Write a quadratic function in standard form with zeros 5 and 6. Plzzzz awnserrrrr

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

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

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

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

The primal problem is:

Maximize Z = 3x + 4y + 5z

Subject to:

x + 2y + z ≤ 10

7x + 3y + 9z ≤ 12

x, y, z ≥ 0

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

Minimize Z' = 10a + 12b

Subject to:

a + 7b ≥ 3

2a + 3b ≥ 4

a + 9b ≥ 5

a, b ≥ 0

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

The primal problem is:

Minimize Z = y1 + 2y2

Subject to:

3y1 + 4y2 > 5

2y1 + 6y2 ≥ 6

y1 + y2 ≥ 2

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

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

Subject to:

3a + 2b + c ≤ 1

4a + 6b + c ≤ 2

a + b ≤ 0

a, b, c ≥ 0

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

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so it starts with 30

monday: 30-6   24 copies left

tuesday: 24-3     21 copies left

wenesday: 21+ 24   45-8   37 copies

its has 37 copies left

If the Wardrobe consists of 2 shirts , 3 pair of pants and 16 bow ties , then the number of different outfits that can be made are 96 outfits .

The number of shirts in the Wardrobe is = 2  shirts ,

The number of pairs of pants in the wardrobe is = 3 pairs of pants ,

the number of bow ties in the wardrobe is = 16 bow ties ,

The number of different outfits that can be made from the wardrobe  can be calculated by the Multiplication Principle ;

That means , the number of different outfits made is = (number of shirts) × (number of pair of pants ) × (number of bow ties )

substituting the values ,

we get ,

= 2 × 3 × 16 ,

= 6 × 16 ,

= 96 .

Therefore , 96 different outfits can be made from the Wardrobe .

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By using probability You can mix and match the two shirts, three pairs of pants, and sixteen bow ties to create 48 different outfits.

To calculate the number of possible outfits, you would first multiply the number of shirts (2) and pants (3) to get 6. Then, you would multiply 6 and the number of bow ties (16) to get 96. Finally, you would divide 96 by the number of shirts (2) to get 48

2 x 3 = 6

6 x 16 = 96

96 / 2 = 48

You can create different outfits by mixing and matching the items in your wardrobe. To calculate the number of possible outfits, you would first multiply the number of shirts (2) and pants (3) to get 6. Then, you would multiply 6 and the number of bow ties (16) to get 96. Finally, you would divide 96 by the number of shirts (2) so that each shirt is accounted for only once, resulting in 48 different outfits.

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Answer:

\(C = 1000S + 500B\)

Step-by-step explanation:

Given

\(S = Banana\ Splits\)

\(B=Bacon\ Rolls\)

Reading through the question, we have:

Number of calories per serving:

\(S \to 1000\)

\(B \to 500\)

Let

\(x = Cholesterol\)

\(y =Sugar\)

So, we have:

Each serving of S

\(x \to 1S\)

\(y \to 3S\)

Each serving of B

\(x \to 4B\)

\(y \to 1B\)

Recommendation

\(x \to \le 10\) - i.e. not more than 10 units of cholesterol

\(y \to \ge 2 \& \le 9\) i.e. At least 2units but not more than 9 units of sugar

So, the constraints are:

\(S + 4B \le 10\)

\(3S + B \ge 2\)

\(3S + B \le 9\)

Recall that the calories per serving is:

\(S \to 1000\)

\(B \to 500\)

Hence, the objective function is:

\(C = 1000S + 500B\)

Answer:

Simplifying the expression 8z+x−5−9z+2:

8z - 9z + x - 5 + 2

= -z + x - 3

Therefore, 8z+x−5−9z+2 simplified to -z + x - 3.

Answer:

SAS (unless angle lines are drawn on by you, then it would be not enough info)

Step-by-step explanation:

Two sides both have the tick line to show that they are the same length.

They both share the same side

And if those angle lines were drawn by the question, then it would show that those angles are the same.

