6 = x + 2/3
Show your work please;w;

Answers

Answer 1

Answer:

x = 5 1/3

Step-by-step explanation:

6 = x + 2/3

-2/3 -2/3

5 1/3 = x

Answer 2

Answer:

\(\boxed {x = \frac{16}{3}}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(6 = x + \frac{2}{3}\)

-Switch sides:

\(6 = x + \frac{2}{3}\)

\(x + \frac{2}{3} = 6\)

-Subtract \(\frac{2}{3}\) to both sides and convert 6 to a fraction:

\(x + \frac{2}{3} - \frac{2}{3}= 6 - \frac{2}{3}\)

\(x = \frac{18}{3} - \frac{2}{3}\)

-Since both fractions have the same denominator, then you subtract the numerators:

\(x = \frac{18 - 2}{3}\)

\(\boxed {x = \frac{16}{3}}\)

Therefore, the value of \(x\) is \(\frac{16}{3}\).


Related Questions

Find the volume of the rectangular prism. Enter your answer in the box
u will get 50 points don't answer if you don't know

Find the volume of the rectangular prism. Enter your answer in the boxu will get 50 points don't answer

Answers

Answer:

151.7 cm^3

Step-by-step explanation:

3.7 x 10 x 4.1 = 151.7

BRAINLIEST? TY!!

Answer:

151.7 cm^3

Step-by-step explanation:

If you didn't know already the volume of a rectangular prism is

length x witdh x height.

Multiply 10x4.1 and you will get 41

Then multiply 41 by 3.7 to get 151.7.

find a formula an for the -n- th term of the following sequence. assume the series begins at =1.n=1. 11,−14,19,…

Answers

a formula an for the -n- th term of the following sequence. assume the series begins can be represented by the formula an = (-1)^(n+1)(8 + 3n).



To find the formula for the -n- th term of the sequence, we need to observe the pattern in the given sequence. We can see that the sequence is alternating between positive and negative numbers, and the difference between the consecutive terms is increasing by 5.

Starting from the first term, 11, we can write the sequence as:

11 - 14 + 19 - 24 + ...

To find the pattern, we can write the terms in terms of their positions:

a1 = 11
a2 = -14
a3 = 19
a4 = -24

We can see that the sign of each term is alternating. To represent this in the formula, we can use (-1)^(n+1), which will give -1 for odd values of n and 1 for even values of n.

The other part of the formula should represent the increasing difference between the consecutive terms. We can see that the difference between the first two terms is 25, between the second and third terms is 33, and between the third and fourth terms is 43. We can observe that the difference between the consecutive terms is increasing by 8, which is 5 times the position of the term.

Therefore, the formula for the -n- th term of the sequence is:

an = (-1)^(n+1)(8 + 3n)


The formula for the -n- th term of the given sequence is an = (-1)^(n+1)(8 + 3n).

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Wyatt is going to a carnival that has games and rides. Each game costs $1. 25 and each ride costs $2. 75. Wyatt spent $20. 25 altogether at the carnival and the number of rides he went on is twice the number of games he played. Determine the number of games Wyatt played and the number of rides Wyatt went on.

Answers

In the carnival the number of games number of rides Wyatt went on is 3 and 6 respectively.

What is system of equation?

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

The number of unknown objects can be find using the system of solution.

Given information-

The cost of each game is $1.25.

The cost of each ride is $2.75.

Total amount of money spent by the Wyatt is $20.25.

The number of rides he went on is twice the number of games he played.

Suppose the number of games Wyatt played is x and the number of rides he went in the carnival is y.

As, the number of rides he went on is twice the number of games he played. Thus,

\(y=2x\)

Let the above equation as equation one.

As total amount of money spent by the Wyatt is $20.25 and The cost of each game is $1.25 and the cost of each ride is $2.75. Thus,

\(1.25x+2.75y=20.25\\\)

Put the value of y in the above equation from the equation one as,

\(1.25x+2.75(2x)=20.25\\1.25x+5.5x=20.25\\6.75x=20.25\\x=3\)

Thus the number of games he played is 3.

Put this value of x in the equation one as,

\(y=2\times3\\y=6\)

Thus the number rides Wyatt went on is 6.

Hence, In the carnival the number of games number of rides, Wyatt went on is 3 and 6 respectively.

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which of the following sentence completions are a binary search tree, every element 'a' is .....group of answer choices... a. lesser than all elements in its left subtree.... b. greater than all elements in its left subtree.... c. lesser than all elements in its right subtree.... d. greater than all its descendants... e. greater than all elements in its right subtree.

Answers

Options a, d, and e could describe a binary search tree while the rest doesn't.

In a binary search tree (BST), every element 'a' has certain properties regarding its position relative to other elements in the tree. Let's analyze it:

a. "Lesser than all elements in its left subtree": This statement would hold true in a BST. In a BST, the left subtree contains elements that are smaller than the current element.

b. "Greater than all elements in its left subtree": This statement would not hold true in a BST. In a BST, the left subtree contains elements that are smaller than the current element, so 'a' cannot be greater than all elements in its left subtree.

c. "Lesser than all elements in its right subtree": This statement would not hold true in a BST. In a BST, the right subtree contains elements that are greater than the current element, so 'a' cannot be lesser than all elements in its right subtree.

d. "Greater than all its descendants": This statement would hold true in a BST. In a BST, all elements in the left subtree are smaller than the current element, and all elements in the right subtree are greater. Therefore, 'a' would be greater than all its descendants.

e. "Greater than all elements in its right subtree": This statement would hold true in a BST. In a BST, the right subtree contains elements that are smaller than the current element, so 'a' can be greater than all elements in its right subtree.

In summary, options a, d, and e could describe a binary search tree, while options b and c would not accurately describe a binary search tree.

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P is a point on the terminal side of θ in standard position. Find the exact value of the six trigonometric functions for θ.
18. P(-3, 2)
19. P(4, -2)
20. P(0, -6)
21. P(-3, -4)

Answers

Answer:

  see below

Step-by-step explanation:

When you're doing a bunch of these, it is helpful to make a table with reminders as to how they're calculated. That table is shown below.

__

In the attached, we have used ...

  r² = x² +y²

  √20 = 2√5

  √36 = 6

  √25 = 5

and 1/(2√5) = √5/10. (The division is outside the radical.)

P is a point on the terminal side of in standard position. Find the exact value of the six trigonometric

What is the decimal equivalent of 6/13 ? Round to tenths place. If answer doesn't
have a tenths place then use zero on the end to make the answer have a tenths place
to be counted correct.

Answers

Answer:

0.5

Step-by-step explanation:

6/13 is the same as saying 6 ÷ 13

6 ÷ 13 = 0.4615384615

The first position after the decimal is the tenths column. Round up, because 6>5.

The area of a rectangle can be represented by the
expression 3x2 - 5x - 2. Which expression could
represent the length of one side?
O (3x + 2)
0 (x + 2)
o (3x - 1)
o(x-2)
Previous
Next

Answers

Answer:

x - 2

Step-by-step explanation:

3x² - 5x - 2

Factor the trinomial.

(3x + 1)(x - 2)

Answer: x - 2

Answer:
O (x - 2)

Step-by-step explanation:

To find the expression that represents the length of one side of a rectangle, we need to factor the given expression 3x^2 - 5x - 2.

The factored form of the expression 3x^2 - 5x - 2 is:
(3x + 1)(x - 2)

From the factored form, we can see that the length of one side is represented by the expression (x - 2).

Therefore, the expression that represents the length of one side is
(x - 2).

Need help with this English assignment due now pls hurry up I need #10-13 poem help me out now

Need help with this English assignment due now pls hurry up I need #10-13 poem help me out now

Answers

Answer:

Step-by-step explanation:

Question 13- I remember the year of 2001 because that was the year the twin towers were bombed and that was the year the pentagon got bombed too.  

brainliest, thanks, five stars

brainliest, thanks, five stars

Answers

Answer:

5(X+2y-3)

Step-by-step explanation:

5x+10y-15

5(X+2y-3)

What is a Type II Error?

Answers

A Type II Error, also known as a "false negative," is a statistical term used in hypothesis testing. In hypothesis testing, we start with two competing hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha).

The goal of hypothesis testing is to determine which hypothesis is more likely to be true given the data. A Type II Error occurs when we fail to reject the null hypothesis when it is actually false. In other words, we incorrectly conclude that the null hypothesis is true when it is actually false.

For example, consider a medical test for a certain disease. The null hypothesis is that the patient does not have the disease, and the alternative hypothesis is that the patient does have the disease.

If the test results are negative (i.e., the patient does not have the disease), and the patient actually does have the disease, then we have made a Type II Error.

The probability of making a Type II Error is represented by the Greek letter β (beta). A common goal in hypothesis testing is to keep the probability of making a Type II Error as low as possible, while also keeping the probability of making a Type I Error (false positive) low as well.

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These are the percentages of people that went to the talent show.
2008. 84%
2009. 91%
2010. 92%
2012. 87%
2013. 94%

This year there is 360 students in the whole school.
How many students went to the talent show?

Answers

Approximately 1613 students went to the talent show.

We have,

To find the number of students who went to the talent show, we need to calculate the percentage of students from the total number of students in the school.

Let's calculate the number of students for each year:

2008: 84% of 360 students = 0.84 x 360 = 302.4 students

2009: 91% of 360 students = 0.91 x 360 = 327.6 students

2010: 92% of 360 students = 0.92 x 360 = 331.2 students

2012: 87% of 360 students = 0.87 x 360 = 313.2 students

2013: 94% of 360 students = 0.94 x 360 = 338.4 students

To find the total number of students who went to the talent show, we add up the values for each year:

= 302.4 + 327.6 + 331.2 + 313.2 + 338.4

= 1612.8 students

Therefore,

Approximately 1613 students went to the talent show.

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Find the volume of a parallelepiped if four of its eight vertices are A(0,0,0), B(3,1,0), C(0, – 4,1), and D(2, – 5,6).
The volume of the parallelepiped with the given vertices A, B, C and D is____units cubed. (Simplify your answer.)

Answers

The volume of the parallelepiped formed by the vertices A(0,0,0), B(3,1,0), C(0, –4,1), and D(2, –5,6) is 75 cubic units.

To find the volume of the parallelepiped, we can use the determinant of a matrix method. First, we calculate the vectors AB, AC, and AD by subtracting the coordinates of the vertices. Next, we form a matrix using these vectors as columns.

Taking the determinant of this matrix will give us the volume of the parallelepiped. Evaluating the determinant, we find that it is equal to -75. The volume of a parallelepiped is always positive, so we take the absolute value of -75, resulting in a volume of 75 cubic units.

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Write the prime factorization of 21. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).

Answers

The prime factorization of the number 21 is:

21 = 3*7

How to write the prime factorization?

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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What is the x and y intercept absolute min/max

What is the x and y intercept absolute min/max

Answers

x and y-intercept :

The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.

Absolute min:

An absolute maximum point is a point where the function obtains its greatest possible value.

Absolute max :

An absolute minimum point is a point where the function obtains its least possible value.

Local Extrema (Local Maxima/Minima): The local maxima and minima on a graph refer to the maximum and minimum points of the graph over a specific interval of the graph as opposed to the entire graph, so there can be multiple local maxima and minima of a given graph.

When considering which points are the absolute maximum and the absolute minimum of a graph, we not only need to consider local extrema (a maximum/minimum of a graph on some interval that contains the point), but we also need to consider the endpoints (the furthest left/right points on our graph). By looking at the y-values for each of these points, we can identify the absolute maximum of the graph as the point with the highest y-value, and we can identify the absolute minimum as the point with the lowest y-value.

Step 1: Identify local maxima/minima, as well as the endpoints.

From this graph, we can see that our graph is on the interval

This means we have our endpoints at [-1,-1] , [4,1] ,

to consider. We also observe that we have one local minima and one local maxima in between these points on our interval. The estimated points are all shown in the image.

absolute minimum point : [-1,-1]

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¿Cuáles son las longitudes de un terreno rectangular, si se sabe que el ancho es dos veces más pequeño que el largo, y que su área es de 16, 200 m2? cuanto mide el ancho cuanto mide el largo

Answers

Answer:

El largo tendrá un valor de 180 m y al ancho tendrá un valor de 90 m

Step-by-step explanation:

Un rectángulo es un cuadrilátero con dos lados de igual longitud y dos lados de igual ancho que contiene cuatro ángulos rectos. Para encontrar el área de un rectángulo, debes multiplicar su longitud por su ancho. Es decir, el área del rectángulo es igual al largo por el ancho.

En este caso, sabes que el ancho es dos veces más pequeño que el largo. Entonces, siendo el largo x, el ancho tendrá un valor de x÷2.

Siendo el área del terreno rectangular 16,200 m², entonces

x*(x÷2)= 16,200 m²

Resolviendo:

x² ÷2= 16,200 m²

x²= 16,200*2 m²

x²= 32,400 m²

x= √32.400 m²

x= 180 m

Entonces, el largo tendrá un valor de 180 m y al ancho tendrá un valor de 90 m (180 m÷ 2)

Look at the graph. How many nails are less than 1 1/2 inches long?

Look at the graph. How many nails are less than 1 1/2 inches long?

Answers

They is 15 Nails under 1 1/2 inches

if a carpenter wants to make sure that the corner of a room is square and measures 5 ft and 12 ft along the walls, how long should he make the diagonal?

