show that x²-8x+20 can be written in the form (x-a)²+a where a is an integer

This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

Learn more about nonlinear problem: brainly.com/question/31457669

#SPJ11

Answer: A= −2.50x+50

Step-by-step explanation:

A = -2.50x+b

45 = -2.50(2)+b

45 = -5+b

50 = b

A= -2.50x + 50

Correct answer for function f(x) is: x = -√(43/S) for x < 0, and x = -11/2 for x > 0.

We need to analyze the function separately for the cases x < 0 and x > 0.

1. For x < 0, the function is defined as f(x) = Sx². We need to find x such that Sx² = 43.

Sx² = 43
x² = 43/S

Since x < 0, we have x = -√(43/S)

2. For x > 0, the function is defined as f(x) = 10 - 6x. We need to find x such that 10 - 6x = 43.

10 - 6x = 43
-6x = 33
x = -33/6
x = -11/2

Thus, the correct answer is: x = -√(43/S) for x < 0, and x = -11/2 for x > 0.

Learn more about function f(x).

brainly.com/question/28049372

#SPJ11

Answer:

See below

Step-by-step explanation:

1).  A = k / (B^3)   <==== this becomes   A = 512/(B^3)  when you use the                                                                               answer from 2).      (below)

2).     When A = 64  and B = 2 :

           64 = k / (2^3)

              64 = k / 8

                   k = 64*8 = 512

Answer: This is gonna be a long one

1)Winston grows green dragon apples. This year, he shipped 80%of these apples to sell at supermarkets and kept the rest to make cider. Of all the green dragon apples he sold to the supermarkets, only 60% of them were bought. If a total of 420 green dragon apples were bought, how many green dragon apples did Winston keep to make cider?

 Call the number he shipped to the store, N

So .

60N  = 420   divide both sides by  ,60

420 / .60  = N  = 700 were shipped to the stores

But this number was  80%  of the total he grew = T

So

.80T  = 700   divide both sides by  .80

700/.80 = T  = 875

But..he kept 20% of these =   875 * .20  = 175

2)Ms. Forsythe gave the same algebra test to her three classes. The first class averaged 80%, the second class averaged 85%, and the third 89%. Together, the first two classes averaged 83%, and the second and third classes together averaged 87%. What was the average for all three classes combined? Express your answer to the nearest hundredth.

The average  =  total points / number of students

So....total points = average*number of students

Let the total number of students in  each class = x , y  and z

The total number of points the first class amassed  was   80x

The total number of points amased by the second class was  85y

The total number of points amassed by the third class = 89z

So...for the first two classes we have

[ 80x + 85y ] / [ x + y] = 83

80x + 85y = 83x + 83y  subtract  80x, 83y from both sides    

3x = 2y

x = 2/3y

And,,,for the second two classes we have

[ 85y + 89z ]  / [ y + z ]  =  87  

[  85y + 89z ]  = 87 [y + z]

85y + 89z = 87y + 87z      subtract  85y, 87z from both sides

2z = 2y  

y  = z

So...for the three classes.....

Total points by all three classes /  number of class members  = the average for all three classes

[ 80x + 85y  + 89z ] /  [ x + y + z ]   =

[sub for  x and z ]  

[80 (2/3)y  + 85y  + 89y]  /  [ (2/3)y  + y  + y ]  

y [ 80 (2/3)  + 85  + 89 ]  / [  y [( 2/3) + 1 + 1] ]       [cancel the y's ]

[ 80 (2/3) + 85 + 89]  [  8/3 ]

[ 160/3 + 85 + 89 ] /  [8/3] =

[ 160/3  + 255/3 + 267/3]  / [8/3]     multiply  top/bottom by 3

[160 + 255 + 267 ] / 8  =  

85.25  = average for all three classes

Step-by-step explanation:

Hope it helps

Pls mark me as brainliest

Peace out

Answer:

11/20

Step-by-step explanation:

3/4 - 1/5

= 15/20 - 4/20

= 11/20

So, the answer is 11/20

Answer: Trapezoid

Step-by-step explanation:

Answer:

Step-by-step explanation:

Trapezoid square and the down right all the way

Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

To learn more about transportation

https://brainly.com/question/32750280

#SPJ11

The product pick list generated by an order processing system is used by warehouse personnel or fulfillment staff to gather and prepare items for shipment.

The product pick list is a crucial tool in the order fulfillment process. It contains detailed information about the products ordered by customers, such as their names, quantities, and locations within the warehouse. Warehouse personnel or fulfillment staff rely on this pick list to efficiently gather the required items from the shelves or storage areas.