Add them all together to get SAS as you have (Side, Angle, Side)

Dominik used 7/8 cup of sugar for a bread recipe. he used 3/4 cup of sugar for a muffin recipe.

To find out how much sugar Dominik used in total for both recipes, we need to add the amounts of sugar he used in each recipe.

7/8 cup + 3/4 cup

To add these two fractions, we need to find a common denominator. In this case, the smallest common denominator is 8, which is the same as the denominator of the first fraction.

7/8 cup + 3/4 cup = (7/8) cup + (6/8) cup

Now we can add the two numerators

(7/8) cup + (6/8) cup = 13/8 cup
Hence, Dominik used 13/8 cups of sugar for both recipes combined.

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The solution to the system of equations is x = 2 and y = 1.

First, let's manipulate each equation into slope-intercept form (y = mx + b):

3x - 2y - 10 = 0

-2y = -3x + 10

y = (3/2)x - 5

x + 2y - 14 = 0

2y = -x + 14

y = (-1/2)x + 7

Next, we can plot the two lines on a graph by finding their y-intercepts and slopes:

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

y-intercept: -5

slope: 3/2

To plot this line, we can start at the y-intercept of -5 and then use the slope to find additional points. For example, we can go up 3 units and over 2 units to get the point (2, 1).

Line 2: y = (-1/2)x + 7

y-intercept: 7

slope: -1/2

To plot this line, we can start at the y-intercept of 7 and then use the slope to find additional points. For example, we can go down 1 unit and over 2 units to get the point (2, 6).

Now, we can graph the two lines on the same coordinate plane:

```

    |

 8  -|      .

    -|   .

 6  -|  .

    -|.

 4  -|

    -|

 2  -|   .

    -|      .

 0  -|_____________

       0  2  4  6  8

```

From the graph, we can see that the two lines intersect at the point (2, 1). Therefore, the solution to the system of equations is x = 2 and y = 1.

We can verify this solution algebraically by substituting x = 2 and y = 1 into both equations and verifying that they are both true:

3x - 2y - 10 = 0

3(2) - 2(1) - 10 = 0

6 - 2 - 10 = 0

0 = 0 (true)

x + 2y - 14 = 0

2 + 2(1) - 14 = 0

4 - 14 = 0

-10 = 0 (false)

Since the second equation is false when x = 2 and y = 1, this means that (2, 1) is not a solution to that equation alone, but it is a solution to the system as a whole. Therefore, our solution is correct.

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The required cycle-time is approximately 57.6 seconds.

To find the required cycle time, we need to divide the total available time by the number of units to be produced.

Total available time: 16 hours = 16 * 60 minutes = 960 minutes = 960 * 60 seconds = 57,600 seconds

Number of units to be produced: 1,000 units

Required cycle time: Total available time / Number of units

Cycle time = 57,600 seconds / 1,000 units

Cycle time ≈ 57.6 seconds

Therefore, the required cycle time is approximately 57.6 seconds.

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Answer: the answer is 2 or C

-8/2 x -3/6

*Always do the recipical*

(-8 x -3) / (2 x 6)

-8 x -3= +24

2 x 6= 12

24/12= 2

The solution of the given expression -8/2 x -3/6 is 2. The correct option is B.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that the expression is,

-8/2 x -3/6

The expression will be solved as below,

E = (-8 x -3) / (2 x 6)

The numerator will get reciprocal and multiplied to the denominator,

E = 24 / 12

Divide the number 24 by 12 and get the solution,

E = 2

Therefore, the solution of the expression will be 2. The correct option is B.

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Hello !

\(3x + 4 = 2x - 1\\\\3x - 2x = -1 - 4\\\\x = -5\)

x = -5

Answer:

\(\sf{x=-5}\)

Step-by-step explanation:

Let's solve this equation.

Our equation is:

\(\sf{3x+4=2x-1}\)

Rearrange the terms

\(\sf{3x-2x+4=1}\)

\(\sf{3x-2x=-1-4}\)

Combine

\(\sf{x=-5}\)

Therefore, x = -5

Answer: ∠z=48°

Vertical angles are always congruent, and because 87 and z are adjacent angles, but equal 135, the equation would be 87+z=135. Subtract 87 on both sides to get z=48.

