you'd walk 3 miles, in 2 hours you'd walk 3+3=3*2=6 miles,etc.). If distance is represented by d, we get 3*h=d. Since you have to figure out the distance from the equation (that's the purpose of it!), the distance is the dependent variable. In addition, since you can't have 2 separate variables in one equation, h is the independent variable due to that you have to put a number for h in to figure out the distance 

Answer:d

Step-by-step explanation:

Round 894-352 to the nearest ten

Answers

the correct answer is 540
the answer is 540 because you just subtract the round your answer.

solve for y, 3xy+x=9 Then find f(x) when x=2

Answers

3xy+x=9
3xy = 9 - x
    y = 3/x - 1/3

if x = 2
f(2) = 3/2 - 1/3
f(2) = 9/6 - 2/6
f(2) = 7/6
f(2) = 1 1/6

I need help with this

Answers

The expression would be: 11.5-1 1/2x
x represents the number of weeks she would cut her hair off.

Please vote my answer brainliest. thanks!
y=-1.5x+11.5
This is the correct expression because it shows how much hair she has left per week in consideration of how much hair she started out with.

When 75% of a number is added to 6, the result is 3 more than the number. find the number?

Answers

hello : 
let : x  this the number
(75/100)x +6  = x+3

(3/4)x - x = 3 -6
(-1/4)x = -3
x = 12

To find the number in question, an equation is set up and solved, resulting in the number 12, which satisfies the given conditions where 75% of the number added to 6 equals 3 more than the number itself.

The question asks to find a number such that when 75% of it is added to 6, the result is 3 more than the number itself. To find this number, we can set up an equation: Let the number be represented by x. So, we have 0.75x + 6 = x + 3. To solve for x, we subtract 0.75x from both sides of the equation to get 6 = 0.25x + 3. Next, we subtract 3 from both sides to get 3 = 0.25x. Finally, dividing both sides by 0.25 gives us x = 12. Therefore, the number we are looking for is 12

What times what equals 75

Answers

25x3=75 !!!!!!!!!!!!!!!!!!!!
-75,-25,-15,-5,-3,-1,1,3,5,15,25,75. Good luck

This year your brother jack will be 2 years from being twice as old as your sister jen. the sum of jack’s age and three times jen’s age is 66. how old is jen?

Answers

Let the age of Jen 2 years later be x,

age of jack two years later = 2x
total age of jack and jen now = 2x + x - 2 - 2
= 3x - 4
3x - 4 = 66
3x = 70
x = 70/3
= 23.3 (to three significant figures)
age of jen now = x - 2
= 23.3 - 2
= 21.3

Jen is 21.3 years old now.

What is the answer to question 3. Letter A?

Answers

Your answer should be Line Graph.
The answer is a bar graph because a bar graph is used to measure more than one thing. In this case, each bar would represent each species of birds, x would represent the years and y would represent the number of birds.

If JK LM , which statement is true ?

Answers

The answer to this question would be: B. JK and LM meet at a right angle.

The reversed T symbol in this question means "perpendicular". That means the JK and LM line have 90-degree angle difference. A straight angle is 180 degree and right angle mean 90 degrees.
A perpendicular line should be in the same plane and intersect each other.

The measure of one of the acute angles in a right triangle is 59°. what is the measure of the other acute angle?

Answers

The answer is:  31° .
________________________________

59 + 90 + x = 180


59 + 90 = 149 ;

x + 149 = 180 ;

Subtract 149 from each side of the equation:

x + 149 - 149 = 180 - 149 = 31 .

The answer is:  31° .
in a right triangle, the acute angles will add to 90 degrees

that is because one of the angles is 90 and the sum of all the angles is 180
so if x and y are the acute angles and z is the right angle then
x+y+z=180, subsitutuing 90 for z
x+y+90=180
minus 90
x+y=90

so if one is 59 degrees then
59+y=90
minus 59 from both sides
y=31

the other acute angle is 31 degrees

is 5.75 greater than 5 8/12

Answers

Yes, as 5 8/12 is equal to 5.667

Yes, 5.75 is greater than 5 8/12 because 5 8/12 is equal to 5.67 which is less than 5.75.

What is the fraction?

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

What are Arithmetic operations?

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

We have been given two numbers as

5.75 and 5 8/12

To determine the value 5.75 is greater than or less than 5 8/12

We have to convert the fraction 5 8/12 into the decimal,

⇒ 5 8/12

⇒ (60 + 8)/12

⇒ (68)/12

Apply the division operation,

⇒ 5.67

Therefore, 5.75 is greater than 5 8/12 because 5 8/12 is equal to 5.67 which is less than 5.75.

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After observing this pattern, Hideko made a conjecture for the next shape in the pattern. Five circles in a row. Each circle is divided into 4 equal-sized sectors. In the first circle, the top left sector is shaded. In the second circle, the bottom left sector is shaded. In the third circle, the bottom right sector is shaded. In the fourth circle, the top right sector is shaded. In the fifth circle, the top left sector is shaded. Which shape was most likely her conjecture for the next shape?

Answers

The left bottom sector will be the next shape that is going to be shaded.

Given that,
Five circles in a row. Each circle is divided into 4 equal-sized sectors.
In the first circle, the top left sector is shaded.
In the second circle, the bottom left sector is shaded.
In the third circle, the bottom right sector is shaded.
In the fourth circle, the top right sector is shaded.
In the fifth circle, t the bottom right sectoris shaded.
Which shape was most likely her conjecture for the next shape is to be determined.


What is the fraction?

Fraction is defined as the number of compositions that constitutes the Whole.

Here,
Let assign a number of shading to the various sector of the circle,
1 =  the top left sector
2 =  the bottom left sector
3 =  the bottom right sector
4 =  the bottom right sector

Now,
Series of shading the sector of a circle,
1, 2, 3, 4, 3, 2,1
We need to find what is the 6th conjecture
at 6th = 2
2 =  the bottom left sector

Thus, the left bottom sector will be the next shape that is going to be shaded.

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put in least to highest order 6.86,6.8,7,6.9,6.827 and 12.03,1.2,12.3,1.203,12.301

Answers

6.8,6.827,6.86,6.9

1.2,1.203,12.03, 12.301,12.31

Answer:

6.8,6.827,6.86,6.9

Step-by-step explanation:I hope it helps

Dennis cutting 4.7 foot length of twine from a 240 foot spool of twine he needs to cut 42 lenghts and says that 45 feet of twine will remain. Show that this is reasonable

Answers

sorry i had sent something wrong

Which property justifies the following equation 7 [6+5+(-6)=7 [6+(-6)+5]

Answers

Commutative property
I believe that is the commutative property because u r moving the numbers around. 

I'm stuck on this problem also
Find the Perimeter of the polygon with the vertices X(-1,3), Y(3,0), and Z(-1,-2). Round the answer to the nearest hundredth

Answers

The perimeter is 14.47
 
Since you have 3 vertices, the polygon you have is a triangle. The sides of the triangle will be XY, XZ, and YZ. Just use the pythagorean theorem to calculate the length of each side and then add the lengths together for the result. Side XY = sqrt( (-1-3)^2 + (3-0)^2) = sqrt(16+9) = sqrt(25) = 5 Side XZ = sqrt ( (-1-(-1))^2 + (3-(-2))^2) = sqrt(0+25) = sqrt(25) = 5 Side YZ = sqrt( (3-(-1))^2 + (0-(-2))^2) = sqrt(16 + 4) = sqrt(20) = 4.47 Now add the length of each side together 5 + 5 + 4.47 = 14.47

Daniel income tax rate is 15% if he made 32,000 this year what will his pay be in taxes this year

Answers

Final answer:

Daniel will pay $4,800 in taxes for the year by applying a 15% tax rate to his $32,000 income.

Explanation:

To calculate the amount of income tax Daniel will pay on his $32,000 income, we will apply the 15% tax rate that corresponds to the income bracket provided in the reference material. Here's how the calculation is done:

First, identify the total income: $32,000.Next, multiply the total income by the tax rate: $32,000 * 15% (or 0.15).The calculation will be: $32,000 * 0.15 = $4,800.

Therefore, Daniel will pay $4,800 in taxes for the year.

What is the fraction 3/2 squared in fraction form?

Please help

Answers

(3/2)^2 would equal 9/4 as you are just squaring both the numerator and the denominator. And if you wanted to simplify that you would get 3/2 again.

Fraction 3/2 squared in fraction form is 9/4.

What is Fraction?

A fraction represents a part of a whole.

Given,

The fraction is 3/2

In the given fraction the numerator is three and denominator is 2

Three by two which is a improper fraction

We have to square 3/2

Three by Two whole square

(3/2)²

Three square by two square

3²/2²

Nine by four

9/4

Hence fraction 3/2 squared in fraction form is 9/4.

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Given that (-4,5) is on the graph of f(x), find the corresponding point for the function f(2x)

Answers

Answer:

the correct answer is (-2,5)

Step-by-step explanation:

you multiply 1/2 by -4 to get the x value

To find the corresponding point on the function f(2x) given a point on the original function f(x), simply multiply the x-coordinate by 2. In this case, the corresponding point is (-8,5).

Given: Point (-4,5) is on the graph of f(x).

To find: Corresponding point for the function f(2x).

Solution:

When x = -4, 2x = 2*(-4) = -8.So, the corresponding point for f(2x) would be (-8,5).

How to you solve this problem

Answers

5x + x = 90
6x = 90
x = 90/6
x = 15

9y + 18 = 90
9y = 72
y = 8

Hope this helps!

Solve the system of equations. y =9x y =2x + 63

Answers

y=2x+7 
y=9x+8 
From (1),
x= (y-7)/2
Substituting value of x in eqn (2) we get, 
y= 9.(y-7)/2 + 8
y=9x and
y=2x+63

subsitute 9x for y

9x=2x+63
minus 2x from both sides
9x-2x=2x-2x+63
7x+0=63
7x=63
divide both sides by 7
7x/7=63/7
(7/7)x=9
(1)x=9
x=9

sub back to find y


y=9x
y=9(9)
y=81

(x,y)
(9,81)

the solution is (9,81)

Please answer all 3 questions thank you.

Answers

1) Since 8 is 3 units away from 5 we know the radius is 3. When we put that in the circumference formula we get 6(pi) which is 18.8

2) When we use pythagorean thereom we get that the radius is 5 time the square root of 2. When we put this in the area formula we get 25(2)(pi) which is 157.1

Rita bought a table on sale for $278.80 . this price was 66% less than the original price. what was the original price?

Answers

if it was 66% less then the original, then u paid 34%

34% of the original price = 278.80
0.34x = 278.80
x = 278.80 / 0.34
x = 820 <== original price was $ 820

The population of a city increases by 4000 people each year. In 2025, the population is projected to be 450,000 people. What is an equation that gives the city’s population p (in thousands of people) x years after 2010?

Answers

p = 390,00 + 4000x

450,000 people - (15years x 4000) = 390k in 2010
 
15 years is the difference between 2010 and 2025
subtract 60k (that is the 15 years multiplied by 4k) from 450k and you get 390k.

Sorry if my explanations suck, I'm not great at explaining my thought process

Find the root that is a real number. rootindex 4 startroot 4096 endroot

Answers

the answer would be C.

Answer: 8

Step-by-step explanation:[tex]\sqrt[4]{4096}[/tex]

We need to factor this, so

[tex]4096|2\\2048|2\\1024|2\\512|2\\256|2\\128|2\\64|2\\32|2\\16|2\\8|2\\4|2\\2|2\\1[/tex]

[tex]4096 = 2^{12}[/tex]

We have to remember that [tex]x^{n+m}=x^{n}.x^{m}[/tex]

This way, we have [tex]\sqrt[4]{4096}=\sqrt[4]{2^{12}} = \sqrt[4]{2^{4}.2^{4}.2^{4}}  = 2.2.2=8[/tex]

what seperates the places larger than 1 from those that are fractions of 1 such as tenths,hundreths

Answers

the decimal point separates them.
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