Let K be the set of all constant polynomials in Z[x]. Prove that K is a subring but not an ideal in Z[x].
Answers
If K is a set of all constant polynomials in Z[x], then K is subring but not an ideal in Z[x], because it does not absorb multiplication from Z[x].
The set K, consisting of all constant polynomials in Z[x], is a subring of Z[x] because it is closed under subtraction and multiplication. Any two constant polynomials subtracted or multiplied together result in another constant polynomial.
However, K is not an ideal in Z[x] because it does not absorb multiplication from Z[x]. When a non-constant polynomial is multiplied by a constant polynomial from K, the result is generally a non-constant polynomial, which falls outside of K.
Therefore, while K satisfies the criteria to be a subring, it does not meet the requirements to be an ideal in Z[x].
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Related Questions
f(x) = 2x – 4/?
What are the domain and range
Answers
Answer:
domain
Step-by-step explanation:
range
Given that
x
:
20
=
5
:
x
Calculate the positive value of
x
.
Answers
Answer:
x/20 = 5/x
x^2 = 100
x = 10
Let me know if this helps!
Answer:
X=10 because 5/10 is equal to 10/20 and both values are equivalent to 1/2.
Step-by-step explanation:
HOPE THIS HELPS :D PLEZZZ MARK ME AS BRAINLYEST!!!!!!
Are the given lines parallel, perpendicular, or neither?
3x + 12y = 9
2x - 8y = 4
Answers
Answer:
The line are neither.
Step-by-step explanation:
2x -8y = 4 subtract 2x from both sides
-8y = -2x + 4 Divide all the way through by -8 and simplify
y = \(\frac{1}{4}\)x - \(\frac{1}{2}\)
3x + 12y = 9 Subtract 3x from both sides
12y = -3x + 9 Divide all the way through by 12 and simplify
y = \(\frac{-1}{4}\)x + \(\frac{3}{4}\)
For the lines to be parallel, the slopes (1/4 and -1/4) need to be the same. They are not. They are opposites of each other.
For the lines to be perpendicular, the slopes (1/4 and -1/4) need to be opposite reciprocals of each other. The opposite reciprocal of 1/4 would be -4,
A water supply system is to be installed at a distance of 54 meters using 6 meters long PVC pipe with a diameter of 100mm. determine the number of length of PVC pipe to be used? a. 7 b. 8 c. 9 d. 10
Answers
To determine the number of lengths of PVC pipe to be used, we need to divide the total distance to be covered (54 meters) by the length of each PVC pipe (6 meters) and round up to the nearest whole number.
Number of lengths of PVC pipe = Total distance / Length of each PVC pipe
Number of lengths of PVC pipe = 54 meters / 6 meters
Number of lengths of PVC pipe = 9
Therefore, the number of lengths of PVC pipe to be used is 9.
So, the answer is option c. 9.
The moment of inertia depends on the distribution of masses relative to the axis of rotation. It is a measure of an object's resistance to rotational motion. The formula for the moment of inertia varies depending on the specific shape and distribution of masses.
If you can provide more details about the arrangement of masses and the axis of rotation, I can help you derive the expression for the moment of inertia in terms of m and l.
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can you help me solve this
Answers
9514 1404 393
Answer:
a) $2.40
b) $16.80
c) y = -2.40x +16.80
Step-by-step explanation:
a. Dylan's daily spending is the opposite of the slope of the line on the graph. That slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (4.8 -12)/(5 -2) = -7.2/3 = -2.4
Dylan spends $2.40 at lunch every day.
__
b. The y-intercept can be found from the formula ...
b = y1 -m(x1)
b = 12 -(-2.40)(2) = 16.80
Dylan's dad gives him $16.80 at the beginning of each week.
__
c. The slope-intercept equation is ...
y = mx + b
y = -2.40x +16.80
May someone please help me with this :)
Answers
Answer:
24
Step-by-step explanation:
6+8=14 14+10=24
Kevin runs a legal services company. He charges a registration fee of $150 when a new client is registered. He will then meet with the client to discuss their legal needs and bills they $200 per hour. Write an linear equation that models this relationship.
Answers
A bakery offers a sale price of $2.70 for 3 muffins. What is the price per dozen? The price per dozen muffins
Answers
Answer:
Step-by-step explanation:
i think your asnwer would be 14 dollers but im not to sure
hope this helps
i am so sorry if i am wrong
Which of the following is true regarding the sampling distribution of the mean for a large sample size?
