Write a polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.
x= -2, x=7
P(x)=_____

(Type an expression using x as the variable. Do not factor.)

Write A Polynomial Function Of Least Degree With Rational Coefficients So That P(x) = 0 Has The Given

Answers

Answer 1

The polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14

What is polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that the zeroes of the polynomial are, x= -2, x=7

The polynomial expression is obtained as,

=(x+2)(x-7)

=x²-7x+2x+14

=x²-5x+14

Thus, the polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14.

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Related Questions

A textbook store sold a combined total of 429 chemistry and biology textbooks in a week. The number of chemistry textbooks sold was 51 more than the number of biology textbooks sold. How many textbooks of each type were sold?

Answers

Using system of linear equation, the store sold 240 chemistry books and 189 biology books

System of Linear Equation

A system of equations is a set or collection of equations that you deal with all together at once. The general representation of linear equations are given as y = mx + c

m = slopec = y-intercept

Let set our variables as;

chemistry = x biology = y

x + y = 429 ...eq(i)

x = 51 + y ...eq(ii)

Put eq(ii) into (i)

(51 + y) + y = 429

51 + 2y = 429

2y = 429

y = 189

x = 51 + 189

x = 240

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Fill in the blanks. (Enter the domain in interval notation.) Function Alternative Notation Domain Range 2. -12 points LarPCakcCC3 4.7002 Fill in the blanks. (Enter the range in interval notation.) Function Alternative Notation Domain Range y cos-1x -1 s x s 1 3. -3 points LarPCakcc3 4.7.003 Fill in the blanks. (Enter the domain and the range in interval notation.) Function Alternative Notation Domain Range y-arctan x y-

Answers

The interval notation of domain and range is (-∞, ∞).

Interval notation:

In algebra, interval notation refers the way to describe continuous sets of real numbers by the numbers that bound them.

Given,

Here we need to write the interval notation of domain and range.

In order to find the interval notation, first we have to know the definition of domain and range.

In math domain refers the domain of a function is the set of values that we are allowed to plug into our function. Basically, this set is the x values in a function such as f(x).

And where as the range of a function is the set of values that the function assumes. And it is the values that the function shoots out after we plug an x value in.

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any help on this question

Answers

Option A satisfy the equation after simplification that is y(y-1) / 3(y+1) when the equation that is 36y / (y²- 2y+1) ÷ 12y² / (y²-1)

Given that,

We have to simplify the equation that is

36y / (y²- 2y+1) ÷ 12y² / (y²-1)

We know that,

We have to divide the equations,

36y / (y²- 2y+1) ÷ 12y² / (y²-1)

We can write in multiplication form that is

36y / (y²- 2y+1) × (y²-1) / 12y²

Now we can divide the 36y by 12 y² we get 3/y

3(y²-1)/ y(y²- 2y+1)

We can write the y²-1 as (y-1)(y+1) and by formula y²-2y+1 as (y-1)²

3(y-1) (y+1)/ y (y-1)²

Now we can divide

3(y+1)/ y(y-1)

So we can see in the options

Therefore, Option A satisfy the equation after simplification that is y(y-1) / 3(y+1) when the equation that is 36y / (y²- 2y+1) ÷ 12y² / (y²-1)

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An international company has 13,500 employees in one country. If this represents 19.6% of the company's employees, how many employees does it have in total?
Round your answer to the nearest whole number.

Answers

The required number of employees does it have in total is 68877.

What is percentage?

A percentage is a part of an entire communicated as a number somewhere in the range of 0 and 100 as opposed to as a small portion. Something is all 100%, a big part of it is 50%, none of something is zero percent. To decide a rate, you partition the piece of the entire by the actual entire and duplicate by 100.

According to question:

Let total population of the company be X

So,

19.6% of x = 13500

x(19.6/100) = 13500

X = 13500×100/19.6 = 68877 employees

Thus, required number of employees is 68877.

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A retirement account is opened with an initial deposit of $6,500 and earns 9.11% interest compounded monthly. What will the account be worth in 45 years?

Answers

Answer: $385,993.09

Step-by-step explanation:

Initial Amount: 6500

Rate: 0.0911 comp. monthly

Time: 45 years

Answer: 385,993.09

Quadra, PQRS is dilated by scale factor of 1/2 with point or as the center of dilation resulting in the image PQRS which statement is true about line Ps

Answers

The statement that is true about line segment P'S' is (c) Segment P'S' s 4 units long and lies on a different segment.