Answer:

Negative

Step-by-step explanation:

From the scatter plot displayed, we could clearly observe the direction of the trend line as it produces a negative slope. For high values of y, the values of x are low and similarly, high values of x have low y values. Therefore, this kind of relationship between the two variables is considered negative.

Answer:

26°

Step-by-step explanation:

use the inverse trig functions (in this case, sin^-1)

sin^-1(4/9)

Answer:

26.39

Step-by-step explanation:

khan

The ratio of male to female attendees was 1:1, then we can estimate that 100 ladies attended the party as well (\($1000 / $5\) per ticket).

A fraternity charged admission for two different categories of people to their finals week bash, and they made and sold tickets.

How many individuals attended the party in each category?
Given the information provided, it is clear that the fraternity charged different amounts for admission to their finals week bash based on the gender of the attendees.

They collected separate ticket sales for the two categories.
In order to calculate the number of attendees in each category, we need to know the total revenue generated by ticket sales, as well as the price of admission for each category.

Unfortunately, these details are not provided in the question.
If we make some assumptions, we can attempt to estimate the number of attendees.

If we assume that the price of admission for both categories was the same, then we can simply divide the total revenue by the price of admission to get the total number of attendees.
Alternatively, if we assume that the ratio of male to female attendees was equal, then we can use the information provided to calculate the number of female attendees.

If the fraternity charged \($10\) per ticket for dudes and \($5\) per ticket for ladies, and they collected \($1000\) in total ticket sales, then we can calculate the number of male attendees as 100 (\($1000 / $10\) per ticket).
It is important to note that these calculations are based on assumptions, and the actual number of attendees could be different depending on the actual price of admission and the actual ratio of male to female attendees.

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Answer:

x = -3

Step-by-step explanation:

\(-4x-5-11x=40\\-15x=40+5\)

\(x=\frac{45}{-15}\)

\(x=-3\)

Hope this helps.

c. 11%. This means that the average forecasted demand deviates from the actual demand by approximately 11%.

The Mean Absolute Percent Error (MAPE) measures the accuracy of a forecast by calculating the percentage difference between the actual demand and the forecasted demand. To calculate the MAPE, you can follow these steps:

1. Calculate the absolute percent error (APE) for each day by subtracting the forecasted demand from the actual demand, taking the absolute value of the difference, and dividing it by the actual demand. Here are the APE values for each day:
  Day 1: |(16-20)/16| = 20%
  Day 2: |(19-20)/19| = 5.26%
  Day 3: |(21-20)/21| = 4.76%
  Day 4: |(21-20)/21| = 4.76%
  Day 5: |(22-20)/22| = 9.09%
  Day 6: |(17-20)/17| = 17.65%

2. Calculate the mean of the APE values by summing them up and dividing by the total number of days:
  (20% + 5.26% + 4.76% + 4.76% + 9.09% + 17.65%)/6 ≈ 10.98%

3. Finally, multiply the mean APE by 100 to convert it into a percentage. This gives us the MAPE:
  10.98% * 100 = 10.98%

Therefore, the MAPE for the given dataset is approximately 10.98%.

c. 11%. This means that the average forecasted demand deviates from the actual demand by approximately 11%.

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The derivative of f(x) = cos(x² - x) is \(3(2x - 1)cos(x^{2} - x)sin(x^{2} - x).\)

To find the derivative of the function f(x) = cos(x² - x), we can use the chain rule.

The chain rule states that if we have a composite function, such as cos(g(x)), the derivative of this composite function is given by the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is cos(u), where u = x² - x, and the inner function is u = x² - x.

The derivative of the outer function cos(u) is -sin(u).

To find the derivative of the inner function u = x² - x, we apply the power rule and the constant rule. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1), and the constant rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function.

Applying the power rule and the constant rule, we find that the derivative of u = x² - x is du/dx = 2x - 1.

