Let R be a commutative ring with 1. Let M (R) be the 2 2 matrix ring over R and R[x] be the polyno- mial ring over R. Consider the subsets a b 0 s={[*]IGUER} {]a,bR} S and 2={[88] INSER} J a, a 0 of M (R), and consider the function 6 : R[x] M(R) given for any polynomial p(x) = co+cx++x R[x] by C1 (()) = [ % % ] 0 Show that S is a commutative unital subring of M(R).

We have to show S is a commutative unital subring of M(R).We are given, M(R), a 2 2 matrix ring over R, and R[x] the polynomial ring over R. We have, [tex]S=\{ \left[\begin{array}{ccc}a&b\\0&a\end{array}\right]: a,b \in R \}[/tex]and : R[x] M(R) such that (P(x))= [tex]\left[\begin{array}{ccc}C_0&C_1\\0 & C_0\end{array}\right][/tex] where P(x)= [tex]C_0+C_1x+C_2x^2+.............+C_nx^n[/tex]. We have to show S is a commutative unital subring of M(R). We first have to show is a ring homomorphism. Let p(x)= [tex]a_0+a_1x+a_2x^2+.............+a_nx^n[/tex]and q(x)= [tex]b_0+b_1x+b_2x^2+.............+b_mx^m[/tex]1) (p(x)+q(x)) = [tex]\left[\begin{array}{ccc}a_0+b_0&a_1+b_1\\0 & a_0+b_0\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}a_0&a_1\\0 & a_0\end{array}\right]+\left[\begin{array}{ccc}b_0&b_1\\0 & b_0\end{array}\right][/tex] = (p(x))+(q(x))2) (p(x)[tex]\cdot[/tex]q(x)) = [tex]\left[\begin{array}{ccc}a_0b_0&a_1b_0+b_1a_0\\0 & a_0b_0\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}a_0&a_1\\0 & a_0\end{array}\right]\cdot\left[\begin{array}{ccc}b_0&b_1\\0 & b_0\end{array}\right][/tex] = (p(x)) [tex]\cdot[/tex] (q(x))Now, we have (R[x])= {(p(x)): p(x)[tex]\in[/tex] R[x]} = [tex]\{ \left[\begin{array}{ccc}a_0&a_1\\0&a_0\end{array}\right]: a_0,a_1 \in R \}[/tex] = SWe have proved, : (R[x])M(R) is a homomorphism (R[x]) is a subring of M(R) S is subring of M(R) as (R[x]) =S Also, (1)= [tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex] is unity in S. S is a commutative unital subring of M(R).Therefore, S is a commutative unital subring of M(R).Learn more about subring here:https://brainly.com/question/31975728#SPJ4

Mathematics High School

Let R be a commutative ring with 1. Let M₂ (R) be the 2 × 2 matrix ring over R and R[x] be the polyno- mial ring over R. Consider the subsets a b 0 s={[*]IGUER} {]a,b€R} S and 2={[88] INSER} J a, a 0 of M₂ (R), and consider the function 6 : R[x] → M₂(R) given for any polynomial p(x) = co+c₁x+···+²₂x² € R[x] by C1 (()) = [ % % ] 0 Show that S is a commutative unital subring of M₂(R).

Answers

Answer 1

We have to show S is a commutative unital subring of M₂(R).

We are given, M₂(R), a 2 × 2 matrix ring over R, and R[x] the polynomial ring over R. We have,

$S=\{ \left[\begin{array}{ccc}a&b\\0&a\end{array}\right]: a,b \in R \}$

and Ф: R[x] → M₂(R) such that Ф(P(x))= $\left[\begin{array}{ccc}C_0&C_1\\0 & C_0\end{array}\right]$ where

P(x)= $C_0+C_1x+C_2x^2+.............+C_nx^n$. We have to show S is a commutative unital subring of M₂(R). We first have to show Ф is a ring homomorphism.