A. It has a normal distribution with the same mean and standard deviation as the population.
B. It has the same shape and mean as the population, but has a smaller standard deviation
C. It has the same shape, mean, and standard deviation in the population.
D. It has a normal distribution with the same mean as the population but with a smaller standard deviation.
Answers
It has a normal distribution with the same mean as the population but with a smaller standard deviation.
For a large sample size, according to the Central Limit Theorem, the sampling distribution of the mean approaches a normal distribution, regardless of the shape of the population distribution. This is true as long as the sample size is sufficiently large (typically greater than 30).
Option A is incorrect because the sampling distribution of the mean does not necessarily have the same standard deviation as the population. In fact, the standard deviation of the sampling distribution of the mean is smaller than the standard deviation of the population, and it decreases as the sample size increases.
Option B is incorrect because while the shape and mean of the sampling distribution of the mean are the same as the population, the standard deviation is smaller.
Option C is incorrect because the standard deviation of the sampling distribution of the mean is smaller than the standard deviation of the population.
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Art walked 4.1 km in preparation for the Community Walk–a–thon. Bill walked 3600 m. How many more metres did Art walk than Bill?
Answers
Answer:
.5 more kilometres.
Step-by-step explanation:
3600 m = 3.6 km. 4.1 is .5 greater than 3.6
First you need to convert 4.1 km into meters.
1 kilometer (kilo=1000) equals 1000 meters, so to convert 4.1 kilometers into meters you need to multiply 4.1 x 1000
4.1 x 1000 = 4,100
4.1 km = 4,100 m
To find out how many more meters art walked than Bill, you need to subtract the amount of meters Bill walked (3600 m) from the amount of meters Art walked (4100 m).
4,100 - 3,600 = 500
Art walked 500 more meters than Bill
Each child in the Martin family decided to save money for the family vacation.
Mrs. Martin asked the children to show how they would spend the money if given $20 each week for 8 weeks.
Which person would have the most money left for the vacation?
Answers
Answer:
The story is not clear enough to provide the answer
Step-by-step explanation:
First of all we do not know how many childen are in the Martin Family
\(20 \times 8\)
=$160
So depending on how each child sends and how many children will determine which kid will have most of the money left
how do i find a functions formula when dealing with word problems?
Answers
how do i find a functions formula when dealing with word problems?
I will be depend on the situation given in the problem
For example :
if the wage is 50
Use the substitutions u= 1/x^2 and v= 1/y^2 to solve the system of equations. express numbers as integers or simplified fractions.
-5/x^2 + 1/y^2 =-16
13/x^2- 1/y^2 =48
Answers
Answer:
-5 u + 1 v = (-16)
12 u - 1v = 48
adding,
7 u = 32
u = 32/7V = (-16) + 5(32/7)
V = (-16) +160/7
V = -112 + 160/7
V = 48/7Can y’all help me with this ASAP please?
Answers
Answer:
x + 3
5
Explanation:
x+3 is the equation for the first line to the left, and f(x)=5 is the second equation for the second line at the top.
An ice field is melting at a rate of M(t)=4-sin^3 t acre-feet per day. How many acre feet of this ice field will melt from the beginning of day 1 (t=0) to the beginning of day 4 (t=3).
Answers
the amount of ice that will melt from the beginning of day 1 to the beginning of day 4 can be found by integrating the rate of melting over that time period.
To find the amount of ice that melts over the time period from t=0 to t=3, we need to integrate the given rate of melting function, M(t)=4-sin^3 t, over that time period. Using the fundamental theorem of calculus, we can find the antiderivative of M(t):
∫M(t)dt = ∫(4-sin^3 t)dt = 4t + (3/4)cos(t) + (1/12)cos^3(t)
Evaluating this antiderivative from t=0 to t=3, we get:
(4(3) + (3/4)cos(3) + (1/12)cos^3(3)) - (4(0) + (3/4)cos(0) + (1/12)cos^3(0))
Simplifying this expression, we get:
12 + (3/4)cos(3) + (1/12)cos^3(3) - (3/4)
Therefore, the amount of ice that will melt from the beginning of day 1 to the beginning of day 4 is approximately 11.56 acre-feet.
we can find the amount of ice that will melt over a given time period by integrating the rate of melting function over that time period. In this case, we found that approximately 11.56 acre-feet of the ice field will melt from the beginning of day 1 to the beginning of day 4.
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An amusement park charges an admission fee of 25 dollars per person. The cost, C (in dollars), of admission for a group of p people is given by the following.
C = 25 p
What is the cost of admission for a group of 3 people?
Answers
Answer:
75 dollars.
Step-by-step explanation:
Each person costs 25 dollars and p=3 we just put this into a equation.
25 × 3 = 75
C = 75
Q1W7 Learning Task 1 (Introduction)
Factoring Polynomials
On the chart below, find a factor in Column B of each of the given polynomials in Column A using the Factor Theorem.
Column A
1. x² + 6x + 8
2. x³ - 7x + 6
3. x³ - 2x² - 5x + 6
Column B
x-3
x-1
x+2
x+3
x+1
Answers
Answer:
Column A Column B
1. x² + 6x + 8 x-3,x+2
2. x³ - 7x + 6 x+1, x+2, x+3
3. x³ - 2x² - 5x + 6 x-1, x+2, x-3
Step-by-step explanation:
Column A Column B
1. x² + 6x + 8 x-3,x+2
2. x³ - 7x + 6 x+1, x+2, x+3
3. x³ - 2x² - 5x + 6 x-1, x+2, x-3
Using Factor theorem we put values of x = ±1,±2,±3 in each of the polynomials unless we get a zero.
1. x² + 6x + 8
= 1+6(1) +8= 15
1. x² + 6x + 8
4+ 12+8 = 24
1. x² + 6x + 8
(-1)² + 6(-1)+ 8
= 1-6+8= 3
1. x² + 6x + 8
(-2)² + 6(-2)+ 8
= 4-12+8= 0
1. x² + 6x + 8
(3)²+ 6(3) +8
= 9+18+8 ≠ 0
1. x² + 6x + 8
(-3)²+ 6(-3) +8
= 9-18+8 =-1
For this polynomial we have x+2= 0 or x=-2, x-3= 0 , x=3
2. x³ - 7x + 6
1-7+6= 0
2. x³ - 7x + 6
(-1)³-7(-1) +6
= 13-1≠0
2. x³ - 7x + 6
(2)³-7(2) +6
= 8-14+6= 0
2. x³ - 7x + 6
(-2)³-7(-2) +6
= -8 +14+6
2. x³ - 7x + 6
(-3)³-7(-3) +6
= -27+21+6 = 0
For this polynomial we have x+1= 0 , x+2 = 0 and x+3= 0, or x=-1,-2,-3
3. x³ - 2x² - 5x + 6
(1)³-2(1)²-5(1)+6
= 0
3. x³ - 2x² - 5x + 6
(-1)³-2(-1)²-5(-1)+6
= -1 -2 +5+6
=8
3. x³ - 2x² - 5x + 6
(2)³-2(2)²-5(2)+6
= 8-8-10+6
=-4
3. x³ - 2x² - 5x + 6
(-2)³-2(-2)²-5(-2)+6
= -8-8+10+6
=0
3. x³ - 2x² - 5x + 6
(3)³-2(3)²-5(3)+6
= 27-18-15+6
=0
3. x³ - 2x² - 5x + 6
(-3)³-2(-3)²-5(-3)+6
= -27-18+15+6
=-14
For this polynomial we have x-1= 0 ,x+2=0, x-3= 0or x=1,-2,3
A 9-ounce box of strawberry gelatin costs $0.90, and a 6-ounce box costs $0.42. What is the difference in
cost (per ounce) between the larger and the smaller boxes?
Answers
Answer:
0.16 per ounce
Step-by-step explanation:
0.16 + 0.42 = 0.58, 0.58 + 0.16 = 0.74, 0.74 + 0.16 = 0.90
Answer:
0.17
Step-by-step explanation:
Kameron wrote the following equation:
4x - (x - 3) = 18
Using the distributive property, what would her next step be?
Answers
Answer:
hope it helps you..........
Heather owns a bakery that makes fruit pies. A whole pie, cut into 8 pieces, is sold for
$10.00. The expression below can be used to determine p, the cost of one piece of pie,
in dollars.
8p=10
What is the cost of one piece of pie?
$0.80
$1.25
$2.00
$8.00
Answers
Answer: $1.25
Step-by-step explanation:
I believe to get p by itself, you would have to divide 8 on both sides, leaving you with p = 1.25. This results in one piece of pie costing $1.25.
Last year Melissa was paid £2200 per month.Last year Natalie was paid £3200 per month. Melissaʼs salary is increased by 35. Natalieʼs salary is increased by 18. Who is paid more each month this year? You must show your workings.
Answers
Natalie is paid more each month this year with £3776.
What is salary ?
Salary is a fixed amount of money paid to an employee by an employer in return for work performed. It is usually paid on a regular basis such as weekly, bi-weekly, or monthly. Salaries are typically based on the employee's job title, level of responsibility and the company's budget and compensation policies.
solution
Melissa's salary this year is £2200 + £2200 * 35/100 = £2970.
Natalie's salary this year is £3200 + £3200 * 18/100 = £3776.
Therefore, Natalie is paid more each month this year with £3776.
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PLZ PLZ PLZ PLZ PLZ HELP HELP
Answers
Part A
Which angles are congruent to 5? Select all that apply.
Part B
If 6=85, what is the measure of 3?
Answers
Part B. 95°
The rectangle below is dilated by a scale factor of 5. Find the perimeter and area of
the rectangle below, as well as the perimeter and area of the dilated rectangle. Figures
are not necessarily drawn to scale.
10
Perimeter of given rectangle
Area of given rectangle
Submit Answer
units
units²
Perimeter of dilated rectangle
Area of dilated rectangle
units
units2
Answers
Area of rectangle = 50 \(unit^2\).
Perimeter of rectangle =30 unit.
Area of dilated rectangle = 1250 \(unit^2\).
Perimeter of dilated rectangle = 150 unit.
What is dilation?
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.
Here the given rectangle length l = 10 unit and width = 5 unit.
Now using formulas,
Area of rectangle = lw square unit.
=> A = 10*5 = 50 \(unit^2\).
Perimeter of rectangle = 2(l+w) unit
=> P =2(10+5) = 2(15) = 30 unit.
Here scale factor= 5
The dilated rectangle length \(l_1\)= 10*5 = 50 unit and
width \(w_1 = 5\times5 = 25\) unit
Now area of dilated rectangle \(A_1\)= \(l_1w_1\) square unit.
=> \(A_1\)= 50*25 = 1250 \(unit^2\).
Perimeter of dilated rectangle \(P__1\) = 2(\(l_1+w_1)\) unit.
=> \(P__1\) = = 2(50+25) = 2(75) = 150 unit.
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one of the five quadratics below has a repeated root. (the other four have distinct roots.) what is the repeated root? \begin{align*}
Answers
Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.
Quadratics representing repeated roots has discriminant equals to zero.
Standard quadratic equation is:
ax² + bx + c = 0
Discriminant 'D' = b² - 4ac
option a. -x²+ 18x + 81
Discriminant
'D' = 18² - 4(-1)(81)
= 324 + 324
= 648
D>0 has distinct roots.
option b. 3x²- 3x - 168
Discriminant
'D' = (-3)² - 4(-3)(-168)
= 9 - 2016
= -2007
D< 0 has distinct roots.
option c. x²- 4x - 4
Discriminant
'D' = (-4)² - 4(1)(-4)
= 16 + 16
= 32
D>0 has distinct roots.
option d. 25x²- 30x + 9
Discriminant
'D' = (-30)² - 4(25)(9)
= 900 - 900
= 0
D = 0 has repeated roots.
Repeated roots are:
x = ( -b ±√D ) / 2a
= [-(-30)±√0 ]/ 2(25)
= 30/ 50
= 3/5.
option e. x² - 14x + 24
Discriminant
'D' = (-14)² - 4(1)(24)
= 196 - 96
= 100
D>0 has distinct roots.
Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.
The above question is incomplete, the complete question is:
One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?
a. -x²+ 18x + 81
b. 3x² - 3x - 168
c. x² - 4x - 4
d. 25x² - 30x + 9
e. x² - 14x + 24
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how much work is done raising an 8 lb mass to a height of 18 ft above the ground? (use decimal notation. give your answer as an exact number.)
Answers
Therefore, the work done in this problem comes out to be 144 ft pound.
Where is the work done?The work a force does is calculated as the product of the object's displacement and the components of the applied force of the object in the displacement direction. Pushing a block with some force and accelerating the body results in work being completed.
Here,
Given : an 8 lb mass
a height = 18ft
So, we find the work done
Using formula
=> Work done = m*g*h
=> Work done = weight * height
=> Work done = 8*18
=> Work done=144 ft pound
Therefore, the work done in this problem comes out to be 144 ft pound.
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The formula for the volume of a cylinder is V = srh.
Solve v = rn for h, the height of the cylinder.
Answers
Answer:
A
Step-by-step explanation:
Have a great summer :)
Help please! What part of the model represents "n" in the
equation?
Answers
Solve and write your answer as a fraction
Answers
Step-by-step explanation:
please mark me as brainlist please
Hello um I need help if anyone could help me with this that would be perfect:))!!
Answers
Answer:
1. If D= whole numbers then the answer is B.0 if it is integers the answer is A.-10
2. The answer is D. That number is an irrational number.
Step-by-step explanation:
Im pretty sure that #1 is B.0, but since there are no labels and i haven't done this in a while, I wasn't quite sure. Sorry.