Answers

The diagonal of a room measuring 5 ft and 12 ft along the walls should be 14.6 ft.

The diagonal of the room can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse would be the diagonal, the other two sides would be 5 ft and 12 ft.

Thus, the equation would be: a² + b² = c², with a = 5 ft, b = 12 ft, c = 14.6 ft.

The calculation for this equation is as follows:

5² + 12² = c²; 25 + 144 = c²; 169 = c²; √169 = c; c = 14.6 ft.

This means that the diagonal of a room measuring 5 ft and 12 ft along the walls is 14.6 ft.

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Let's say someone is conducting research on whether people in the community would attend a pride parade. Even though the population in the community is 95% straight and 5% lesbian, gay, or some other queer identity, the researchers decide it would be best to have a sample that includes 50% straight and 50% LGBTQ+ respondents. This would be what type of sampling?
A. Disproportionate stratified sampling
B. Availability sampling
C. Snowball sampling
D. Simple random sampling

Answers

The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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Image has details below with FACTORING

Image has details below with FACTORING

Answers

Twelve would equal x

Answer:

12

Step-by-step explanation:

1) Substitute x into the equation

To substitute you would need to multiply the number before it by 2 (in other questions it would be the value told that is x)

-3 x 2 = -62.5 x 2 = 58 x 2 = 16

2) Put the numbers you have worked out into the equation

-6 + 1.5 + 5 - 4.5 + 16

3) Work out the final equation

-6 + 1.5 = -4.5-4.5 + 5 = 0.50.5 - 4.5 = -4-4 + 16 = 12

Hope this helps, have a great day!

a water jug is in the shape of a prism the area of the base is 100 square inches and the height is 20 inches how many gallons of water can it hold (1 gallon equals 231 inches cubed)

Answers

The amount of gallons of water the Jug can hold is  8.66 gallons.

How to find the gallons of water the prism can hold?

The water jug is in the shape of a prism the area of the base is 100 square inches and the height is 20 inches.

Therefore, the number of gallons of water the jug can hold can be calculated as follows:

volume of the prism = Bh

where

B = base area h = height of the prism

Therefore,

volume of the prism = 100 × 20

volume of the prism = 2000 inches³

Therefore,

231 inches³ = 1 gallon

2000 inches³  = ?

cross multiply

amount of water the jug can hold = 2000 / 231

amount of water the jug can hold = 8.66 gallons

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What is the length of a segment in the complex plane with endpoints at 4 2i and 7 – 2i?

Answers

The length of the segment in the complex plane is 5.

The length of a segment in the complex plane can be found using the distance formula. To find the length of the segment with endpoints at 4+2i and 7-2i, we can use the formula:

Distance formula = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of the first endpoint are x1 = 4 and y1 = 2i, while the coordinates of the second endpoint are x2 = 7 and y2 = -2i.

Plugging these values into the formula, we have:

Distance = sqrt((7 - 4)^2 + (-2 - 2)^2)
         = sqrt(3^2 + (-4)^2)
         = sqrt(9 + 16)
         = sqrt(25)
         = 5

Therefore, the length of the segment in the complex plane is 5.

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An Amtrak official obtains data on a particular day concerning the length of time (in minutes) that the metroliners leaving New York take to reach Philadelphia, with the following results:

93 89 91 87 91 89
Find the sample variance.
a. 3.6
b. 5.6
c. 6.8
d. 7.6
e. 4.4

Answers

The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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Working together, Beth and Katy can wash a car in 6 minutes. Had she done it by herself, it would have taken Katy 18 minutes. How long would it take Beth to wash the car herself?

Answers

Answer:

It would take Beth twelve minutes to wash the car herself

Step-by-step explanation:

If they do it together in 6 minutes.

& Katy can do it in 18 minutes alone

Then 18 - x = 6

replace x for twelve

18 - twelve = 6

Ans: twelve

4. Write an equation in the form of y = kx for the following situation. A person can burn 750
calories in 60 minutes.

Answers

Answer:

k750×60x=Ohio

Step-by-step explanation:

Swag like Ohio down in Ohio

as the number of potential bi applications increases, the need to justify and prioritize them arises. this is not an easy task due to the large number of ________ benefits.

Answers

As the number of potential business intelligence (BI) applications increases, organizations face the challenge of justifying and prioritizing them. This task is not easy primarily because of the large number of potential benefits associated with BI.

BI applications have the potential to provide numerous benefits to organizations. These benefits include improved decision-making through data-driven insights, enhanced operational efficiency, cost savings, increased revenue, better customer understanding, and competitive advantage, among others. Each BI application may contribute to one or more of these benefits, making it difficult to evaluate and prioritize them.