Let p(x)= $a_0+a_1x+a_2x^2+.............+a_nx^n$

and q(x)= $b_0+b_1x+b_2x^2+.............+b_mx^m$

1) Ф(p(x)+q(x)) = $\left[\begin{array}{ccc}a_0+b_0&a_1+b_1\\0 & a_0+b_0\end{array}\right]$

= $\left[\begin{array}{ccc}a_0&a_1\\0 & a_0\end{array}\right]+\left[\begin{array}{ccc}b_0&b_1\\0 & b_0\end{array}\right]$

= Ф(p(x))+Ф(q(x))

2) Ф(p(x)$\cdot$q(x)) = $\left[\begin{array}{ccc}a_0b_0&a_1b_0+b_1a_0\\0 & a_0b_0\end{array}\right]$

= $\left[\begin{array}{ccc}a_0&a_1\\0 & a_0\end{array}\right]\cdot\left[\begin{array}{ccc}b_0&b_1\\0 & b_0\end{array}\right]$

= Ф(p(x)) $\cdot$ Ф(q(x))

Now, we have Ф(R[x])= {Ф(p(x)): p(x)$\in$ R[x]}

= $\{ \left[\begin{array}{ccc}a_0&a_1\\0&a_0\end{array}\right]: a_0,a_1 \in R \}$

= S

We have proved, Ф: (R[x])→M₂(R) is a homomorphism

⇒ Ф(R[x]) is a subring of M₂(R)

⇒ S is subring of M₂(R) as Ф(R[x]) =S

Also, Ф(1)= $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$ is unity in S.

⇒ S is a commutative unital subring of M₂(R).

Therefore, S is a commutative unital subring of M₂(R).

Learn more about subring here:

https://brainly.com/question/31975728

#SPJ4

Related Questions

Please Help me please

Answers

It would be the bottom answer assuming the lines are parallel

Find the dual for the following linear programming problem: (i) Maximize Z= 3x + 4y + 5z Subject to: X + 2y + z ≤ 10 7x + 3y + 9z ≤ 12 X, Y, 2 ≥ 0. [2 MARKS] (ii) Minimize Z = y1 + 2y2 Subject to: 3yi + 4y2 > 5 2y1 + 6y2 ≥ 6 Yi + y2 ≥ 2

Answers

The dual for the given linear programming problems are as follows:

(i) Minimize Z' = 10a + 12b Subject to: a + 7b ≥ 3 2a + 3b ≥ 4 a + 9b ≥ 5 a, b ≥ 0.

(ii) Maximize Z' = 5a + 6b + 2c Subject to: 3a + 2b + c ≤ 1 4a + 6b + c ≤ 2 a + b ≤ 0 a, b, c ≥ 0.

What are the dual formulations for the given linear programming problems?

In the first problem, we have a maximization problem with three variables (x, y, z) and two constraints. The dual formulation involves minimizing a new objective function with two variables (a, b) and four constraints. The coefficients of the variables and the constraints are transformed according to the rules of duality.

The primal problem is:

Maximize Z = 3x + 4y + 5z

Subject to:

x + 2y + z ≤ 10

7x + 3y + 9z ≤ 12

x, y, z ≥ 0

To find the dual, we introduce the dual variables a and b for the constraints:

Minimize Z' = 10a + 12b

Subject to:

a + 7b ≥ 3

2a + 3b ≥ 4

a + 9b ≥ 5

a, b ≥ 0

In the second problem, we have a minimization problem with two variables (y1, y2) and three constraints. The dual formulation requires maximizing a new objective function with three variables (a, b, c) and four constraints. Again, the coefficients and constraints are transformed accordingly.

The primal problem is:

Minimize Z = y1 + 2y2

Subject to:

3y1 + 4y2 > 5

2y1 + 6y2 ≥ 6

y1 + y2 ≥ 2

To find the dual, we introduce the dual variables a, b, and c for the constraints:

Maximize Z' = 5a + 6b + 2c

Subject to:

3a + 2b + c ≤ 1

4a + 6b + c ≤ 2

a + b ≤ 0

a, b, c ≥ 0

The duality principle in linear programming allows us to find a lower bound (for maximization) or an upper bound (for minimization) on the optimal objective value by solving the dual problem. It provides useful insights into the relationships between the primal and dual variables, as well as the economic interpretation of the problem.

Learn more about maximization

brainly.com/question/29787532

#SPJ11

In the equation 6x-2=-4x 2 spencer claims that the first step is to add 4x to both sides

Answers

yes, for your x to be positive and to make it remain on the left hand side you actually have to add 4x to both side to eliminate x from the right hand side.

Please answer this math problem... I will mark you brainliest

Answers

Answer:

18x + 6 = 6(3x + 1)

2x + 4= 2(x + 2)

Explanation:

For 2x +4:

group the common factor

2x + 4

and you'll get 2(x + 2)

For 18x + 6:

You'll do the same thing

18x + 6

and you'll get

6(3x + 1)

Tyrone looked so sad that his mother felt bad.
Tomorrow was his birthday. She smiled to herself.
"Tyrone will be so surprised," she thought. "He has no
idea that we have a puppy waiting for him at Grandma's
house." Tyrone saw his mother smiling to herself and
wondered what she was thinking.
3. Underline the words in the passage that can help you
find the point of view.
4. Which characters' thoughts are in this passage?

Answers

Answer:

3. This would be third person view

4. Tyrone's mother and Tyrone himself

Step-by-step explanation:

3. Explanation: "Tyrone will be so surprised," she thought. "He has no

idea that we have a puppy waiting for him at Grandma's

house." This is third person view because it says "thought" and whilst it is her view point, Tyrone wondered to himself - Tyrone saw his mother smiling to herself and wondered what she was thinking.- therefore, causing it to be third person point of view.

Which of the following ordered pairs is on the linear function 2x + 3y = 6?
(0,3)

(-4, 0)

(3, 0)

Answers

I believe the answer is (3,0)!

at a party, each man danced with exactly three women and each woman danced with exactly two men. twelve men attended the party. how many women attended the party?

Answers

The total number of women who attended the party is 72.

Expression:

An act, process, or instance of representing in a medium (such as words): utterance. freedom of expression. b(1): something that manifests, embodies, or symbolizes something else. this gift is an expression of my admiration for you.

Here we have to find the number of women who attended the party.

Here it is given that 12 men attended the party.

Each woman danced with exactly two men and each man danced with exactly three women.

So we have to find the number of women.

Number of women = 12 × 3×× 2

= 72

Therefore the number of women is 72.

To know more about the expression refer to the link given below:

https://brainly.com/question/24734894

#SPJ4

PLEASE HELP ASAP!!!!

Answers

Answer:

Step-by-step explanation:

3x4=12 not 7

Graph (3,-5) and sslope -1/2

Answers

y = (-1/2)x - 7/2 is the equation of the given point and slope.

To graph the point (3, -5) and a line with a slope of -1/2, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents a point on the line, and m represents the slope.

Plugging in the values, we have:

y - (-5) = (-1/2)(x - 3)

Simplifying:

y + 5 = (-1/2)x + 3/2

Subtracting 5 from both sides:

y = (-1/2)x + 3/2 - 5

y = (-1/2)x - 7/2

Now we have the equation y = (-1/2)x - 7/2, which represents a line with a slope of -1/2 passing through the point (3, -5).

To graph the line, plot the point (3, -5) on the coordinate plane and then use the slope to find additional points. For every 2 units you move to the right, move 1 unit down to find other points. Connect the plotted points to draw the line.

The resulting graph will show the point (3, -5) and a line with a slope of -1/2.

For more question on slope visit:

https://brainly.com/question/16949303

#SPJ8

Determine which function(s) are exponential. Select all that apply.

Answers

B C D are exponential functions

The functions in option B and option C are exponential function.

What is exponential function?

A mathematical function with the formula f (x) = $a^{x}$ is an exponential function. where an is 'a' constant known as the function's base and 'x' is a variable.

Step 1: Exponential function for option B.

The data for the values of x and y are given as

x = 0 1 2 3 4

y = 1/3 1 3 9 27

From the data it can be seen that the value of x goes constant change of '1'.

1 - 0 = 1

2 - 1 = 1

3 - 2 = 1

4 - 3 = 1

And the value of y also have the same ratio,

1/(1/3) = 3

3/1 = 3

9/3 = 3

27/3 = 3

Step 2: Exponential function for option C.

The data for the values of x and y are given as,

x = 0 1 2 3 4

y = 5 5/2 5/4 5/8 5/16

From the data it can be seen that the value of x goes constant change of '1'.

1 - 0 = 1

2 - 1 = 1

3 - 2 = 1

4 - 3 = 1

And the value of y also have the same ratio,

(5/2)/5 = 1/2

(5/4)/(5/2) = 1/2

(5/8)/(5/4) = 1/2

(5/16)/(5/8) = 1/2

Therefore, the functions given in option B and option C are exponential functions.

To know more about the exponential functions, here

https://brainly.com/question/12940982

#SPJ2

10. Set up and evaluate the definite integral for the area of the surface generated by revolving the curve a) (3 pts.)y= 6x 3+ 2x1 ,1≤x≤2, about the x-axis; b) (3 pts.) x= 4y−1,1≤y≤4, about the y-axis.

Answers

The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

To know more about integral follow the link:

https://brainly.com/question/33191486

#SPJ11

The length of the base of an isosceles triangle is x. The length of a leg is 4x-3. The perimeter of the triangle is 129 Find x.

Answers

The value of x in the given isosceles triangle is x = 15

Perimeter of an isosceles triangle: Calculating the value of x

From the question, we are to determine the value of x.

From the given information,

The length of the base of the isosceles triangle is x

Also,

The length of a leg is 4x - 3

Since, the length of the legs of an isosceles triangle are equal,

Then,

The length of the other leg is 4x - 3

Also, form the given information,

The perimeter of the triangle is 129

Thus,

x + 4x - 3 + 4x - 3 = 129

Now, solve for x

x + 4x - 3 + 4x - 3 = 129

Collect like terms

x + 4x + 4x = 129 + 3 + 3

9x = 135

Divide both sides by 9

9x/9 = 135/9

x = 15

Hence, the value of x is 15

Learn more on Perimeter of a triangle here: https://brainly.com/question/24696949

#SPJ1

Explain the steps how to solve 4(x-1)-1=15

Answers

Add to both sides:

Simplify the arithmetic:

Simplify the arithmetic:

Can a set of data have more than one line of best fit? Why or why not?

Answers

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least squares method to arrive at the geometric equation for the line, either though manual calculations or regression analysis software. A straight line will result from a simple linear regression analysis of two or more independent variables. A regression involving multiple related variables can produce a curved line in some cases.

one thanks give me motivation for answering

plz follow me

plz mark me brainliest

HELPP PLSSSSSSSSSS i would really appreciate it

Answers

Applying exponential properties, we have that the solution to the given expression is:

$-\frac{125}{343}$

How do we proceed when a fraction is elevated to the exponent?

When a fraction is elevated to the exponent, we apply the exponent to both the numerator and the denominator.

In this problem, we have that:

The numerator is of 5, hence 5³ = 125.The denominator is of 7, hence 7³ = 343.

Negative base with odd exponent, hence the solution is negative and given as follows:

$-\frac{125}{343}$

More can be learned about exponential properties at https://brainly.com/question/25263760

#SPJ1

What are the x-intercepts of the quadratic function? parabola going down from the left and passing through the point negative 2 comma 0 then going to a minimum and then going up to the right through the points 0 comma negative 2 and 1 comma 0 a (0, −2) and (0, 1) b (0, −2) and (0, 2) c (−2, 0) and (2, 0) d (−2, 0) and (1, 0)

Answers

The x-intercepts of a quadratic function are the points where the function graph intersects the x-axis. To find the x-intercepts of the given quadratic function, we need to determine the values of x when the y-value (or the function value) is equal to 0.