Now, using the chain rule, the derivative of f(x) = cos(x² - x) is given by:

df/dx = \(-sin(x^{2} - x) * (2x - 1)\)

Simplifying, we have:

df/dx = -\(2xsin(xx^{2} - x) + sin(x^{2} - x)\)

Therefore, the correct answer is option a. 3(2x-1)cos(x²-x)sin(x²-x).

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The two other pairs of polar coordinates for the same point are (r, θ) = (-3, 7/4).

For the first case (a), the polar coordinates are given as (1, 7/4). To plot this point, we start at the origin and move along the polar axis (positive x-axis) by a distance of 1 unit, then rotate counterclockwise by an angle of 7/4 (in radians). The resulting point will be (r, θ) = (1, 7/4).

To find another pair of polar coordinates for the same point with r > 0, we can choose any positive value for r and keep the angle θ the same. For example, we can choose r = 2. This means that the distance from the origin to the point is now 2 units, while the angle remains 7/4. Therefore, the new polar coordinates become (r, θ) = (2, 7/4).

Similarly, to find a pair of polar coordinates with r < 0, we can choose any negative value for r. For example, let's choose r = -3. This means that the distance from the origin to the point is now -3 units, while the angle remains 7/4. Therefore, the new polar coordinates become (r, θ) = (-3, 7/4).

By adjusting the value of r while keeping the angle θ the same, we can find different polar coordinates that represent the same point in the polar coordinate system.

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Step-by-step explanation:

Two corresponding sides and two corresponding angles are equal

There are 52 weeks of data included in this frequency distribution.

The given frequency distribution displays the weekly sales of a certain brand of television at an electronics store.

We need to find the number of weeks of data included in this frequency distribution.From the given data, we can see that the frequency column represents the number of televisions sold per week.

To find the number of weeks of data included, we need to sum up the frequency column. Summing up the frequency column gives us:12 + 5 + 5 + 5 + 25 = 52

Therefore, there are 52 weeks of data included in this frequency distribution.

The given frequency distribution displays the weekly sales of a certain brand of television at an electronics store. We need to find the number of weeks of data included in this frequency distribution.

From the given data, we can see that the frequency column represents the number of televisions sold per week. To find the number of weeks of data included, we need to sum up the frequency column. Summing up the frequency column gives us:

12 + 5 + 5 + 5 + 25 = 52

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To find the loss values we have to find the equation of the line .

The slope is given by:

We are going to take the points:

(2 , 6) and (5 , 3)

Notice that both points are part of the graph.

Replacing:

The slope is equal to -1.

Now, the equation of the line in the slope-intercep form is given by:

Replacing the point (2 , 6) and the slope m=-1 to find the y-intersect (b):

The equation of the line is:

Finally, we are going to find the loss during the first year, it means x=1. Substituing:

Answer: The loss during the first year was 7 thousands of dollars.

Answer:

53

Step-by-step explanation:

Answer: Opposite of -53 = -(53) = 53

Step-by-step explanation: An opposite number of n is the exact same number as n on the other side of the number line. the opposite of n is n.

Answer: 9

Step-by-step explanation: there are 36 students in total. Since 25% of students wore a jacket, you would multiply 36 by 1/4 which gets you 9, so 9 students wore jackets

Step-by-step explanation:

x = the number

6x = 2x - 40

4x = -40

x = -10

The space left after parking is 1 feet 5.5in

A garage shields a vehicle from the elements and, if it has a locking garage door, it also safeguards the vehicles from theft and damage.

The majority of garages also double as workshops for other tasks like painting, woodworking, and assembling.

∵1 feet  = 12 inches

∴21 feed and 9 inches = 21*12+9

                                      = 261 inches

So, when company truck is parked, the garage is left with 261 - 239.5 = 21.5 inches of space behind the truck

But 4 inches are taken up by the garage door so we are left with 21.5 - 4 inches = 17.5 inches of space

So the space left after parking is 12+5.5 inches or 1 feet 5.5 inches.

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Answer:

3^x+15=3 i think this is what you are looking for

Step-by-step explanation: