What is the missing reason for line 2 in this proof?

The correct answer is option A: the optimal corner point won't change.

The optimal corner point is the point where the objective function reaches its maximum value, with the constraints of the problem being satisfied. If the slope of the objective function stays between the slopes of the binding constraints, it means that the current optimal corner point will remain unchanged.

This is because if the objective function's slope is within the slopes of the binding constraints, then the set of points where the objective function reaches its maximum value will be the same. Therefore, the optimal corner point will not change.

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Answer:

8.25cm²

Step-by-step explanation:

the area of the triangle = (half x base x height )=

(1.5x3)÷2= 2.25cm²

the area of the rectangle= length x width = 3x2= 6cm²

total = 2.25+6= 8.25cm²

The log2 function is a mathematical function that returns the logarithm of a given number to the base 2.

It is used to calculate the power to which a number must be raised to get a particular result.

For example, the log2 of 16 is 4, since 2^4 = 16. It can also be expressed as log2 16 = 4. Log2 is used in many areas of mathematics, including number theory, probability theory, and calculus.

It is also used in computer science and engineering to solve complex problems. Furthermore, it is used in cryptography to calculate the key sizes of encryption algorithms. In general, it is an essential tool for solving mathematical and scientific problems.

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Answer:56

Step-by-step explanation:

Let ttt be the initial number of trees.

Hint #22 / 5

MacDonald now has t-5t−5t, minus, 5 trees and each one produced 210210210 oranges this harvest.

The total number of oranges produced is 210(t-5)210(t−5)210, left parenthesis, t, minus, 5, right parenthesis.

Hint #33 / 5

Since the trees produced a total of 417904179041790 oranges, let's set this equal to 417904179041790:

\qquad210(t-5)=41{,}790210(t−5)=41,790210, left parenthesis, t, minus, 5, right parenthesis, equals, 41, comma, 790

Now, let's solve the equation to find the initial number of trees (t)(t)left parenthesis, t, right parenthesis.

Hint #44 / 5

\begin{aligned}210(t-5)&=41790\\&\\ \dfrac{210(t-5)}{\blue{210}}&=\dfrac{41790}{\blue{210}}&&\text{divide both sides by $\blue{210}$}\\ \\ t-5&=199\\ \\ t-{5}\pink{+5}&=199\pink{+5}&&\pink{\text{add }} \pink{5} \text{ to both sides}\\ \\ t&=204\end{aligned}

210(t−5)

210

210(t−5)

​

t−5

t−5+5

t

​

=41790

=

210

41790

​

=199

=199+5

=204

​

​

divide both sides by 210

add 5 to both sides

​

Hint #55 / 5

The equation is 210(t-5)=41790.210(t−5)=41790.210, left parenthesis, t, minus, 5, right parenthesis, equals, 41790, point

MacDonald's farm initially had 204204204 orange trees.

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A large rectangular box has a volume of 15. 75 cubic feet the box is 2. 5 feet long and 1. 5 feet wide. So the height of the box is 4.2 feet.

The formula to find the volume of a rectangular box is

V = lwh

where l is the length, w is the width, and h is the height.

Given that the volume of the box is 15.75 cubic feet, the length is 2.5 feet and the width is 1.5 feet, we can use the formula to find the height.

V = lwh

15.75 = 2.5 × 1.5 × h

h = 15.75/ (2.5 × 1.5)

h = 4.2

Therefore, the height of the box is h = 4.2 feet

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Answer:

Δ ABC is isosceles

Step-by-step explanation:

∠ ABC and ∠ BCE are alternate angles and are congruent , that is

∠ BCE = ∠ ABC = 80°

since DE id a straight line then the angles lying on it sum to 180° , that is

∠ ACD + ∠ ACB + ∠ BCE = 180°

50° + ∠ ACB + 80° = 180°

∠ ACB + 130° = 180° ( subtract 130° from both sides )

∠ ACB = 50°

∠ BAC and ∠ ACD are alternate angles and are congruent , that is

∠ BAC = 50°

then

∠ BAC = ∠ ACB = 50°

Since the 2 base angles are congruent then Δ ABC is isosceles

The second ordered pair using the terms in each sequence is B (6, 24).