From the given information, we can see that the quadratic function passes through the points (-2, 0) and (1, 0), which indicates that the function intersects the x-axis at x = -2 and x = 1. Therefore, the quadratic function x-intercepts are (-2, 0) and (1, 0).

The correct answers are (d) (-2, 0) and (1, 0).

lydia bought a car for $20,000. it is expected to depreciate at a rate of 10% per year. what will be the value of the car in 2 years? use the formula y=a(1-r) and round to the nearest dollar.

answers:
a. 19,980
b. 16,000
c.16,300
d. 18050

Answers

Answer:

Using the formula y = a(1 - r), where

y is the value of the car after 2 years,

a is the initial value of the car, which is $20,000, and

r is the rate of depreciation, which is 10% or 0.1 per year,

we can calculate the value of the car in 2 years as:

y = 20,000(1 - 0.1)^2

y = 20,000(0.9)^2

y = 20,000(0.81)

y = 16,200

Therefore, the value of the car in 2 years will be $16,200, which is closest to option C, 16,300.

Find the missing term(s) of each arithmetic sequence. 104, □, 99, ...... .

Answers

Answer:

a₂ = 101.5

Step-by-step explanation:

the nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₁ = 104 and a₃ = 99 , then

104 + 2d = 99 ( subtract 104 from both sides )

2d = - 5 ( divide both sides by 2 )

d = - 2.5

then

a₂ = 104 - 2.5 = 101.5

Maya uses 1 1/3 cups of papaya juice for every 3 1/3 cups of carrot juice to make a fruit drink.How many cups of papaya juice would Maya use for 1 cup of carrot juice?

Answers

Answer:

2/5 or 0.4 cup papaya juice per carrot juice

Cam someone help plss

Answers

Answer:

let y=0

3x+6(0)=18

3x=18

x=6

(6;0)

Answer: 3

Step-by-step explanation: If you solve the equation, like I did in the attached image, you will see that the x-intercept is 3.

What is the y intercept of this quadratic? (Picture)

Answers

Answer:

We know that the y intercept is -3 because that is where it intersects! The point for the y intercept is (0, -3)

Step-by-step explanation:

This is the coordinates of the point wher the graph cuts the y axis It is (0,-3)

Find the values of x and y in parallelogram PQRS.

PT=y, TR=4x+1, QT=2y, TS=5x+8

Answers

The values of x and y in parallelogram PQRS are x =2 and y = 9

How to determine the values of x and y in parallelogram PQRS

From the question, we have the following parameters that can be used in our computation:

The parallelogram

On the parallelogram, we have the following readings

PT=y, TR=4x+1, QT=2y, TS=5x+8

Rewrite them as

PT= y

TR = 4x + 1

QT = 2y

TS = 5x + 8

Because the point T is the midpoint of the parallelogram, we have

PT = TR

QT = TS

Substitute the known values in the above equation, so, we have the following representation

y = 4x + 1

2y = 5x + 8

This means that

8x + 2 = 5x + 8

Evaluate the like terms

3x = 6

So, we have

x = 2

Substitute x = 2 in y = 4x + 1

y = 4 x 2 + 1

So, we have

y = 9

Hence, the values are 2 and 9

Answers

The height of the triangle would be

7.2 bc

10x7.2:72

So to find the area of a triangle u have to divide by 2, so

72 divided by 2 is 36, so 7.2 is the height

Triangle ABC is shown below, with the angle measures as marked.
What is the measure of Angle A and B?

Answers

The measure of Angle A and Angle B are 54° and 122° respectively.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle ABC,

The measure of angle A = (n + 20)°

The measure of angle B = (3n - 10)°

The measure of angle C = n°

Now,

The sum of all the angles of the triangle = 180°

So, we can formulate;

(n + 20)° + (3n - 10)° + n° = 180°

Solve for n as;

n + 20 + 3n - 10 + n = 180

5n + 10 = 180

5n = 180 - 10

5n = 170

Divide by 5, we get;

n = 170/5

n = 34

Thus, The measure of angle A = (n + 20)°

= 34 + 20

= 54°

And, The measure of angle B = (3n - 10)°

= 3 x 34 + 20

= 102 + 20

= 122°

Therefore,

The measure of Angle A and Angle B are 54° and 122° respectively.