When an order is received, the order processing system automatically generates a pick list based on the products included in the order. This pick list serves as a guide for the warehouse staff, enabling them to quickly locate and pick the items needed to fulfill each order accurately. The pick list typically organizes the items in a logical order, such as by aisle or location, to optimize the picking process and minimize the time spent searching for items.

By using the product pick list, the warehouse personnel can ensure that the correct items are picked and prepared for shipment, reducing the likelihood of errors or mix-ups. This helps streamline the order fulfillment process, improve efficiency, and ultimately deliver a positive customer experience.

Learn more about logical order here: https://brainly.com/question/31039553

#SPJ11

The difference between the left-hand side and right-hand side of a greater-than-or-equal-to constraint is referred to as a slack. Specifically, it represents the amount by which the left-hand side of the constraint can increase while still satisfying the constraint.

In other words, the slack is the surplus of available resources or capacity beyond what is required to satisfy the constraint.

On the other hand, the difference between the optimal objective function value and the right-hand side of a greater-than-or-equal-to constraint in a linear programming problem is referred to as a shadow price. The shadow price represents the increase in the optimal objective function value for each unit increase in the right-hand side of the constraint, while all other parameters are held constant.

Therefore, the shadow price provides valuable information about the economic value of additional resources or capacity that could be allocated to the corresponding activity or resource constraint.

Learn more about greater-than here:

https://brainly.com/question/29163855

#SPJ11

Answer:

Step-by-step explanation:

1. Distribute

3x + 3 = -2x + 2 - 4

2. Simplify

-2x + 2 - 4

2-4 = -2

-2x - 2

3. Solve

3x + 3 = -2x - 2

+2x       +2x

4. Cont. Solving

5x + 3 = -2

     -3     -3

5x = -5

5. Divide by 5

5x = -5

/5      /5

Hope this helped,

Kavitha Banarjee

Answer:

B) \(\$8395.80\)

Step-by-step explanation:

\(A=P(1+rt)\\A=7996(1+0.06\cdot\frac{10}{12})\\A=7996(1+0.05)\\A=7996(1.05)\\A=\$8395.80\)

This is all assuming that r=6% is an annual rate, making t=10/12 years

The regression model (A) underestimates the data based on it since the residual is positive.

When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method.

Simple linear regression is used when there is only one explanatory variable, and multiple linear regression is used when there are numerous variables.

The statistical link between a dependent variable and one or more independent variables can be ascertained using regression.

The independent variable's change is connected to the independent variable's change.

Two major sorts can be broadly distinguished from this. A linear regression. Regression using logit.

A roadrunner's total length and tail length in the given situation is 59.0 cm and 31.1 cm, respectively.

Because the residual is positive, the regression model underestimates the data based on it.

Therefore, the regression model (A) underestimates the data based on it since the residual is positive.

Know more about a regression model here:

https://brainly.com/question/25987747

#SPJ4

Correct question
A roadrunner is a desert bird that tends to run instead of fly. While running, the roadrunner uses its tail as a balance. A sample of 10 roadrunners was taken, and the birds’ total length, in centimeters (cm), and tail length, in cm, were recorded. The output shown in the table is from a least-squares regression to predict tail length given total length. Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?

a. Underestimate, because the residual is positive.

b. Underestimate, because the residual is negative.

c. Overestimate, because the residual is positive.

d. Overestimate, because the residual is negative.

e. Neither, because the residual is 0.

The reason why Jon's lender most likely approved his loan is because;

A: He has been making most payments on time.

There are different reasons why lenders approve money for those who want to borrow but for the sake of this question, we will just access the options.

Read more on giving out loans by financial institutions at; https://brainly.com/question/14997152

Answer:

A

Step-by-step explanation:

Took the test and got it right.

a) Vertical plane not passing through the cone's topmost point - hyperbola.

b) Horizontal plane - circle.

c) Diagonal plane - ellipse or parabola

What is a cone?

A cone is a three-dimensional geometric shape that narrows smoothly from a flat base (typically circular base) to a point called the apex or vertex (which creates an axis to the center of the base).

Cross section of a cone:

A cross section is a representation of a shape's axis of symmetry intersected by a plane. When a plane cuts a solid, such as a cone, cylinder, or sphere, it creates a shape known as a cross-section. Depending on how the plane cuts the cone, the cross-section of a solid, such as a cone, can be a circle, a parabola, or a triangle.

When a cone's cross-section is split horizontally, it is circular.

When a cone is cut vertically, its cross-section is an isosceles triangle, and this plane slices through the center of the cone.

When a cone is cut vertically, the cross-section is parabolic except for the plane running through the center.

To learn more about cross-section, click on the below link:

https://brainly.com/question/29081672

#SPJ1

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

To know more about equation here:

brainly.com/question/29292690

#SPJ11

The correct option is (1) less than 10 times the original distance.The original distance was  30 cm and the new distance is 94.86 cm which is less than 10 times the original.

The force of attraction and repulsion among two charged bodies are directly proportional to a product of their charges but inversely proportional to a square of a distance between them, according to Coulomb's law.

It works along the line that connects the two charges that are called point charges.

The formula for Coulomb's law is-

\(f_{}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{}^{2}}\)

where, q₁ and q₂ are the charges;

d is the distance between them.

Now, according to the question;

Two charges that were initially separated by a particular distance are pushed closer together until force between the two is reduced by a factor of ten.

Coulomb's law of force

\(f_{1}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{1}{ }^{2}}\)

d₁ is the initial distance.

So when charges are separated further, a new force is f₂, which is represented as

\(f_{2}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}^{2}}\)

d₂ is the moved distance

As a result, the given force is decreased by ten times its original value.

Thus, \(f_{2}=\frac{f_{1}}{10}\)

use the expression in both forces

\(\begin{gathered} \frac{f_{1}}{10}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}{ }^{2}} \\\frac{q_{1} q_{2}}{4 \times 10 \pi \epsilon d_{1}{ }^{2}}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}{ }^{2}} \\ \frac{1}{10 \times d_{1}{ }^{2}}=\frac{1}{d_{2}{ }^{2}} \\ d_{2}=\sqrt{10} d_{1}\end{gathered}\)

Now, calculate the moved distance d₂,

\(\begin{aligned}& d_{2}=\sqrt{10} d_{1} \\ & d_{2}=\sqrt{10} \times 30 \\& d_{2}=3.162 \times 30 \\ & d_{2}=94.868 \mathrm{~cm}\end{aligned}\)

The new distance is 94.868 cm.

Therefore, the new obtained distance is less than the 10 times the original distance.

To know more about the Coulomb's law of force, here

https://brainly.com/question/506926

#SPJ4

The complete question is-

Two charges originally separated by a certain distance are moved farther apart until the force between them has decreased by a factor of 10.  Is the new distance

(1) less than 10,

(2) equal to 10, or

(3) greater than 10;

times the original distance? If the original distance was 30 cm.

subtract 5 from both sides -

5x - 7 = -10x + 8

-5 -5

-7 = -15x + 8

subtract 8 from both sides -

-7 = -15x + 8

-8 -8

-15 = -15x

now divide both sides by -15 -

-15/-15 = -15x/-15

The answer: x = 1

(x alone also equals 1)

hope this helps! :)

Answer:

The equation of the circle is (x+3)^2 + (y-4)^2 = 16.

Step-by-step explanation:

The equation of a circle can be calculated if the center and the radius are known. The equation of a circle is given by  (x-h)² + (y-k)² = r²

Where  (h, k) = center coordinates  and r = radius.

1) you can use the following steps:
Step 1: Generate a list of Fibonacci numbers. The Fibonacci Sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding numbers. For example, the sequence begins as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.
Step 2: Divide each Fibonacci number by its previous number in the sequence. For example, dividing 1 by 0 gives an undefined result, so we skip this division. Dividing 2 by 1 gives 2, dividing 3 by 2 gives 1.5, dividing 5 by 3 gives 1.6667, dividing 8 by 5 gives 1.6, and so on.
Step 3: As you continue dividing the Fibonacci numbers, you will notice that the quotient gets closer and closer to the golden number φ. As you reach larger Fibonacci numbers, the quotient will become more accurate.
Step 4: To perform a sample calculation, let's divide 21 by 13. The result is approximately 1.6154. This is close to the value of φ, which is approximately 1.6180. As you divide larger Fibonacci numbers, such as 144 by 89 or 987 by 610, the approximations will be even closer to φ.

2)Here's how it works:
Step 1: Create a list of consecutive numbers starting from 2 up to the given limit.
Step 2: Mark the number 2 as prime and cross out all multiples of 2 in the list.
Step 3: Move to the next number in the list that hasn't been crossed out, which is 3. Mark it as prime and cross out all multiples of 3 in the list.
Step 4: Repeat this process for the remaining numbers in the list, marking them as   and crossing out their multiples.
Step 5: Continue until you have processed all numbers up to the given limit.

