The operation is defined on thet set of R by by a*b-1 for all abER Is R Closed under the operation?​

Answers

Answer 1

When the operation is defined on the set of R by a*b-1, it is commutative rather than associative.

what is equation ?

In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, the point-slope form, and the slope-intercept form are the three primary kinds of linear equations. Algebra is used in many equations. When it comes to arithmetic, algebra is used when it's difficult to compute an exact amount.

Given,

a∗b=1+ab,∀a,b∈R

Commutativity a∗b=1+ab

=1+b.a

=b∗a

∵ Set of real numbers is commutative.

So, a∗b=b∗a

∴ is commutative Associativity (a∗b)∗c=(1+ab)∗c

=(1+ab)c

=2+abc

a∗(b∗c)=a∗(1+bc)=1+a∗(a+bc)

=1+a+abc

It is clear that (a∗b)∗c

=a∗(b∗c)

So, * operation is not associative.

So, option (a) is correct.

When the operation is defined on the set of R by a*b-1, it is commutative rather than associative.

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Related Questions

Data definition involves describing the properties of the data that go into each database table, specifically the ____ or columns that make up the database.

Answers

Data definition involves describing the properties of the data that go into each database table, specifically the fields or columns that make up the database.

Database. a collection of related information organized for rapid search and retrieval.Record. a collection of fields that appear as a row in a database or table.The term DATABASE describes a collection of data organized in a manner that allows access, retrieval, and use of that data.

What is a field record table and query?

Field: A field refers to an area within a record which is reserved for a specific piece of data. Eg. Employee ID. Table: Table is the collection of records of specific types. E.g. Employee table is a collection of record related to all the employees.Queries can perform many different functions in a database. Their most common function is to retrieve specific data from the tables.

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Experiments done without replacement will result in:

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When sampling is finished without replacement, each member of a population could also be chosen just once. during this case, the chances for the second pick are full of the results of the primary pick. The events are considered to be dependent or not independent.

lets understand with the help of an Example

You have a good, well-shuffled deck of 52 cards. It consists of 4 suits. The suits are clubs, diamonds, hearts and spades. There are 13 cards in each suit consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king) of that suit.

Sampling without replacement:

Suppose you decide three cards without replacement. the primary card you choose out of the 52 cards is that the K of hearts. you place this card aside and pick the second card from the 51 cards remaining within the deck. it's the three of diamonds. you place this card aside and pick the third card from the remaining 50 cards within the deck. The third card is that the J of spades. Your picks are . Because you have got picked the cards without replacement, you can not pick the identical card twice.

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30) A student has not been to class and must pass a 20 question true/false exam to continue in the course. The student will guess on every question and must get at least 14 correct to pass the test. What is the probability that the student will pass the test

Answers

The probability that the student will pass the test is 0.057

In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli,[1] is the discrete probability distribution of a random variable which takes the value 1 with probability [tex]p[/tex] and the value 0 with probability [tex]{\displaystyle q=1-p}[/tex]. Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. Such questions lead to outcomes that are boolean-valued: a single bit whose value is success/yes/true/one with probability p and failure/no/false/zero with probability q.

The student will pass if he at least answers 14 questions correctly .

This can be written as a Bernoulli distribution function [tex]P(Q=i)= 20C_{i} (\frac{1}{2} )^i(1-\frac{1}{2} )^(20-i)[/tex]

P(Q≥ 14) = P(Q=14) + P(Q=15) + P(Q=16) +P(Q=17) + P(Q=18)+ P(Q=19) +   P(Q=20)

 P(Q=14) = 20[tex]C_{14}[/tex][tex](1/2)^{20}[/tex]

 P(Q=15) = 20[tex]C_{15}[/tex][tex](1/2)^{20}[/tex]

 P(Q=16) = 20[tex]C_{16}[/tex][tex](1/2)^{20}[/tex]

 P(Q=17) = 20[tex]C_{17}[/tex][tex](1/2)^{20}[/tex]

 P(Q=18) = 20[tex]C_{18}[/tex][tex](1/2)^{20}[/tex]

 P(Q=19) = 20[tex]C_{19}[/tex][tex](1/2)^{20}[/tex]

 P(Q=20) = [tex]20C_{20}(1/2)^{20}[/tex]

On summing up all we get,

P(Q≥ 14) = (38760 + 15504 + 4845+ 1140 + 190 + 20 + 1)/2^(20)

= 15115/262144=0.057

Thus the probability that the student will pass the test is 0.057

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Barack is travelling to dubai. he wants to bring $350 cad with him. the conversion rate from cad to uae dirham is 2.94. how much money, in dirham, will barack be able to bring with him?

Answers

Barack be able to bring 1029 dirham with him.

What is currency conversion rate?

The amount of one currency needed to buy items in another is shown by conversion rates.

Currency rates and spot prices on the foreign exchange market are comparable to conversion rates.

In relation to supply and demand, conversion rates are impacted.

Governments and central banks implement policies in response to supply and demand dynamics that affect the conversion rate.

According to the question,

The conversion rate from cad to uae dirham is 2.94

Money, in dirham,  Barack would be able to bring with him,

=(350*2.94) dirham

=1029 dirham

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If the original recipe made 14 pancakes and the cafeteria plans to charge $.50 per pancake, how much money will they make if they sell all of the

Answers

If they sell all the pancakes, they will win $7

how much money will they make if they sell all of the pancackes?

We know that they can make a batch of 14 pancakes, such that each one can be sold for $0.50

Then the total amount that they get if they sell all the pancakes is given by the product:

P = 14*$0.50 = $7

If they sell all the pancakes, they will win $7

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Please help!!! Answer asap!!!

Other than translation, what transformation is used to create this frieze pattern?

180° rotation

horizontal reflection

glide reflection

vertical reflection

Answers

Answer:

Horizontal reflection

Step-by-step explanation:

a math chart that was labeled had these pattern examples with the the translation and transformation.

The planner needs a clearance of 9 feet under the arch has the planner met the minimum

Answers

Yes, the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of the arc is 9.6 feet

How to explain the information?

As we can see that at the mid value, for x=4, the value of f(x)=9.4

It means that the maximum height occurs at mid of the arc where it is height is 9.6 feet above the ground.

It means that the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of arc is 9.6 feet

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Question 5 of 10
Suppose f(x) = x² and g(x)= (1x)
graph of g(x) with the graph of f(x)?
Which statement best compares the
A. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 4.
B. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 4.
C. The graph of g(x) is the graph of f(x) shifted units right.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 4.

Answers

Answer: A

Step-by-step explanation:

See attached image.

Write an equation of a line that passes through (3, -1) and is parallel and perpendicular to y = 6x - 4

Answers

Here,

y=mx+c

the slope of the line 6x+4y= -16 is -20.

if the two lines are perpendicular, the slope of 1st line * slope of second line=-1

the slope of the 2nd line is -1/2

y-y1=m(x-x1)

y-13=-1/2(x- -18)

when you solve, you get the equation of the line as 2y+x=50

In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.

If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.

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The length of the rectangle is 4 times its width. If the
erimeter of the rectangle is 80 m, find the length and
readth of rectangle.

Answers

Answer:

width is 8, length is 32

Step-by-step explanation:

* = multiply or times

Let the width be x, then the length would be 4x

Perimeter = 2*length+2*width

80 = 2*4x+2*x

80 = 8x+2x

80 = 10x

8 = x (width)

32 = 4x (length)

i don’t know this answer help pls

Answers

Answer:

c

Step-by-step explanation:

Starting price is $5.50. And for every mile it costs $1.50.

The table shows how far a distance runner has traveled since the race began. what is her average rate of change, in miles per hour, during the interval 0.75 to 1.00 hours?

Answers

The average rate of change will be 5 miles per hour from 0.75 to 1 hour.

The average rate of change is the ratio of change in the y-value or the function value by the change in the x-value.

So according to the question,

the interval between 0.75 to 1 hour is =1-0.75=0.25 hour.

At 0.75 hours elapsed, the distance traveled is 3.5 miles

at 1 hour elapsed, the distance traveled is 4.75miles.

during the interval, 0.75 hours to 1-hour distance travelled=4.75-3.5=1.25 miles.

the average rate of change will be = change in distance traveled during the interval/interval time.

=(4.75-3.5)/(1-0.75)=1.25/0.25=5 miles per hour

Therefore the average rate of change will be 5 miles per hour from 0.75 to 1 hour.

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Answer:

B

Step-by-step explanation:

If you don’t want to read

Given the functions:
f(x) = 6x + 11 and g(x) = x + 6,

which of the following represents f[g(x)] correctly?

A. F[g(x)] = 6x + 47
B. F[g(x)] = 6x + 17
C. F[g(x)] = 6x^2 +47
D. F[g(x)] = 6x^2 + 17

Answers

Answer:

f[g(x)] = 6x + 47

Step-by-step explanation:

The expression f[g(x)] represents a composite function. You need to plug the function g(x) into the "x" value of the f(x) function. Then, you can simplify.

f(x) = 6x + 11               g(x) = x + 6

f[g(x)]                                                    <----- Composition expression

f[g(x)] = 6(x + 6) + 11                             <----- Plug g(x) into x

f[g(x)] = 6x + 36 + 11                             <----- Multiply terms in parentheses by 6

f[g(x)] = 6x + 47                                  <----- Add 36 and 11

Explain and demonstrate the multiplication of complex conjugates using 2+3i and its complex conjugate. Be sure to discuss all steps of the process, including the solution and to which number set it belongs.

Answers

The product of a complex number and its conjugate is (a + i b) · (a - i b), where a and b are real numbers, and the result for the complex number 2 + i 3 is 13.

What is the multiplication of a complex number and its conjugate

Let be a complex number a + i b, whose conjugate is a - i b. Where a and b are real numbers. The product of these two numbers is:

(a + i b) · (a - i b)

Then, we proceed to obtain the result by some algebraic handling:

a · (a + i b) + (- i b) · (a + i b)

a² + i a · b - i a · b - i² b²

a² - i² b²

a² + b²

If we know that a = 2 and b = 3, then the product of the complex number and its conjugate is:

[tex]z\cdot \bar z = 2^{2} + 3^{2}[/tex]

[tex]z\cdot \bar z = 13[/tex]

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PLEASE ASAP: The tennis club has 5 new members each member buys a racet and a tube of balls. If 6 racket cost $186.00 and 6 tubes of balls cost $27.00 how much do the 5 people pay for rackets and balls?

Answers

Answer:

Total cost is $177.50.

Step-by-step explanation:

Rackets:

Divide the cost for racket by 6 to find the cost per racket.

186÷6=31

Multiply 31 by 5 to find the cost for 5 rackets.

31×5=155

$155

Tubes of balls:

Divide 27 by 6 to find the cost per a tube of balls.

27÷6=4.50

Multiply 4.50 by 5 to find the cost for 5 tubes of balls.

4.50×5=22.50

$22.50

Add the amounts for rackets and tubes of balls to find the total cost.

155+22.50=177.50

The total cost is $177.50.

Hope this helps!

Please help me!! due today. Find the volume of the right triangular prism !:)

Answers

Answer: 115.5 cubic m

Step-by-step explanation:

[tex]V=\frac{1}{2}(7)(11)(3)=115.5[/tex]

A friend asked lara to help her divide 456.3 by 100. what should lara tell her? a. move the decimal point three places to the right. b. move the decimal point two places to the right. c. move the decimal point three places to the left. d. move the decimal point two places to the left.

Answers

Answer:

Step-by-step explanation:

The correct answer is D.  If we are multiplying by 10 we would move the decimal place one place to the right to show that the number is now 10 times bigger.  If we multiply by one hundred.  We are getting 100 times bigger, so we would move the decimal place 2 places to the right.

The opposite is true if we are dividing.  Instead of moving the decimal to the right to show that the number is getting bigger, we move to the left to show that the number is getting smaller.  If we are getting smaller by 10, we would move the decimal one place to the left. In this case, we are getting 100 times smaller so we move the decimal two places to the left.

omg please help me!!!

Answers

area = pi * r^2

here, the radius is 2 as its the diameter/2.

so the area is 4pi.

circumference = 2*pi*r.

so the circumference is 4pi as well.

Which of these statements is true for f(x) = 2.3*?
OA. The y-intercept is (0, 1).
OB. The domain is x > 0.
OC. The y-intercept is (0, 2).
OD. It is always decreasing.

Answers

The true statement for f(x) = 2(3)^x is the y-intercept is (0, 2).

How to determine the true statement?

The function is given as:

f(x) = 2(3)^x

Set x = 0 to determine the y-intercept

f(0) = 2(3)^0

Evaluate

f(0) = 2

This means that the y-intercept of f(x) = 2(3)^x is (0,2)

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4. The area of a rectangle is x² + 5x - 24. Which of the following could be one of the dimensions?
O(x-8)
O(x-6)
O(x+8)
O(x-4)

Answers

Answer:

the correct answer is c (x+8)

Step-by-step explanation:

x+8=0

=x= -8

put x= -8 in the given polynomial

(-8)²+5(-8)-24

= 64-40-24

=24-24= 0

If the parabola of the form y = a(x – h)2 + k is always shifted horizontally h units and vertically k units, then its vertex is always

(–h, –k)

(h, k)

(–h, k)

(h, –k)

Answers

The vertex of the transformed parabola with the equation [tex]y=a(x-h)^2+k[/tex] is (h, k).

What are the transformation rules for horizontal and vertical shifts?

The transformation rules are:

Translation: (x, y) → (x + a, y) or (x, y) → (x - a, y) (Horizontal shift)

Translation: (x, y) → (x , y + b) or (x, y) → (x , y - b) (Vertical shift)

Calculation:

It is given that, the transformed parabola is [tex]y=a(x-h)^2+k[/tex]

This parabola has vertex at (h, k).

Since this equation is obtained by shifting h units horizontally and k units vertically.

So, the original vertex is at (h - h, k - k) = (0, 0)

Thus, the equation of the actual parabola is [tex]y=ax^2[/tex]

Therefore, the given transformed equation of parabola has vertex (h, k).

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Answer:

B] (h,k)
The next answer is Vertex (-5, -4)


EDGE2022; Good luck :3!!!!


solve using substitution:

4x- 2y = 6 and x + y = 6


solve using elimination:

4x- 2y = 6 and x + y = 6

Answers

Answer:

Step-by-step explanation:

Substitution is a method that rewrites one of the equations in terms of one variable, and substitutes that in the other equations.

We can easily rewrite x + y = 6 by subtracting y from both sides, giving us

[tex]x = -y+6[/tex]

By putting this equation in place of x in the first equation, we can solve for y:

[tex]4(-y+6)-2y=6[/tex]

[tex]-4y+24-2y=6[/tex] [Distributing 4 into the parentheses]

[tex]-6y+24=6[/tex] [Combining like terms]

[tex]-6y = -18[/tex] [Subtracting 24 from both sides]

[tex]y=3[/tex] [Dividing both sides by -6]

Since we solved for y, we can again substitute by putting it into the second equation.

[tex]x+3=6[/tex]

[tex]x=3[/tex] [Subtracting 3 from both sides]

The solution for this system of equations is (3,3).

Elimination is another method of solving systems of equations. In this method, we multiply one equation such that when both equations are combined, only one variable is left.

We can first multiply both sides of the second equation by 2.

[tex]2x+2y=12[/tex]

Now, let's add both equations to cancel out y.