Learn more about the triangle visit:

https://brainly.com/question/17335144

#SPJ1

The equation of a line is x+3y=14

Answers

Answer:

then slope intercept form would be

y= -1/3 x +14/3

the slope would be -1/3

the y-intercept would be 14/3

Step-by-step explanation:

plz brainliest :)

What is 11 kg in lbs ?

Answers

11 kg is equal to 24.25 lbs. both are unit of measurement of weight.

To convert kilograms (kg) to pounds (lbs), you can use the conversion factor 1 kg = 2.20462 lbs. To convert 11 kg to lbs, you would multiply 11 by 2.20462, which after the calcualtion gives you 24.25 lbs.

it's important to note that lbs and kg are different units of measurement for weight. Pounds are commonly used in the United States and the United Kingdom, while kilograms are used in most other parts of the world.

When converting between different units of measurements, one should be careful as the conversion factors are different for different units of measurements.

To know more about conversion factor click on the link below:

brainly.com/question/30166433#

#SPJ11

What is the relationship between the slopes of two perpendicular lines?

Answers

relation between two slopes of two perpendicular line are equal.

The relationship between the slopes of two perpendicular lines is that the product of the slopes of the two lines is equal to -1.

What are perpendicular lines?

Two geometric objects are perpendicular in elementary geometry if they intersect at a right angle. When two lines cross at a straight angle, they are said to be perpendicular.

The relationship between the slopes of two perpendicular lines is that the product of the slopes of the two lines is equal to -1. Therefore, assuming that there are two lines that are perpendicular to each other such that the slope of the two lines is m₁ and m₂. Therefore, we can write the relation as,

m₁ × m₂ = -1

Hence, the relationship between the slopes of two perpendicular lines is that the product of the slopes of the two lines is equal to -1.

Learn more about Perpendicular lines here:

https://brainly.com/question/18271653

#SPJ2

OLZ HELP I ONLY HAVE 5 MINUTES

The point N lies on the segment MP.

Find the coordinates of N so that MN is 1/5 of MP.

the point k lies on the segment JL

Find the coordinates of K so that JK is 5/7 of JL.

I CANT INSERT THÉ OTHER PHOTO

Answers

The coordinates of N so that line segment MN is 1/5 of line segment MP are (1, 14).

What is a line segment?

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

How to determine the midpoint of a line segment?

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

From the image, we have the following:

Point M = (x₁, y₁) = (-1, 3)

Point P = (x₂, y₂) = (9, -22)

MN/MP = 1/5

Moving along line segment MP from M to P, the value of x increases by 10 (from -1 to 9) and y decreases by 25 (from 3 to -22). Thus, the x-coordinate and y-coordinate of N are given by:

x-coordinate of N = -1 + 1/5(10) = -1 + 2 = 1.

y-coordinate of N = 9 + 1/5(25) = 9 + 5 = 14

In conclusion, the coordinates of N so that line segment MN is 1/5 of line segment MP are (1, 14).

Read more on line segments here: https://brainly.com/question/24659351

#SPJ1

21) True or false: If x) is a linear function with a graph that extends through points at
(-2, 4), (0, 0), and (2. - 4), then it has a relative maximum when x = 4.

Answers

Answer:

true

Step-by-step explanation:

got it right

Select the correct answer.
Over which interval is this function continually decreasing?
f(x) = |4(x - 1)| +2

Answers

Step-by-step explanation:

See figure below .....

