What is the image of ( − 8 , − 12 ) after a dilation by a scale factor of 1 4 centered at the origin?

Answers

Answer 1

The image of 8,12 after dilation by a scale factor of 1/4 will be 2,3.

What is dilation?An object can grow in size while preserving its shape through a process called dilation. The object's size can go up or down depending on the scale factor. The scale factor is defined as the ratio of the new image's size to the old image's size. decision-making. A dilation in mathematics is a function f from a metric space M into itself that fulfills the formula d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real number. A resemblance of the space exists in Euclidean space when a dilation like this occurs.

Given that the image of (8,12) after dilation by a scale factor of 1/4 centered at the origin.

The image of the dilated point will be:-

x : - 8 ⇒ 8 / 4 = 2

y : - 12 ⇒ 12 / 4 = 3

Therefore, the image of 8,12 after dilation by a scale factor of 1/4 will be 2,3.

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Related Questions

the rate of college enrollment immediately after high school completion was 67

Answers

The statement " Rate of college enrollment immediately after completing high school was 67% by 1997" is an example of (a) Descriptive Statistics.

The Descriptive statistics involves the use of measures, such as averages, proportions, and frequencies, to summarize and describe the main features of a set of data.

In this statement, the rate of 67% is a summary statistic that describes the proportion of high school graduates who enrolled in college immediately after completing high school in 1997.

Whereas; the inferential statistics involves making inferences or predictions about a population based on a sample of data.

The statement provides a summary statistic for the rate of college enrollment for a specific year, 1997, but it does not provide any inferences or predictions about the rate of college enrollment for other years or other populations , so it denoted a Descriptive Statistics .

The given question is incomplete , the complete question is

What type of Statistics does the statement "the rate of college enrollment immediately after high school completion was 67" represents ?

(a) Descriptive

(b) Inferential

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The population of a town is 7,000, and it grows at a rate of 4.6% per year. What will the population be in 10 years?

Answers

Answer:

10,975

Step-by-step explanation:

If you multiply 7,000 by 0.046 10 times and added them together, it would be 10,975

Answer:

10975

Step-by-step explanation:

express the following limit as a definite integral: limn→[infinity]∑i=1ni8n9=∫baf(x)dx

Answers

The limit of the definite integral will be limn→[infinity]∑i=1ni8n9 = ∫baf(x)dx = ∫abxdx = [x^2/2]ab = (b^2/2 - a^2/2).

We can use the Riemann Sums method to find the definite integral representation of the given limit.

Given: limn→[infinity]∑i=1ni8n9 = ∫baf(x)dx

Step 1: Define the function f(x) = x.

Step 2: Divide the interval [a, b] into n equal subintervals with the width of (b-a)/n. Let xi = a + i(b-a)/n be the right endpoint of the i-th subinterval.

Step 3: Evaluate the value of the sum for n subintervals, ∑i=1ni8n9. This is the Riemann Sum for the function f(x) = x over the interval [a, b].

Step 4: Let n tend to infinity. The limit of the Riemann Sums as n approaches infinity is the definite integral of the function f(x) = x over the interval [a, b].

Thus, limn→[infinity]∑i=1ni8n9 = ∫baf(x)dx = ∫abxdx = [x^2/2]ab = (b^2/2 - a^2/2).

Note: To make the calculation more precise, we need to choose the values of a and b such that the limit of the Riemann Sums will be a definite value. However, in this case, we have not been given any specific values of a and b, so we have used general values for the purpose of demonstration.

Therefore, the limit of the definite integral will be limn→[infinity]∑i=1ni8n9 = ∫baf(x)dx = ∫abxdx = [x^2/2]ab = (b^2/2 - a^2/2).

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2 x minus 7 over 4 = x plus 3 over 3

Answers

Answer:

we have

Remember that

Multiply by both sides

Simplify

The formula to solve a quadratic equation of the form is equal to

in this problem we have

substitute in the formula

therefore

the answer is the option

x = negative 4 over 3 and x = 5

a 10 foot ladder is leaning against a wall. the ladder will be sturdy if the angle it makes with the wall is between pi/12 and pi/6. how high up the wall can the ladder make contact with the wall

Answers

The ladder can reach up to approximately 6.12 feet on the wall while still being sturdy.

