Are the following polynomial sets open or closed?

6. (x ^ 2 + x - 4) - (x ^ 2 + x + 8)
7. (2 - x)(1 + 3x)
8. (5b - 3c)(7b - 3c)

Answers

Answer 1

Answer:

All closed.

Addition, subtraction as well as multiplication of polynomials result into another polynomial. Therefore, the set of polynomials is closed under addition, subtraction and multiplication.

Answer 2

Open polynomial set is (x² + x - 4) - (x² + x + 8)

Closed polynomial sets are (2 - x)(1 + 3x) and (5b - 3c)(7b - 3c)

What is polynomial?

A polynomial is an expression consisting of variables and their coefficients, operations of addition, subtraction, multiplication, and positive-integer powers of variables are involved in polynomial. If the result of a polynomial set applying different operations is polynomial then it is closed under that operation.

Given, polynomial sets

(x² + x - 4) - (x² + x + 8)

Applying subtraction operation

x² + x - 4 - x² - x - 8

Subtracting like terms

-12

The result is integer, it is open polynomial set

(2 - x)(1 + 3x)

Applying multiplication operation

2 - x - x - 3x²

= 2 - 2x - 3x²

The result is polynomial, it is closed polynomial set

(5b - 3c)(7b - 3c)

Applying multiplication operation

35b² - 15bc - 21bc + 9c²

= 35b² - 36bc + 9c²

The result is polynomial, it is closed polynomial set

Hence, (x² + x - 4) - (x² + x + 8) is an open polynomial set

(2 - x)(1 + 3x) and (5b - 3c)(7b - 3c) are closed polynomial sets.

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Related Questions

HELP ME OUT PLEASE!!!!!!!!

Which associations best describe the scatter plot?

Select each correct answer

Nonlinear association

Linear association

Negative association

Positive association​

Answers

Answer:

linear association, correct

Answer:

There are two answers: it is Nonlinear association and Linear association

Step-by-step explanation:

Nonlinear association- When comparing two data sets if the data from one set increase, the data from the second set decrease (it basically means a scatter plot that is decreasing).

Linear association- arranged in extending along a straight or nearly straight line.

I also took the test it it was correct.

In a certain chemical the ratio of zinc to copper is 4 to 15. A jar of the chemical contains 345 of copper how many grams of zinc does it contain ?

Answers

Answer:

92.

Step-by-step explanation:

By proportion the mass of zinc = (345/ 15) * 4

= 92.

6. Jasper pays $42.8 for his cell phone. Marco pays $38.15 for his cell phone plan.
How much more does Jasper pay? Do not use a $ sign. Just type in the numbers.

Answers

Answer: 4.65

Step-by-step explanation: 42.80 - 38.15 = 4.65

Where is the blue point on the number line ?

Answers

Answer:

-20

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

one period is 5, so -5×4 = -20

Find the equation of the line shown!!!

Answers

Answer:

y = x + 6

Step-by-step explanation:

Jeremy can row 2/3 of a mile in 1/2 hour how long will it take him to row 1 mile?

Answers

Answer:

It takes 3/4 of an hour to go 1 mile

Step-by-step explanation:

You can do this by setting up a proportion and by using decimals for some fractions

2/3 = 0.66667 Miles

1/2 = 0.5  hours

0.66667/0.5 = 1/x                         Cross multiply

0.66667 * x = 0.5 * 1                     Simplify

0.66667 * x = 0.5                         Divide both sides by 0.66667

x = 0.5 / 0.66667

x =  0.74999625                           Notice when rounded this is 0.75

x = 0.75                                         Now notice that 0.75 as a fraction is 3/4

x = 3/4

Jeremy can row 2/3 of a mile in 1/2 hour then it will take him 3/4 hour to row 1 mile.

If Jeremy can row 2/3 of a mile in 1/2 hour, then the time it takes him to row 1 mile can be found by setting up a proportion:

(2/3 mile) / (1/2 hour) = 1 mile / (x hours)

Cross-multiply:

(2/3) × x = 1 × (1/2)

Now solve for x:

x = (1/2) / (2/3)

x = 3/4

So, it will take Jeremy 3/4 of an hour (or 45 minutes) to row 1 mile.

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Mrs lee bought four times as many ties as wallets. He spent $840 altogether. A wallet cost $50 more than a tie. The total cost of the ties was $184 more than the total cost of the wallets. How many wallets did he buy?

Answers

Answer:

wa

at you ım prenses

Step-by-step explanation:

you ind soluk

Pre college need help with 5

Answers

Answer:

parallel

Step-by-step explanation:

maybe I guess it parallel, cause it not perpendicular

Answer:

Step-by-step explanation:

3x - 8y = 19

    -8y = -3x + 19

        y = (3/8)x - 19/8

32x + 12y = 19

         12y = -32x + 19

             y = (-32/12)x + 19/12

             y = (-8/3)x + 19/12

as the slopes of the lines are negative reciprocals of each other, the lines are PERPENDICULAR

this is really hard help me please

Answers

Use the formula
V = pi(r^2)(h)
r = 3.75, h = 6.21
V = pi(3.75^2)(6.21)
V = pi(87.33)
V = (3.14)(87.33) = around 274
Now you can figure out the rest

What is the value of v?

Answers

By isosceles triangle theorem,

Angle ZXY = Angle ZYX

The sum of the angles in a triangle is 180 degrees.

106 + 2 same angles (-106) = 180 (-106)  (Subtract 106 by both sides)

2 same angles (/ 2) = 74 (/ 2)   (Divide 2 by both sides)

V = 37

Answer:

The value of v is 37°.

Step-by-step explanation:

Given that △ XYZ is an isosceles triangle where both sides have the equal angles. The total angle of △ is 180°. Let ∠ZXY and ∠ZYX be the same angles:

Let ∠ZXY = v, ∠ZYX = v, ∠ XZY = 106°,

∠ZXY + ∠ZYX + ∠XZY = 180°

v + v + 106° = 180°

2v + 106° = 180°

2v = 180° - 106°

2v = 74°

v = 74 ÷ 2

v = 37°

Will mark brainliest, pls help

If you earn both hourly wages and a commission at your job, your gross wages, w, can be calculated with the following equation:

cs + rh = w
where c is your commission rate, s is your total sales in dollars, r is your hourly rate, and h is your hours worked.

Solve for s to rewrite the equation for total sales.



s = c(w + rh)

s = c(w − rh)

s = w + rh/c

s = w − rh/c

Answers

Answer:

None of the answer options are correct

Step-by-step explanation:

cs + rh = w

cs = w - rh

s = (w - rh)/c

The second one could be corrected by exchanging c with 1/c

The last one would be correct with judiciously applied parentheses.

The first and third have too many errors to even bother trying to correct.

answer could also be written

s = w/c - rh/c  

but it is not considered reduced form.

9514 1404 393

Answer:

  (d)  s = (w − rh)/c

Step-by-step explanation:

Undo what is done to the variable. It is multiplied by c and rh is added to that product.

  cs +rh = w . . . . . given

  cs = w -rh . . . . . undo the addition of rh: add -rh to both sides

  s = (w -rh)/c . . . . undo the multiplication by c: divide both sides by c

_____

Additional comment

Each entire side of the equation is divided by c. That means the entire expression (w-rh) is divided by c. It is incorrect to write that division as w-rh/c. The division bar (/) in plain text only refers to the immediately preceding and the immediately following tokens as its operands. When the expression is typeset, the division bar serves as a grouping symbol, showing you the entire numerator.

  [tex]s=\dfrac{w-rh}{c}[/tex]

Please help this is due tomorrow and I have no idea what to do

Answers

Yes for the first one beacuse of the numbers on the graph

Step-by-step explanation:

#1

Yes

If you connect the points plotted, they will form a line and will pass through the origin.

This is indication of the proportional relationship.