- Start with a list of numbers from 2 to 30.
- Mark 2 as prime and cross out its multiples: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30.
- Move to the next number, 3, mark it as prime, and cross out its multiples: 6, 9, 12, 15, 18, 21, 24, 27, 30.
- Move to the next number, 5, mark it as prime, and cross out its multiples: 10, 15, 20, 25, 30.
- Move to the next number, 7, mark it as prime, and cross out its multiples: 14, 21, 28.
- The remaining numbers that are not crossed out are prime: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Fibonacci Sequence :

https://brainly.com/question/16934596

#SPJ11

Answer:

the Profit for the month is $2,083.43

Step-by-step explanation:

The computation of the profit for the month is shown below:

Profit for the month is

= Monthly gross receipts - expenses

= $20,834.34 - $18,750.91

= $2,083.43

hence, the Profit for the month is $2,083.43

We simply applied the above formula so that the correct value could come

And, the same is to be considered

The solution of the system is (x,y) = (-1,5).

What is linear equation ?
A linear equation is an equation of a straight line in two variables, typically x and y. It can be written in the form:

y = mx + b

where m is the slope (or gradient) of the line, and b is the y-intercept, which is the point where the line intersects the y-axis.

According to question:
We are given the system of equations:

4x - 2y = -14 (1)

3x - y = -8 (2)

We can solve this system using any method such as elimination, substitution, or matrices. Here, we will use the substitution method.

From equation (2), we can express y in terms of x as:

y = 3x + 8 (3)

Now we substitute equation (3) into equation (1) and solve for x:

4x - 2(3x + 8) = -14

4x - 6x - 16 = -14

-2x = 2

x = -1

Now, we substitute x = -1 into equation (3) to find y:

y = 3(-1) + 8

y = 5

Therefore, the solution of the system of equations is x = -1 and y = 5. We can check the solution by verifying that it satisfies both equations:

4(-1) - 2(5) = -14 (satisfied)

3(-1) - 5 = -8 (satisfied)

Hence, the solution of the system is (x, y) = (-1, 5).

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

Answer:

I. Length = 600 meters

II. Width = 30 meters

Step-by-step explanation:

Given the following data;

Length = 120m

Width = 6m

Drawing scale = 1:5

To find the length and width using the given drawing scale;

This ultimately implies that, with this drawing scale, the length and width of the rectangle would increase by a factor of 5 (multiplied by 5) i.e the rectangle is 5 times bigger in real-life than on the diagram.

For the length;

120 * 5 = 600 meters

For the width;

6 * 5 = 30 meters

Therefore, the dimensions of the rectangle using the given drawing scale is 600 meters by 30 meters.

If the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds

The quantity of fuel releases from the container = 5 gallon per second

Consider the fuel remaining in the container = y

Consider the number of seconds that have passed since the fuel started dispensing = x

Then x and y satisfy a linear relationship

The quantity of fuel in the tank at the beginning = 103 gallon

Time taken = 2 seconds

Then the equation will be

y = 103 - 5x

Time taken is x = 2

y = 103 - 5× 2

y = 103 - 10

y = 93 gallon

Hence, if the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds

Learn more about linear relationship here

brainly.com/question/10713055

#SPJ1

The equation that represents the growth or change in the population is p = p =254.9t + 38,655 and it will take 44.5 years to reach 50,000 people.

First, let's determine the growth per year:

41,204 people - 38, 655 people= 2,549 people/ 10 years = 254.9 people per year. Now, based on this, we can write the equation as follows : 254.9t + 38,655 (initial population)

Now, let's calculate the value of t when p is 50,000:

50,000 = 254.9t + 38,655

50,000 - 38,55= 254.9t

11,345/ 254.9= t +

t= 44.5 years

Learn more about growth in https://brainly.com/question/28789953

#SPJ1

The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approx b). 0.9428.

The intelligence quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. The standard deviation of the mean of a sample of 50 adults can be calculated as the population standard deviation divided by the square root of the sample size, or 15/√50 = 1.58.

Using a standard normal distribution table, the probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 can be calculated as the area under the standard normal curve between the z-scores corresponding to 98 and 103. These z-scores can be calculated using the formula z = (x - mean) / standard deviation, where x is the value of interest and mean is the population mean. The z-score for 98 is (98 - 100) / 1.58 = -1.27, and the z-score for 103 is (103 - 100) / 1.58 = 2.53.

The area under the standard normal curve between -1.27 and 2.53 can be found using a standard normal distribution table or a calculator with normal distribution functions. The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approximately 0.9228, which is closest to the answer choice b. 0.9428.

Find out more about probability

brainly.com/question/14987010

#SPJ4

Answer:

love

Step-by-step explanation:

you

When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

Learn.more about consumption

https://brainly.com/question/30623688

#SPJ4

When the consumption schedule lies below the 45-degree reference line, saving what does it means?