Start with the graph of |x| (red) ---this graph is decreasing from - inf to 0

now shift it RIGHT by '1' and multiply it by 4 and shift it up by '2'

this is the blue graph ..... decreasing from - inf to '1'

(-inf, 1]

Select the correct answer.Over which interval is this function continually decreasing?f(x) = |4(x - 1)|

Other Questions

How many moles are there in 80 grams of oxygen gas (O2)? * What role did Henry VIII play in the Reformation?He led the Reformation in Germany.He created the Church of England.He stood trial at the Diet of Worms.He brought reform to Switzerland. Anyone know how to do this???? thanks Present five incidences,as examples, where sports personalities'rights were violated. Explain how your business would engage with the community or other stakeholders in relation to the principle, including specific actions you would take or practices you would put in place to put these principles into practice.COURSE: CSR AND SUSTAINABILITY what was a major provision of the civil rights act of 1964? responses it ended segregation in public education. it ended segregation in public education. it outlawed poll taxes and literacy tests. it outlawed poll taxes and literacy tests. it created equal pay regardless of race. it created equal pay regardless of race. it outlawed segregation in public accommodations. during the month, lathers co. received $468000 in cash and paid out $203000 in cash.if the balance of the cash account is $325000 at the end of the month, what was the cash balance at the beginning of the month? If Real GDP is $9,000, the money supply is $12,000, and velocity is 3, then the price level is O a. 4. O b.2.5. O c3 O d.3.33 some PLEASE help ill give brainliest!! List two explorers who reached Asia fromdifferent directions. allows users to enter text and control the computer with their voice.allows users to enter text and control the computer with their voice. I need help with this can somebody help me please You use substitution to solve a system of equations and, after simplifying the equations, end with an expression that says 0 = 4. What does that say about the the lines and about the number of solutions to the system?Sample Response: Since the statement is false, there are no solutions to the system of equations. This also indicates that the lines are parallel.Check all that you included in your response. The equation is false. False equations indicate no solution. No solution indicates a system with parallel lines.Hope this helps! 5. Your teacher is giving a test worth 100 points. The test contains a total of 40questions. Some questions are worth 2 points and some questions are worth 4points on the test. How many of each type of question are on the test? 30 twopoint questions and 10 four point questions. Harris Clark was admitted to Palm Bay Medical Center with abdominal pain. The following day, after undergoing tests and being diagnosed by the Dr. Blake as having appendicitis, Clark had an appendectomy. A year later, Clark sued Dr. Blake and the medical center claiming they had been negligent for failing to evaluate and treat him in a timely manner. Specifically, Clark claimed that he had been ignored for several hours while awaiting treatment and had suffered severe abdominal pain. He also claimed that the x-ray of his abdomen had not been properly recorded, thereby delaying his treatment. Clark claimed that defendants medical negligence had caused him permanent physical and mental injuries, impairment of his ability to work and earn income, and significant medical expenses. 1. Identify the plaintiff and the defendant in this lawsuit. 2. The attorneys fee arrangement between Clark and his attorney will be most likely be a "contingency fee". What does this mean? 3. A lawsuit is commenced by the service of pleadings. The plaintiff will set forth his claims in the __________________ and the defendant will respond in the _______________. If the defendant fails to respond, the court may enter a __________________________ judgment. How does the conclusion contribute to the overall text? (Paragraphs 11-14) A It discusses how the Holocaust ended and its lasting effects. B It discusses how victims of the Holocaust were able to get justice. C It explains why a tragedy like the Holocaust could never happen again. D It emphasizes that experts will never have an accurate death toll of the Holocaust. 4. Part A A seesaw with the construction shown is being built at a playground. The seating board will be 10 feet long, and the board will make an angle of 30 when it touches the ground. 10feet R Seating Board 300 Central Support Find the height of the central support. Show your work or explain your answer, Round your answer to the nearest tenth of a foot. Under what conditions will the amortization method and the sinking fund method of loan repayment equivalent? The area of a rectangle is given by 10b3-15b2+14b. The width of the same rectangle is given by b-1. Find the length of the rectangle. Remember, the the length times the width of a rectangle is equal to its area. The length of the rectangle is (If there is a remainder r, express it in the form rb-1. ) equivalent equation for x/5+1=-6