To justify and prioritize BI applications, organizations need to carefully assess the potential benefits against their strategic goals and objectives. This requires conducting a thorough analysis of each application's expected impact on key performance indicators (KPIs), such as revenue growth, cost reduction, customer satisfaction, and process efficiency. Additionally, organizations must consider factors such as resource requirements, implementation complexity, and potential risks.

A comprehensive business case should be developed for each BI application, outlining the specific benefits it can deliver, the estimated costs and resources needed, and the alignment with organizational goals. This allows decision-makers to compare and prioritize applications based on their expected return on investment and strategic alignment.

In summary, the need to justify and prioritize BI applications arises due to the multitude of potential benefits they can offer. Organizations must carefully evaluate each application's impact and align them with strategic objectives to make informed decisions and allocate resources effectively.

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Write an equation of the function
g(x) that is the graph of f(x)=|x| , but shifted right 3 units and shifted down 4 units.

Answers

Answer:

g(x) = |x-3| -4

Step-by-step explanation:

to shift right by 3, subtract three from x inside the absolute value.

to shift down by 4, subtract 4 outside of the absolute value.

g(x) = |x-3| -4

Suppose that Σa_n (x - 4)^n converges for x = 8 and diverges for x = 8.5. For each of the following values of x, determine whether or not the power series must converge. Enter C for convergence, D for divergence, or U if convergence cannot be determined. x = 6 x = -1 x = 0 x = 4

Answers

The convergence of the power series Σa_n (x - 4)^n for the given values of x is as follows: x = 6: C (convergence),
x = -1: U (unknown), x = 0: U (unknown), x = 4: C (convergence)


For x = 6, the power series converges. This is because x = 6 lies within the interval of convergence centered at 4, as x = 8 also converges. So, for x = 6, the answer is C (convergence).

For x = -1, the convergence cannot be determined without more information. It lies outside the known interval of convergence (between 4 and 8). Therefore, for x = -1, the answer is U (unknown).

For x = 0, similarly to x = -1, we cannot determine the convergence without more information, as it is outside the known interval of convergence. So, for x = 0, the answer is U (unknown).

For x = 4, the power series converges because it is the center of the interval of convergence. Any power series converges at its center. Therefore, for x = 4, the answer is C (convergence).

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Complete question:

Suppose that Σa_n (x - 4)^n converges for x = 8 and diverges for x = 8.5. For each of the following values of x, determine whether or not the power series must converge. Enter C for convergence, D for divergence, or U if convergence cannot be determined.

x = 6 _____

x = -1 _________

x = 0 _______

x = 4_______

PLEASE HELP! INCLUDE scratch WORK! THANK YOU!​

PLEASE HELP! INCLUDE scratch WORK! THANK YOU!

Answers

The linear function defined from the table is given as follows:

y = -3x + 2.

How to define a linear function?

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.

From the table, we have that the slope and the intercept are given as follows:

Slope of -3, as when x increases by 1, y decreases by 3.Intercept of 2, as when x = 0, y = 2.

Hence the function is defined as follows:

y = -3x + 2.

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70 hundreds = _____thousands​

Answers

Answer:

7000 im pretty sure if not im sorry

7000 I think hope this helps

Solve the following LP problem using level curves. (If there is no solution, enter NO SOLUTION.) MAX: 4X₁ + 5X₂ Subject to: 2X₁ + 3X₂ 126 4X₁ + 3X₂ 152 X₂ 2 70 X₁ + X₁ X₂ 20 What is the optimal solution? (X₁, X₂)-(I What is the optimal objective function value?

Answers

To solve the given LP problem using level curves, we first plot the level curves for the objective function 4X₁ + 5X₂. The level curves are a series of lines with the same value of the objective function.

Next, we determine the feasible region by considering the constraints. The feasible region is the area that satisfies all the constraints simultaneously. From the given constraints, we find that the feasible region is a polygon bounded by the lines 2X₁ + 3X₂ = 126, 4X₁ + 3X₂ = 152, X₂ = 2, X₂ = 70, and X₁ + X₂ = 20. By analyzing the level curves within the feasible region, we identify the highest level curve that intersects the feasible region. The point of intersection between this level curve and the feasible region represents the optimal solution. However, since the feasible region is not explicitly mentioned in the question, it is not possible to determine the exact location of the optimal solution and its corresponding objective function value.

Therefore, the answer to this question is "NO SOLUTION" as we cannot find the optimal solution without the explicit information about the feasible region.

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