The equation of circumference is:

C = 2πr

Since 2π is a constant value, the equation above represents a proportional relationship.

#2AC is the dimeter#3DB is the radius#4Circumference is the perimeter of the circle.


HELLOPPPPPPPPPPPPPPPP

Answers

Answer:

Hello!

Judging by the link you provided I have come up with the correct solution:

x= 61°

y= 29°

Step-by-step explanation:

I will link my work below:

The first step to finding the two solutions it to first identify one of them.

I chose to identify x first.

To identify the value of x in this problem you have to notice that the x value corresponds with the value "29°" to form a perfect right angle, being 90°.

Thus you can simply find the value of x by doing this formula:

x+29°=90°

You then subtract 29° from both sides to simplify, and you come up with the solution

x=61°

Now we need to find the value of y.

To find the value of y I noticed that again, like x, y corresponds with another variable (being x) to form a perfect right angle (90°).

The way I realized this is a perfect right angle is because, as you can see in the picture you provided, the y+x angle are alternate exterior angles with another angle that is 90°.

Thus you can assume that:

x+y=90°

x= 61°

61°+y=90°

You then subtract 61° from both sides to get:

y=29°

What fraction of the rectangle is shaded? PLS PLS PLS help ASAP! Ty

Answers

9514 1404 393

Answer:

  1/3

Step-by-step explanation:

The area of the rectangle is ...

  A = lw = (21)(12)

The area of the shaded triangle is ...

  A = 1/2bh = 1/2(14)(12) = (7)(12)

Then the fraction of the rectangle that is shaded is ...

  (shaded area)/(rectangle area) = (7)(12)/((21)(12)) = 7/21 = 1/3

1/3 of the rectangle is shaded.

How long would it take 100,000 grams of
radioactive iodine, which has a half-life of 60 days, to decay to
25,000 grams? Use the formula N = N() where N is the final amount of the substance, N, is the initial amount, and #
represents the number of half-lives.

Answers

Answer:

t = 2 half-lives = 2*60 days = 120 days

hope this helps

Step-by-step explanation:

The enrollment in summer stuff camp went from 10 people to 28 in 5 days. What was the percent of the increase in enrollment

Answers

Answer:

140%

Step-by-step explanation:

28-10 = 14 person enrolled

14/10 = 140%

A rectangle has a perimeter of 20 inches and an area of 24 square inches. What are the length and width of the rectangle?
5 inches x 4 inches
4 inches x 6 inches
6 inches x 3 inches
3 inches x 8 inches

Answers

Answer:

Length = 6in

Width = 4in

The formula for solving the perimeter of a rectangle is:

P = 2(L+W)

The formula for finding the area of a rectangle is:

A = L x W

If we substitute our values, we will get:

P = 2(6 + 4)

P = 2(10)

P = 20in

A = 6 x 4

A = 24in²


True or False: This table describes a linear function

Answers

Answer:True

Step-by-step explanation:

There is a constant rate of change. For x, it'd be +1. For y, it'd be +3.

Vote brainliest please!

Answer:

true

Step-by-step explanation:

This is because the slope is y= 3x, you can prove that by plugging in the x values, and if they equal the y then that slope is right.

DON’T SEND A LINK!

WHAT IS THE SLOPE OF THIS LINE

THE SLOPE IS NOT 4/1 OR 20/5

Answers

Answer:

slope = -4

Step-by-step explanation:

m=y2-y1/x2-x1

20-0/0-5

20/-5

= -4


Melanie read 52 pages in 1 hours. If she continues reading at the same rate, how
many pages will she read in an hour?

Answers

If she read 52 pages in one hour, then she'll continue at a rate of 52 pages per hour.

Answer:

52 pages

Step-by-step explanation:

Since she reads 52 pages in 1 hour we multiply 52 by the amount of hours she reads.

52 pages times 1 hour equals 52 pages.

52 x 1 = 52

Please help me with the worksheet

Answers

Answer:

9)    a = ¾, vertex: (-4, 2),  Equation: y = ¾|x + 4| + 2

10)  a = ¼, vertex: (0, -3),  Equation: y = ¼|x - 0| - 3

11)   a = -4,  vertex: (3,  1),   Equation: y = -4|x - 3| + 1

12)  a = 1,    vertex: (-2, -2),  Equation: y = |x + 2| - 2

Step-by-step explanation:

Note:

I could only work on questions 9, 10, 11, 12 in accordance with Brainly's rules. Nevertheless, the techniques demonstrated in this post applies to all of the given problems in your worksheet.

Definitions:

The given set of graphs are examples of absolute value functions. The general form of absolute value functions is: y = a|x – h| + k, where:

|a|  = determines the vertical stretch or compression factor (wideness or narrowness of the graph).

(h, k) = vertex of the function

x = h represents the axis of symmetry.

Solutions:Question 9)  ⇒ Vertex: (-4, 2)

Solve for a:

In order to solve for the value of a, choose another point on the graph, (0, 5) and substitute into the general form (equation):

y = a|x – h| + k

5 = a| 0 - (-4)| + 2

5 = a| 0 + 4 | + 2

5 = a|4| + 2

5 = 4a + 2

Subtract 2 from both sides:

5 - 2 = 4a + 2 - 2

3 = 4a

Divide both sides by 4 to solve for a:

[tex]\LARGE\mathsf{\frac{3}{4}\:=\:\frac{4a}{4}}[/tex]

a = ¾

Therefore, given the value of a = ¾, and the vertex, (-4, 2), then the equation of the absolute value function is:

Equation:  y = ¾|x + 4| + 2

Question 10)  ⇒ Vertex: (0, -3)

Solve for a:

In order to solve for the value of a, choose another point on the graph, (4, -2) and substitute into the general form (equation):

y = a|x – h| + k

-2 = a|4 - 0| -3

-2 = a|4| - 3

-2 = 4a - 3

Add 3 to both sides:

-2 + 3 = 4a - 3 + 3

1 = 4a  

Divide both sides by 4 to solve for a:

[tex]\LARGE\mathsf{\frac{1}{4}\:=\:\frac{4a}{4}}[/tex]

a = ¼

Therefore, given the value of a = ¼, and the vertex, (0, -3), then the equation of the absolute value function is:

Equation:  y = ¼|x - 0| - 3

Question 11)  ⇒ Vertex: (3, 1)

Solve for a:

In order to solve for the value of a, choose another point on the graph, (4, -3) and substitute into the general form (equation):

y = a|x – h| + k

-3 = a|4 - 3| + 1

-3 = a|1| + 1

-3 = a + 1

Subtract 1 from both sides to isolate a:

-3 - 1 = a + 1 - 1

a = -4

Therefore, given the value of a = -4, and the vertex, (3, 1), then the equation of the absolute value function is:

Equation:  y = -4|x - 3| + 1

Question 12)  ⇒ Vertex: (-2, -2)

Solve for a:

In order to solve for the value of a, choose another point on the graph, (-4, 0) and substitute into the general form (equation):

y = a|x – h| + k

0 = a|-4 - (-2)| - 2

0 = a|-4 + 2| - 2

0 = a|-2| - 2

0 = 2a - 2

Add 2 to both sides:

0 + 2  = 2a - 2 + 2

2 = 2a

Divide both sides by 2 to solve for a:

[tex]\LARGE\mathsf{\frac{2}{2}\:=\:\frac{2a}{2}}[/tex]

a = 1

Therefore, given the value of a = -1, and the vertex, (-2, -2), then the equation of the absolute value function is:

Equation:  y = |x + 2| - 2

A store pays $65 for a robot and marks the price up by 20%. What is the amount of the
mark-up?

Answers

65 x .20 = $13 $13 is the markup and if added to the initial amount it would be $78 altogether
The answer is 13$ to that


Help no links Pleaseeeeeee

Answers

Answer:

[tex]\huge\boxed{z=6;\ x=12.5}[/tex]

Step-by-step explanation:

If two figures are similar, then corresponding sides are in proportion.

Therefore:

[tex]\dfrac{z}{15}=\dfrac{4}{10}\qquad|\text{cross multiply}\\\\10z=(15)(4)\\\\10z=60\qquad|\text{divide both sides by 10}\\\\\boxed{z=6}[/tex]

[tex]\dfrac{x}{5}=\dfrac{10}{4}\qquad|\text{cross multiply}\\\\4x=(5)(10)\\\\4x=50\qquad|\text{divide both sides by 4}\\\\x=\dfrac{50}{4}\\\\\boxed{x=12.5}[/tex]

th
The Buffaloes scored 20 pointo the first part of the game. The Buffaloes total score at
the end of the game was 35 points.
What is the approximate percentage of the points scored during second part of the
game?
A
15%
43%
C.
57%
D
85%

Answers

The approximate percentage of the points scored during the second part of the  game is 43%

Given the total score at the second part of the game  = 35 points

Score at the first part of the game = 20 points

Amount of score during the second part of the game  = 35  = 20 = 15 points

% score in the second part  = 15/35 * 100

% score in the second part  = 1500/35

% score in the second part = 42.85 ≈ 43%

Hence the approximate percentage of the points scored during the second part of the  game is 43%

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Can someone help me please

Answers

Answer:

sorry i can answer that the asy

Answer:

Q1 - 10080

(sorry couldn't do q2 haha)

step by step;

Determine the intercepts of the line.
Do not round your answers.
y +5 = 2(x + 1)
y-intercept:
r-intercept:

Answers

Answer:

x intercept: (3/2, 0), y intercept: (0, -3)

Step-by-step explanation:

The holding period of property acquired by gift may begin on:

A. The date the property was acquired by the donor only.
B. The date of the gift only.
C. Either the date the property was acquired by the donor or the date of the gift.
D. The last day of the tax year in which the property was originally acquired by the donor.

Answers

Answer:

Step-by-step explanation:

Answer:

The answer is C. Either the date the property was acquired by the donor or the date of the gift.

Step-by-step explanation:

The donor's holding time is included in the holding period connected with the gain basis rule. The loss basis rule's holding period begins on the day of the donation.

The sum of two numbers is 65. The larger number is 5 more than the smaller number. What are the numbers?

Answers

Answer:

30 and 35

Step-by-step explanation:

Put this question into equation form:

Let x be the smaller number, if the larger number is 5 more and the total is 65:

x + 5 + x = 65

2x + 5 = 65

Subtract 5 from both sides

2x + 5 - 5 = 65 - 5

2x = 60

Divide both sides by 2:

2x ÷ 2 = 60 ÷ 2

x = 30

As the larger number is 5 bigger:

30 + 5 = 35

So the two numbers are 30 and 35.

Hope this helps!

Answer:

Small number 30

Large Number 35

Step-by-step explanation:

The sum of x and y is 65. In other words, x plus y equals 65 and can be written as equation A:

x + y = 65

The difference between x and y is 5. In other words, x minus y equals 5 and can be written as equation B:

x - y = 5

Now solve equation B for x to get the revised equation B:

x - y = 5

x = 5 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 65

5 + y + y = 65

5 + 2y = 65

2y = 60

y = 30

Now we know y is 30. Which means that we can substitute y for 30 in equation A and solve for x:

x + y = 65

x + 30 = 65

X = 35

Therefore the large and small number us 35 and 30 respectively.

{3x−5y=4 -2x+6y=18

Please help solve for x and y

Answers

Answer:

hello mam I don't know what to say to someone who makes the way to the way to the way to the way to the way to the way to work now where is my turn to the dark side I will be

find the angle pls it's just 1 question ​

Answers

Answer:

70°

Step-by-step explanation:

isoceles so base angles are 55

55+55 is 110 so 180-110 is 70

Answer:

if the triangle is isosceles

Step-by-step explanation:

traingle angles= 180°

isosceles traingle= base angles are equal

180°-55°-55°= 70°

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