The second rule says to subtract 4 from the second term of the ordered pair, starting from 28. So the second term of the second ordered pair would be 28-4 = 24.

Therefore, the second ordered pair using the terms in each sequence is B (6, 24).

This is because:

C (14,16) can be obtained by adding 4 to first term of B(6,24) which is 6+4 = 10 and subtracting 4 from second term of B(6,24) which is 24-4=20.

D (10,20) can be obtained by adding 4 to first term of C(14,16) which is 14+4 = 18 and subtracting 4 from second term of C(14,16) which is 16-4=12.

So the sequence list of ordered pair would be:

First order: A (2,28)

Second order: B(6,24)

Third order: C (14,16) D (10,20)

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The area of the triangle is equal to the squareroot of 10(10-5)(10-7)(10-8), which is equal to 24.

The area of an acute triangle without height can be calculated using Heron's Formula. Heron's Formula states that the area of a triangle is equal to the squareroot of s(s-a)(s-b)(s-c) where s is the semi-perimeter of the triangle and a, b, and c are the lengths of the three sides.

To find the area, first calculate the semi-perimeter of the triangle. The semi-perimeter is equal to one-half the sum of the three sides. For example, if the lengths of the three sides of a triangle are 5, 7, and 8, the semi-perimeter is equal to 5 + 7 + 8 divided by 2, which is equal to 10.

Next, plug the values into Heron's Formula. Using the same triangle as an example, the area of the triangle is equal to the squareroot of 10(10-5)(10-7)(10-8), which is equal to 24.

Finally, calculate the area of the triangle by taking the square root of 24, which is equal to 4.9. Therefore, the area of the triangle is 4.9 square units.

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Isosceles triangle has three sides, three angles, a base, a height, and an area in which two sides are equal to each other .

What is an isosceles triangle simple definition?

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length and the remaining side has length. . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles

the sum of triangle is 180, sum of all the interior angles is equal to 180.

so if you know two angles then apply sum of triangles and find out the value of the third triangle.

isosceles triangle

An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure.

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The surface area of a regular square pyramid is 332.64 square cm

We know that the surface area of pyramid is nothing but the sum of the areas of its lateral faces and its base.

surface area of pyramid

= areas of lateral faces of pyramid + area of base of pyramid

We know that the formula for the lateral surface area of regular pyramid is:

A = ½ × P × l

where P is the perimeter of the base and l is slant height

Here, a base of regular square pyramid with has sides of 13. 2 cm

a = 13.2 cm and slant height of 6 cm i.e., l = 6 cm

Using the formula of area of square, the base area of pyramid would be,

B = (13.2)²

B = 174.24 sq.cm.

the perimeter of base is:

P = 4 × 13.2

P = 52.8 cm

So, using the above formula of lateral surface area of pyramid the lateral surface area would be

A1 = 1/2 ×  52.8 × 6

A1 = 158.4 sq. cm.

So, the surface area of the pyramid is:

A = A1 + B

A =  158.4 + 174.24

A = 332.64 square cm

Therefore, the surface area of the pyramid = 332.64 square cm

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The university accepts 6000 students out of the 10000 that applied.

Enrolled, in the context of education, is the process of registering a student with a school. The process typically requires a student to complete an application form and submit it to the school, along with any other required documents or fees. Once the student has been accepted and enrolled, they will be given a student ID number and will be able to access all the school's resources, such as classes and activities. In addition, the school may assign an advisor to the student to help them adjust to the school and plan out their academic path.

Of those 6000 accepted students, 45% will actually enroll, which is 2700 students. Therefore, of the 10000 students that applied, 2700 will actually enroll into the university.

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Answer:

See the picture below

Step-by-step explanation:

The estimated value of the multiplication is equivalent to 480.81.

Given is the expression as -

102.3 x 4.7

480.81

Therefore, the estimated value of the multiplication is equivalent to 480.81.

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Answer:i need to know what youre trying to find first

Step-by-step explanation:

The inverse of +5 as calculated is found to be +1 / 5.

To find the inverse of +5 we can simply reciprocate it and the result will be the required answer.

reciprocal of +5 = 1 / 5.

Therefore, the answer is 1 / 5.

The opposite or reciprocal of a number or term in math is known as it's inverse. There are two types of inverse in math, the additive inverse and the multiplicative inverse.

The multiplicative inverse of a number for any n is given as 1/n.  It is also called as the reciprocal of a number and 1 is called the multiplicative identity. On the other hand subtraction is the inverse of addition.

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Answer:

2/15

Step-by-step explanation:

make x= 0.13

multiply it by  10^1 .  

10x = − 1.33

subtract x from 10x

10x−x =

1.33 - 0.13

9x =  1.2  

divide both sides by 9 to get x as a fraction

x =  1.2/9  =  

12/90  =  

2/15

httpssocraticorgquestionshowdoyouconvert0133beingrepeatedtoafraction#242780

A bar over a digit in a decimal number, such as 0.133 with a bar over the 3, indicates that the number is a repeating decimal. In this case, 0.133 is a repeating decimal and the digit 3 is repeating infinitely.

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Answer:

y = -x - 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise / run or (y2 - y1) / (x2 - x1)

Let's pick 2 points ( -6, 0) (-5, -1)

We see the y decrease by 1 and the x increase by 1, so the slope is

m = -1

The y-intercept is located at (0,-6)

So, our equation is

y = -x - 6

There are no solutions for the equation 3x106 3x12.

The equation 3x106 3x12 can be rearranged to 3x106 - 3x12 = 0. This is a linear equation and can be solved using the equation ax+b=0, where a is the coefficient of the variable and b is the constant.

In this case, a = 3 and b = -3x106. To solve this equation, we can use the quadratic formula, which states that x = -b ± √b2 - 4ac / 2a.

Substituting the values for a, b, and c yields x = -(-3x106) ± √(3x106)2 - 4(3)(-3x106)/2(3). Simplifying this yields x = 3x106 ± √9x1012 - 36x1012/6.

This simplifies to x = 3x106 ± √-27x1012/6. Since the square root of a negative number is not a real number, this equation has no real solutions. Therefore, there are no solutions for the equation 3x106 3x12.

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Answer:

Step-by-step explanation:

so since it’s traveling 9mi/m you need to devide 216 by the rate of 9mi/m to find how long it takes.

216/9=24 so it will take 24 minutes!

Answer:1,944 minutes

Step-by-step explanation:

if the question is a plane is traveling 9 miles per minute how much time is needed to travel 216 miles you need it is clear that you are doing a multiplication problem so multiply that and you get 1,944 minutes

your welcome

a) Each person would receive 1/6 of the cake

b) If there are 49 balls in total and each person is to get seven balls, How many persons can share the balls?

We know that we can be able to make us of the principles of algebra so as to be able to obtain the problems that we have to deal with in the question that appears in the image that is attached.

Given that we have the total amount of the cake as 2 1/2 and then we are told that there are 15 persons in the class thus the amount that everyone should receive would be x.

2 1/2 = 15 x

5/2 = 15x

5 = 2 * 15x

x = 5/2 * 15

x = 1/6

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The amount of vanilla in the ice cream is 1/5 in the sundae that is being mad by Peter.

Peter make sundae by using mint chocolate and vanilla ice cream.

It is given to us that, the mint ice cream is 3/5 and chocolate is 1/2 of the remaining.

So, first we calculate the amount of chocolate,

Let us say that, we take the sundae as 1,

so, algebraically, the mint is,

X - 3/5 = 1

X = 2/5

Now, half of the 2/5 is,

Half of 2/5 = 2/5x1/2

Half of 2/5 = 2/10

Half of 2/5 = 1/5

So, the remaining portion after filling chocolate is 1/5

So, the vanilla ice cream will be 1/5.

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The inverse of negative 7 when reciprocled is found to be as - 1/7.

The reciprocal of a number is known as the inverse of that number . The term reciprocal can be defined as,  an expression or function which is related to another in such a manner that their product is unity, which means 1 , the quantity obtained by dividing the number one by a given quantity gives the original number back.

The term inverse means the reciprocal of an operation. Subtraction means to take away, and addition means to obtain the sum. Therefore , we can say that addition is the reverse of subtraction .As a result, addition and subtraction are diametrically opposed operations.

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The inequality that shows the relationship between thier heights is; g < r or r > g

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Now we have the following parameters that can be used in our computation:

Reese is taller than Gage.

Also, we have

Reeses's height = r

Gage's height = g

Since Reese is taller than Gage, then it means that

The value of r is greater than the value of g

So, we have the following inequality expression;

r > g

Also, we have;

g < r

Hence, the inequality is g < r

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Answer:

m∠A=126°

Step-by-step explanation:

Supplementary means that they add up to 180°.

Therefore we can do 180-54 to get 126° for the m∠A.

Hope this helped! :)

The tasks that Keith can delegate to the assistant are List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet, Add the Debit and Credit columns of the trial balance and Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet.

List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet: Keith should delegate this task to his assistant. This is a relatively straightforward task that does not require a deep understanding of accounting principles. The assistant can be provided with clear instructions on how to pull the account balances from the general ledger and list them in the trial balance columns of the spreadsheet.

Add the Debit and Credit columns of the trial balance: Keith should delegate this task to his assistant. This is a simple arithmetic task that the assistant can perform with clear instructions.

Make the adjusting entries on the spreadsheet: Keith should retain this task. Adjusting entries involve more complex accounting knowledge and require a deeper understanding of accounting principles. It would be difficult for the assistant to complete this task without proper training.

Complete the spreadsheet: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.

Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet: Keith should delegate this task to his assistant. The assistant can be provided with clear instructions on how to organize the data from the spreadsheet into formal financial statements. It does not require a deep understanding of accounting principles.

Journalize and post the adjusting entries: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.

--The question is incomplete, answering to the question below--

"Keith Martin is the controller for Daniels Printing Service. Keith has been putting in a lot of overtime; therefore, Mr. Daniels has allowed Keith to hire an assistant. Keith's assistant is a bright, high school graduate, but he has never taken an accounting class. Keith is trying to decide which accounting activities could be delegated to his assistant. Keith is willing to give the assistant a few simple instructions on how to complete each task, but he doesn't have the time to teach the assistant to be an accountant.

For each task listed, state whether Keith should continue to do the work or delegate the task to his assistant. Explain each answer.

1. List the account balances from the general ledger in the Trial Balance columns of the work sheet.

2. Add the Debit and Credit columns of the trial balance.

3. Make the adjusting entries on the work sheet.

4. Complete the work sheet.

5. Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the work sheet.

6. Journalize and post the adjusting entries."

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Answer:

d = 117t

Step-by-step explanation:

The equation is

y = mx + b

Here m is the function's slope, and b is the y-intercept.

We know

As the car moves at a constant speed passes a timing device at t=0.

After 9 seconds, the car traveled 1053ft.

We have to find the slope

Slope = rise/run or (y2 - y1) / (x2 - x1)

We have the slope is

m = 1053/ 9 = 117

So, the equationn is d = 117t

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100 terabytes of data must be used in order for Charles' internet bill to equal Wilma's internet cost.

Assume that there are x gigabytes of data.

The equation for Charles is y = 0.25x since he pays $0.25 for each gigabyte of data.

The calculation for Wilma is y = 0.05x + 20 because she pays a flat rate of $20 and $0.05 per gigabyte.

Charles must pay the same amount for internet service as Wilma, so;

0.25x = 0.05x + 20

0.2x = 20

x = 20/0.2

x = 100

Hence, 100 terabytes of data must be used in order for Charles' internet bill to equal Wilma's internet cost.

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The expectation of X, when X is log-normal and log(X) follows a normal distribution with mean m and standard deviation k, is exp(m + k²/2).

Therefore the answer is exp(m + k²/2).

The log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. In other words, if X is log-normal, then log(X) follows a normal distribution with mean m and standard deviation k.

The expectation of a random variable is the expected value of the variable, which is a measure of the central tendency of the distribution. For a continuous probability distribution, the expectation is also known as the population mean. The expected value of X can be calculated using the probability density function (PDF) of X.

The expectation of X is calculated as the integral of X × f(X) over the range of X. Where f(X) is the probability density function of X and X is the random variable.

For log-normal distribution, the expectation of X is calculated as follows:

E(X) = exp(m + k²/2)

where m is the mean of log(X) and k is the standard deviation of log(X).

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