[tex]4x-2y=6[/tex]

[tex]2x+2y=12[/tex]

[tex]6x=18[/tex]

Now, we can divide 6 from both sides to get the value of x.

[tex]\frac{6x}{6} = \frac{18}{6}[/tex]

[tex]x=3[/tex]

We can now substitute this value into one of the equations to get the value of y. Here, I used the second equation.

[tex]3+y=6[/tex]

[tex]y=3[/tex]

The solution to our system of equations is (3,3).

Please help I NEED IT ASAP

Answers

Answer:

she rides her bike at a rate of 8mph during the second part of the trip.

Step-by-step explanation:

for the first part of the trip, she rides 18 miles in 2 hours which means that she bikes at a rate of 9 miles per hour.

subtracting 18 from 58 gives us the distance she biked during the second part of her trip (which is 40 miles). subtracting 2 from 7 gives us that she biked for 5 more hours. Putting this together means she biked 40 miles in 5 hours.

Now divide miles by hours [tex]\frac{40mi}{5hrs} =8mph[/tex] to get your average rate of change for the second part of the trip.

An arborist examined trees in an orchard to see if they were infected with a virus. 324
out of 540 trees were infected with the virus. What percentage of the trees were infected?

Write your answer using a percent sign (%).

Answers

Answer:

60%

Step-by-step explanation:

324/540 x100=60%

Np!

Describe how the graph of the function g(x) = -5x²-2 is related to the graph of
the function f(x) = 5x².

(A) reflection of f(x) = 5x² across the x-axis and translated left 2 units

(B) translation of f(x) = 5x² down 2 units

(C) reflection of f(x) = 5x² across the x-axis and translated down 2 units

(D) reflection of f(x) = 5x² right 2 units

Answers

Answer:

(C) reflection of f(x) = 5x² across the x-axis and translated down 2 units

there are five chemistry instructors and six physics instructors at a college. if a committee of four instructors is selected,

Answers

The probability of at least one of them being a physics instructor is 120 ways to form the committee.

Probability of Independent Events: The 'At Least One' Rule?

Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.

There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.

Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.

6 select 2; 8 select 3

15×56 =840

We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.

(9) = 20 options for selecting the professors. 3

(3) = 6 options for selecting the professors.

(9) (¹) = 20 × 6 = 120 ways.

Therefore, 120 ways to form the committee.

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Complete question:

There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?

"What is the y-intercept of the line that has a slope of- 4 and passes through the point (A)- 10 (B)-6 (C) 8 (D) 10​

Answers

The y-intercept which is the point at which x = 0 is; A: -10

How to find the y-intercept?

The general form of an equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given the slope;

m = -4

Now, the line passes through the point 0, -10. Thus;

(y - y1)/(x - x1) = -4

(y + 10)/(x - 0) = -4

y + 10 = -4x

y = -4x - 10

Thus, the y-intercept which is the point at which x = 0 is; y = -10

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Solve the equation
3(2x + 2) = 3x - 15​

Answers

3(2x + 2) = 3x - 15

• Using distributive property

[tex]6x + 6 = 3x - 15[/tex]

• Solving the like terms

[tex]6x - 3x = - 15 - 6[/tex]

[tex]3x = - 2 1[/tex]

[tex]x = - \dfrac{21}{3} [/tex]

[tex]x = - 7[/tex]

Hope it helps you any confusions you may ask!

Consider triangle EFG.
F
8
10
12
E
What is the approximate measure of angle G?
G

Answers

The approximate measure of angle G is 41.4°. The correct option is C. 41.4°

Law of cosines

From the question, we are to determine the measure of angle G

From the law of cosines, we can write that

[tex]cos\ G =\frac{e^{2}+f^{2}-g^{2} }{2ef}[/tex]

In the diagram,

e = 12

f = 10

g = 8

Putting the values into the equation

[tex]cos\ G =\frac{12^{2}+10^{2}-8^{2} }{2\times 12 \times 10}[/tex]

[tex]cos\ G =\frac{144+100-64 }{240}[/tex]

[tex]cos\ G =\frac{180}{240}[/tex]

cosG = 0.75

G = cos⁻¹(0.75)

G = 41.4°

Hence, the approximate measure of angle G is 41.4°. The correct option is C. 41.4°

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PLEASE HELP ASAP
Given a graph for the transformation of f(x) in the format g(x) = f(kx), determine the k value.

Answers

The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.

How to find the find the dilation factor

In this problem we have the following relationship bewteen the two quadratic equations: g(x) = f(k · x), which means that for all y the following relationship between f(x) and g(x):

[tex]k = \frac{x_{g}}{x_{f}}[/tex]

Let suppose that y = 3, then [tex]x_{f} = - 5.5[/tex] and [tex]x_{g} = - 1.8[/tex], then the value k is:

k = (- 5.5)/(- 1.8)

k = 3.056

The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.

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Why did the Spanish and Portuguese take a sudden interest in overseas maritime expeditions in the fifteenth century What are three things that make three a great story and how do they all tie together A nursing student is preparing a presentation on minimizing heat loss in the newborn. Which of the following would the student include as a measure to prevent heat loss through convection If the hypotenuse of a right triangle is 2 [tex]\sqrt{3}[/tex] units long and one of the legs is [tex]\sqrt{3}[/tex] units long, then how long is the other leg?[tex]\sqrt{3}[/tex]2[tex]\sqrt{3}[/tex]3 What is the slope of the line that passes through the points ( 8 , 6 ) (8,6) and ( 8 , 9 ) (8,9)? Write your answer in simplest form Maria plots the following points on a coordinate grid. Then, she connects each plotted point to the previous one in the order shown to form a figure. What is the area, in square units, of the enclosed figure? A student is taking an exam with 40 questions on it.To pass the exam she needs to answer 70% of the questions correctly. Unfortunately she answered only 40% of the 15 questions correctly. What percent of the remaining 25 questions does she have to answer correctly to pass the exam? Why have 20th century earthquakes in turkey suggested that some earthquakes beget subsequent earthquakes? Circle S is shown. Line segment R T is a diameter. The length of S T is 4. Sector R S T is shaded.The measure of central angle RST is radians.What is the area of the shaded sector?4Pi units squared8Pi units squared16Pi units squared20Pi units squared The side lengths of a triangle are 9, 12, and 15. Is this a right triangO A. Yes, because 9 + 12 > 15.O B. No, because 9 + 12 15.OC. Yes, because 9 + 12 = 15.OD. No, because 9 + 12 # 15. Questions, are all in picture, please solve The two most basic inventory questions answered by the typical inventory model are. The nurse is monitoring a client who is attached to a cardiac monitor and notes the presence of prominent U waves. The nurse assesses the client and checks his or her most recent electrolyte results. The nurse expects to note which electrolyte value Lemony lemonade has 3,200 gallons of lemonade in wip inventory, with 76% of materials already added. The lemonade is 50% through the process. Assuming all conversion costs are added evenly throughout the process, what are the equivalent units for conversion costs?. Consider the three functions:f(x) = Three-halves(4)x g(x) = Three-halves(4)x h(x) = Three-halves(4)xWhich statements are true about the domain and range of f(x), g(x), and h(x)? Check all that apply.f(x) has a domain of all real numbers.g(x) has a range of y < 0.h(x) has a range of y > 0.g(x) has a domain of all real numbers.h(x) has a domain of x > 0. Fill in the coefficients for the polynomial with degree 3, roots: x = 2, X =-1, and x = 3, and with a leading coefficient of 1 Who did the northern irish catholics hate the most? Type the past tense form of the verb in this sentence. The boys race for the finish line. Discuss the principles of management.Please help Risle Incorporated is a paper supply company. One of its largest customers is Allende Publishers, a publishing house that makes books. If Risle Incorporated decides to acquire and merge with Allende, the merger is most likely to be called a __________ merger. Multiple Choice geographic extension freeze-out vertical horizontal product extension