To find the height up the wall that the ladder can make contact with, we need to use the Pythagorean theorem. Let's call the height up the wall h and the distance from the wall to the foot of the ladder d. We know that the ladder is 10 feet long, so we can write:

d² + h² = 10²

Next, we use the angle constraints to relate d and h. The angle the ladder makes with the wall is between π/12 and π/6, so we can use the tangent function to write:

tan(π/12) < h/d < tan(π/6)

Solving for h, we have:

d × tan(π/12) < h < d × tan(π/6)

Finally, to find the maximum height the ladder can reach, we need to find the maximum value of d while still satisfying the inequality. We know that d + 10 = h / tan(π/12), so we can substitute and simplify:

d × tan(π/12) < d ×× tan(π/6) + 10 × tan(π/12)

d < 10 × tan(π/6) / (tan(π/12) - tan(π/6))

Since tan(π/12) < tan(π/6), the denominator is positive, so d is maximized when it is as large as possible. Plugging in the values, we have:

d < 10 × tan(π/6) / (tan(π/12) - tan(π/6)) = 10 × 2 / (√3 - 2) ≈ 9.35

Finally, the maximum height the ladder can reach is:

h = d × tan(π/12) < 9.35 × tan(π/12) ≈ 6.12 feet

So the ladder can reach up to approximately 6.12 feet on the wall while still being sturdy.

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(12 pts.) a. p(-1.45 < z < .98) = ? b. p(z > -.68) = ? c. the area left of z is .0427. what is z ?

Answers

Probability (p) of a) Φ(.98) - Φ(-1.45), b) 1 - Φ(-.68) and c) standard normal variable (z) is Φ^(-1)(.0427).

In these questions, z refers to a standard normal variable with mean 0 and standard deviation 1. The cumulative distribution function (CDF) of a standard normal variable can be used to find probabilities for given intervals.

a) To find the probability that -1.45 < z < .98, we can use the CDF to find the area under the standard normal curve between these two values:

p(-1.45 < z < .98) = P(z < .98) - P(z < -1.45) = Φ(.98) - Φ(-1.45)

b) To find the probability that z > -.68, we can use the CDF to find the area under the standard normal curve to the right of this value:

p(z > -.68) = 1 - P(z < -.68) = 1 - Φ(-.68)

c) To find the value of z for a given area to the left of z, we can use the inverse CDF (also called the quantile function) of a standard normal variable, denoted as Φ^(-1)(p). This gives us the value of z such that the area to the left of z is equal to p.

p = .0427, so z = Φ^(-1)(.0427).

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11. Write an expression with all fractional
terms that applies four properties of
multiplication to simplify the expression to
one term, Include at least one term being
divided. Show your work and explain how
your expression simplifies.

Answers

The statement claims that the phrase may be reduced to the single fractional term 8/5.

What is fundamental expression?

Expressions serve as the fundamental construction blocks of Statements since every BASIC word is composed of both expressions and keywords (such as GOTO, TO, and STEP). Therefore, in addition to basic mathematical operations and boolean expressions (such as 1 + 2,) expressions can also include functions, constants, and lvalues (scalar constants or arrays).

Let's use the expression: (2/3) x (4/5) ÷ (1/6)

Using the four properties of multiplication:

Associativity: (2/3) x (4/5) ÷ (1/6) = (2/3) x (4/5) ÷ (1/6)

Commutativity: (2/3) x (4/5) ÷ (1/6) = (4/5) x (2/3) ÷ (1/6)

Distributivity: (4/5) x (2/3) ÷ (1/6) = 4/5 x (2/3 ÷ 1/6) = 4/5 x (12/6) = 4/5 x 2

Identity: 4/5 x 2 = 4/5 x 2 = 8/5

As a result, the equation is reduced to the fraction 8/5.Each fractional term in the equation is streamlined using the characteristics of multiplication until only a fractional term is left.

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after the pool was full helens little brotherand his friend splashed g gallon of water out of the pool. there are 7 7/ gallons still left in the pool. write and solve an euation to find how much water was splashed out of the pool.

Answers

The equation for the splash is given by y=1(7/8) x

How much water was splashed out of the pool?

Where y is the amount of water is the pool and x is the number of trips Helen has made.

To fill the pool, Helen must make 6 trips.

The amount of water is the pool y is given by

y=1 (7/8)x

Where x is the number of trips Helen has made. If we wish to find out how many trips she needs to make to fill 10 1/2 gallons in the pool, we solve for x:

y = 10 1/2 = 1(7/8) x

10 1/2 = 10.5 and 1 *7/8) = 1.875.

Thus, 10.5 = 1.875 x

x = 10.5/1.875

= 5.6

Since 5.6 trips makes no sense, we must round up to 6.

Thus, the answer is 6 trips.

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which expression is equivalent to 6x + 2 - 3x

Answers

Answer: 3x+2

Step-by-step explanation:

6x+2-3x

3x+2

PLEASE HELP MEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

every corner here is 90⁰,because it says so.

QRP would be 90-56 =34⁰ and the opposite corner is the same,so 34⁰

Answer:

Step-by-step explanation:

KRL = QRP, so finding QRP can get us our answer. We were given 56 and 90 because 90 is the degree of a right angle.

A straight line is 180 degrees.

If we subtract 90 and 56 from that 180, we'll find out QRP

180-90=90

90-56=34

Since QRP = 34, that means KRL does also

Gerad's DVD club charges a $10 annual fee and then $2 per DVD purchased. Karen's DVD club charges a $15 annual fee and then $1 per DVD purchased. After purchasing how many DVDs will Gerad and Karen pay the same amount?

Answers

Answer: 5

Step-by-step explanation:

Gerad's DVD club costs = Karen's DVD costs = y

Gerad - y = 2x + 10

Karen - y = x +15

2x + 10 = x + 15

x = 5

Problem No. 8
A rectangular schoolroom floor can be covered by 2400 square tiles. If the tiles are 5cm longer and
5cm wider, 1350 tiles are needed.
If none of the tiles are cut, what is the area of the floor in m²?

Answers

The area covered by the tiles is 54 square meters.

How to determine the area of a set of tiles

In this problem we find that 2400 square tiles can cover a rectangular school room and 1350 square tiles if each tile is 5 centimeters longer and 5 centimeters wider. Algebraically speaking, this situation is represented by following formula:

2400 · x² = 1350 · (x + 5)²

Where x is in centimeters.

First, expand and simplify by algebraic properties:

2400 · x² = 1350 · (x² + 10 · x + 25)

2400 · x² = 1350 · x² + 13500 · x + 33750

1050 · x² - 13500 · x - 33750 = 0

Second, find the roots of quadratic equation by quadratic formula:

x₁ = 15 or x₂ = - 15 / 7

Since lengths are positive variables, then only valid solution is x = 15 cm.

Third, calculate the area covered by the tiles:

A = 2400 · (15 cm)²

A = 540000 cm² (54 m²)

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a man is 6’4 tall and weighs 226 lbs. if the max weight for a person at this height is 204lbs, what % overweight is he?

Answers

The man is approximately 10.78% overweight for his height.

To calculate the percentage overweight, you can use the following formula:

Percentage overweight =(Actual Weight−Max Weight)/max weight × 100

Given the information you provided:

Actual Weight = 226 lbs

Max Weight = 204 lbs

Substitute these values into the formula:

Percentage over weight = (226-204)/204 ×100

=22/204×100

=10.78%

Hence, the man is approximately 10.78% overweight.

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An engineer and his helper can do a certain job in 5 hrs. On a given day, they work together for 2 hrs then the helper left and the engineer finishes the rest of the work in 4 more hours. How long will it take for the engineer to do the job alone? 6.7 hrs 15 hrs

Answers

The engineer would take 8.5 hours to do the job alone, which is 3.5 hours more than when the helper was there. This is because the engineer is doing the same amount of work.

The engineer and his helper can do the job in 5 hours with amount of both working together. However, if the helper leaves, the engineer will have to work alone to finish the job. The engineer worked with the helper for 2 hours and then finished the job in 4 more hours, so the total time taken was 6 hours. To calculate how long it would take the engineer to do the job alone, we subtract the 2 hours the helper was there from the 6 hours total that it took to finish the job. This leaves 4 hours that the engineer would have to work alone, so the engineer would take 8.5 hours to do the job alone. This is 3.5 hours more than when the helper was there.

The complete question: An engineer and his helper can do a certain job in 5 hrs. On a given day, they work together for 2 hrs then the helper left and the engineer finishes the rest of the work in 4 more hours. How long will it take for the engineer to do the job alone?

A)6.7 hrs

B) 15 hrs

C) 12 Hrs

D) 8.5 hrs

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Use the line on the graph to write an equation that represents the function.

y = x+

Answers

Answer:

y = -3x - 1

Step-by-step explanation:

We can represent the given line using an equation in slope-intercept form

[tex]y = mx+b[/tex]

In this form, [tex]m[/tex] is the line's slope, and [tex]b[/tex] is the y-coordinate of the point on the line when it touches the y-axis (its y-intercept).

First, we can solve for the line's slope using two points on the line and the formula m = rise / run. We can use the points (0, -1) and (1, -4), whose coordinates correspond to (x₁, y₁) and (x₂, y₂).

[tex]m = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \dfrac{-4 - (-1)}{1 - 0}[/tex]

[tex]m = \dfrac{-4 + 1}{1}[/tex]

[tex]m = -3[/tex]

So, the slope (m) of this line is -3.

We can plug that value into the model for slope-intercept form.

y = -3x + ▢

Now, we have to identify the line's y-intercept (the point on the line when it touches the y-axis). It is (0, -1). Finally, we can put the y-coordinate of that point into slope-intercept form equation.

y = -3x - 1

A linear relationship is given in the table.
x y
4 11
2 7
0 3
−2 −1
What is the slope of the relationship?
(A)−3
(B)−2
(C)2
(D)3

Answers

Answer:

Step-by-step explanation:

slope = diff in Y / diff in X

-4/-2 = 2

Answer: The answer is C

Step-by-step explanation:

First you need to calculate the difference between the data for x and the data for y. Lets start with the x axis.

X axis:

4 - 2 = 2

This means the the difference between each x point is -2.

Now for the y axis.

Y axis:
11 - 7 = 4

7 - 3 = 4

This means the the difference between the y axis points is -4

Now use rise over run to find the slope.

The rise is always the y coordinates and the run is always the x coordinates

So divide the difference of y by the difference of x.

-4/-2 = 2

The answer is C.

Select the correct answer from each drop-down menu. Bob uses two sizes of square tiles, tile A and tile B, to tile his bathroom. The area of tile A is 20 square inches, and the area of tile B is 24 square inches. The length of tile is greater than the length of tile by approximately inches.

Answers

Area of the square figure is equal to the square of one of its sides. The difference in the length of the two tiles is 0.4 meters.

What is the area of the square?

The area of the square figure is equal to the square of one of its sides.

Area of the square Tiles = (length of one side)²

We know that the area of a square is the square of one of its lengths, therefore, the length of each of the square tiles can be written as,

Area of the square Tiles = (length of one side)²

Length of the Tile A

Area of the square Tiles = (length of one side)²

√(Area of the square Tiles) = length of one side

Since, Area of the square tiles A is 20

Thus,

Length of tile A = √20 = 4.5 inches Approx.

Length of Tile B

Area of the square Tiles = (length of one side)²

√(Area of the square Tiles) = length of one side

Since, Area of the square tiles B is 20

Thus,

Length of tile B = √24 = 4.9 inches Approx.

Thus, the difference between the length of the two tiles can be written as,

Difference = 4.9 - 4.5

Difference = 0.4 inches

Hence, the difference in the length of the two tiles is 0.4 meters.

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Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The
hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4
people. Hudson reserved twice as many large rooms as small rooms, which altogether
can accommodate 66 guests. Write a system of equations that could be used to
determine the number of small rooms reserved and the number of large rooms
reserved. Define the variables that you use to write the system.

Check picture for full question.

Answers

Let the number of small rooms = x. Let the number of large rooms = y. and the system of equation is y = 2x and 3x + 4y = 66.

What is system of equation?

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations solved by an identical set of variables is called a scheme of linear equations."

Let the number of small rooms = x.

The number of large rooms = y.

The people that can be accommodated in small room = 3x.

The people that can be accommodated in large room = 4y.

Hudson reserved twice as many large rooms as small rooms, this is represented as:

y = 2x

The total accommodated guests are 66, this is represented as:

3x + 4y = 66

Hence, Let the number of small rooms = x. Let the number of large rooms = y. and the system of equation is y = 2x and 3x + 4y = 66.

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find the coordinates of point p along the directed line segment from j(-4,12) to k(10,-9) that partitions the segment in a ratio of 3:4

Answers

Answer:

Step-by-step explanation:

By graphing the line, it is easy to see that the point (4,10) will partition the line in a ratio of 3:4.

By graphing the line, it is easy to see that the point (4,10) will partition the line in a ratio of 3:4.You could also calculate this by finding the difference in x and y coordinates of the given points, and partitioning those differences in a 3:4 ratio on a number line.In this case,X coord difference: 12 - (-2) = 14Y coord difference: 18 - 4 = 14To partition 14 in a 3:4 ratio, we could use a 6:8 ratio.One way to think of it, is that you are "adding" 6 and 8 to the x and y coordinates of the lower coordinate, in the case (-2,4).

two sides of an isosceles triangle are 20 and 30. what is the difference of the largest and the smallest possible perimeters?

Answers

Two sides of an isosceles triangle are 20 and 30. Then the difference of the largest and the smallest possible perimeters is 10.

Determine the difference of the largest and the smallest possible perimeters

These are the specified parameters:

Two sides of an isosceles triangle are 20 and 30.

The perimeter of the largest isosceles triangle

With a side measurement of 30 feet and a base of 20.

Roving = 30 + 30 + 20

= 80

The perimeter of the smallest isosceles triangle

With a side measurement of 20 feet and a base of 30.

Roving = 20 + 20 + 30

= 70

The difference of the largest and the smallest perimeters

= 80 - 70

= 10

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Solve this problem please (image is attached)

Answers

Answer:

the write abs is b

Step-by-step explanation:

5ax+3ax=4ax+12

8ax-4ax=12

4ax=12

ax=12/4

ax=3

x=3/a

y=3.291x 25.232 what is the predictor variable

Answers

The predictor variable is the value of x. It is used to predict the value of the response variable, which is the value of y. By using the equation y=3.291x+25.232, the value of y can be calculated when the value of x is known.

The predictor variable is the value of x, which can be used to predict the value of the response variable, which is the value of y. To do this, an equation is used to find the relationship between x and y. In this case, the equation is y=3.291x+25.232. This equation can be used to calculate the value of y when the value of x is known. To use the equation, the value of x is inserted into the equation, and the result is the value of y. For example, if the value of x is 5, then the equation would be y=3.291x+25.232, which equates to y=41.455. This means that when the value of x is 5, the value of y is 41.455. This equation can be used for any value of x to predict the corresponding value of y.

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Find the least squares approximating line y=zo+zıx for each of the following sets of data points. a. (1, 1), (3, 2), (4, 3), (6,4) b. (2, 4), (4, 3), (7, 2), (8, 1) c. (-1, -1), (0, 1), (1, 2), (2, 4), (3,6) d. (-2, 3), (-1, 1), (0, 0), (1, -2), (2, -4)

Answers

The least squares approximating line y=zo + zıx is y = 1.80 - 1.00x.

Least squares is a method used to approximate the line of best fit for a set of data points.

In the first set of data points, (1, 1), (3, 2), (4, 3), (6, 4), the least squares approximating line for this set of data points is y = 0.78 + 0.84x.

For the second set of data points, (2, 4), (4, 3), (7, 2), (8, 1), the process is the same.

The least squares approximating line for this set of data points is y = 2.47 - 0.18x.

The least squares approximating line for the third set of data points, (-1, -1), (0, 1), (1, 2), (2, 4), (3, 6), is y = 0.33 + 1.33x.

The least squares approximating line for the fourth set of data points, (-2, 3), (-1, 1), (0, 0), (1, -2), (2, -4), is y = 1.80 - 1.00x.

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Alan gets on a moving walkway. This diagram shows Alan's position every 2
2
seconds.

The table below contains graphs that represent different things about his motion.

Drag a label for the y

-axis for each graph.

Answers

An acceleration is said positive when an object speeds up and the acceleration is negative when object slows down.

How to determine the acceleration?

Point A to B object is not moving.

Point B to C object is positive acceleration.

Point C to D object is at constant velocity.

Point D to E object is not moving.

Point E to F object is negative acceleration.

Acceleration:

It is defined as the rate or direction of change in the velocity.

An acceleration is said positive when an object speeds up and the acceleration is negative when object slows down.

In the given a position vs time graph,

From point B to C, object is increasing its velocity thus the acceleration will be positive.

From point E to F, the object is slowing down thus the acceleration will be negative.

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Correct question:

Drag each label to the correct location on the image. Each label can be used more than once.

The position-time graph describes the motion of a moving object. Describe the motion represented by each segment of the graph.

not moving

constant velocity

positive acceleration

negative acceleration

Can anyone factor these equations?

Answers

The factoring of the expressions would yeild;

a) (3x + 1) (x + 2)

b) Can not be factored

c) 2[(4x - 5) (x - 3)]

How do we carry out factoring?

Factoring is the process of finding the prime factorization of an integer, which is finding the prime numbers that multiply together to give the original number. There are several methods for factoring including:

It is important to choose the right method based on the type of number being factored and the problem at hand.

The factoring of the quadratic expressions would give;

a) (3x + 1) (x + 2)

b) Can not be factored

c) 2[(4x - 5) (x - 3)]

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what is the graters common divisor of 3,4 and 5

Answers

The HCF of 3, 4, and 5 is 1. ∴ The most increased numeral that diverges 3, 4, and 5 is 1.

What is divisor?The dividend is the number that is being divided (in this case, 15), and the divisor is the number that is being divided (in this case, 3). The quotient is the end result of division. A number that divides another number is known as a divisor, sometimes known as a factor (written ). Only positive divisors are typically taken into account for integers, despite the fact that any positive divisor's opposite is obviously also a divisor. a list of the (positive) factors that divide a given number. The number you are dividing by is referred to as the divisor in mathematics. The divisor in the equation 24 6 4 is 6.

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On Thursday, he drinks 15 cups of water.
On Friday, he drinks 12 cups of water.

What is the percent change in his water intake?

What is the original amount of water in this problem?

What is the change in David's water intake in this problem?

What is the percent change?

Is it increasing or decreasing?

Answers

Answer:

The original amount of water in this problem is 15 cups. The change in David's water intake in this problem is a decrease of 3 cups. The percent change is a decrease of 20%.

Step-by-step explanation:

pls mark brainliest

the number t of tickets sold at a concert is a function of the ticket cost c. which is the independent and dependant variable? is the domain discrete or continuous?

Answers

The independent variable is the ticket cost (c), and the dependent variable is the number of tickets sold (t).

The domain of the function could be either discrete or continuous, depending on the specific function and the way the ticket prices are set. For example, if the ticket prices are set in increments of $5, the domain would be discrete, and if the ticket prices can take on any value in a certain range, the domain would be continuous.

Domain Type

The independent variable is considered to be the variable that is manipulated or controlled, while the dependent variable is the outcome or result that is affected by the manipulation of the independent variable.

In this case, the ticket cost (c) is the independent variable, because it is the factor that is being controlled or changed, and the number of tickets sold (t) is the dependent variable because it is the outcome that depends on the cost of the tickets.

To determine if the domain is discrete or continuous, you would need to examine the specific function and the way the ticket prices are set. For example, if the ticket prices are set in increments of $5, the domain would be discrete, meaning that it consists of separate, distinct values.

On the other hand, if the ticket prices can take on any value in a certain range, the domain would be continuous, meaning that it consists of all the values in a range without any gaps or interruptions.

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Determine the limits of each of the following sequences, if they exist, or explain why the sequence diverges. You must indicate if you use any standard limits, continuity or l'Hopital's rule. an = (n + 2)^2n/(n^2 - n - 6)^n bn = cosh(3/n) - 1/sinh(2/n) Verify your answers for both limits >>using MATLAB

Answers

The limit of this sequence is equal to the value of the function evaluated at n = ∞.

The limits of a sequence tell us the value that the sequence tends to approach as the number of terms in the sequence increases.

We'll begin with the first sequence,

=> an = (n + 2)²ⁿ/(n² - n - 6)ⁿ.

To determine the limit of this sequence, we must first determine if it is a continuous function.

In this case, we can see that the function is continuous for all values of n, so the limit is equal to the function evaluated at n = ∞.

Next, we'll examine the second sequence,

=> bn = cosh(3/n) - 1/sinh(2/n).

Again, we'll use the standard limit to determine if the sequence is continuous, and we can see that it is.

Therefore, the limit of this sequence is equal to the value of the function evaluated at n = ∞.

To verify our answers, we can use MATLAB to evaluate each function at n = ∞ and compare the results with our limits.

We can also use MATLAB to plot each sequence, which can help us to visualize the behavior of the sequences and confirm our answers.

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double a then subtract 7 from the result

Answers

The algebraic expression of double a then subtract 7 from the result is 7 - 2a

How to determine the algebraic expression

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

double a then subtract 7 from the result

The "double a" can be represented as 2a

So, we have the following representation

Subtract 2a from 7

subtraction means Minus i.e. 0

So, we have

7 - 2a

Hence, the expression is 7 - 2a