How to determine the true statement?

The complete question is in the attached image

From the image, we have:

PS = 8 units

This means that:

P'S' = 1/2 * PS

So, we have:

P'S' = 1/2 * 8

Evaluate

P'S' = 4

Also, the segment PS and P'S' do not lie on the same segment

Hence, the true statement is (c)

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If my math teacher asked me what's 5÷10+2-9 what would the answer be ?? ​

Answers

Answer:-6.5

Step-by-step explanation:

Answer:

Step-by-step explanation

Use pemdas.

P- Parenthesis

e- Exponents

m- Multiplication

d- Division

a- Additon

s-Subtraction

5÷10+2-9

=5÷12-9

=5÷3

=1.666666666667

Determine the number of imaginary zeros of the function with the given degree and graph. Explain your reasoning.

Answers

Answer:

1

Step-by-step explanation:

Number of roots = number of real roots + number of non-real roots

The graph intersects the x-axis 3 times

4 = 3 + x

x = 1

30 POINTS // A spinner is divided into six equal parts numbered 1, 2, 3, 4, 5, and 6. In a repeated experiment, Ryan spun the spinner twice. The theoretical probability of both spins being even numbers is 9 over 36.

If the experiment is repeated 200 times, predict the number of times both spins will be even numbers.

36
50
100
200

Answers

The number of times both spins will be even numbers in 200 spins is (b) 50

How to predict the number of times both spins will be even numbers.

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

Sections on the spinner = 1, 2, 3, 4, 5, and 6

Also, from the question;

We have the following statement

The theoretical probability of both spins being even numbers is 9 over 36.

This means that

P(Both even) = 9/36

Lastly, we have

Times of experiment = 200

So, we have

Outcomes of both even = P(Both even) * Times of experiment

Substitute the known values in the above equation, so, we have the following representation

Outcomes of both odd =9/36 * 200

Evaluate

Outcomes of both odd = 50

Hence, the outcomes is (b) 50

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What is the probability of obtaining five tails in a row when flipping a​ coin?

Answers

Answer:

1/32  

Step-by-step explanation:

There are  2^5   outcomes from flipping 5 times = 32

  only ONE is   T  T  T  T  T         1 OUT OF 32 =  1/32

Find the sum
5. 1/4+ 1/28+ 1/70+ ,.....

Answers

The sum is 9/28

What is sum ?

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million.

The end result of addition is a sum. For instance, the sum 10, written, is obtained by adding 1, 2, 3, and 4. (1) The sum of the numbers is known as the sum of the addends, or summands occasionally.

1/4 + 1/28 + 1/70 + 1/30 + ............ 1/700

Multiply and divide by 3 in whole series

⇒ 1/3 X [3/4 + 3/28 + 3/70 + 3/130 + ......... 3/700]

⇒1/3 X [1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+..........1/25-1/28]

⇒1/3 x [1 - 1/28]

⇒1/3 * 27/28

⇒ 9 / 28

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How do you solve 12-8x=-5x-5x??
Please help me!!

Answers

Answer:

-6

Step-by-step explanation:

12-8x= -5x-5x

Combine like terms

12-8x= -10x

Add 8x to both sides

12-8x= -10x

  +8x.  +8x

12= -2x

Divide both sides by -2

12= -2x

/-2.   ;-2

-6=x

Hopes this helps please mark brainliest

what is 2×1+2×
1/
10
+1×
1/
100
+3×
1/
1000

Answers

Answer:

2.213

2×1+2(1÷10)+1(1÷100)+3(1÷1000)

2×1+2×0.1+0.01+3×0.001

2+0.2+0.01+0.003

2.213 #

hope this will help ig

Answer:

2.213

Step-by-step explanation:

2×1+2(1÷10)+1(1÷100)+3(1÷1000)

2×1+2×0.1+0.01+3×0.001

2+0.2+0.01+0.003

2.213

Why were goods planned to become obsolete?
A. So that the company would become known for quality goods
B. So that people would keep buying new things
C. So that companies could protect their brand
D. So that people could save as much money as possible

Answers

Answer: B

Step-by-step explanation: B. So that people would keep buying new things

Goods are often planned to become obsolete in order to encourage people to continue buying new things. This can be done by intentionally designing products with a limited lifespan or by using materials that are prone to wear and tear. Companies may also release new versions of products or discontinue support for older models in order to encourage consumers to upgrade to the latest version. By making their products become obsolete, companies can create a sense of urgency for consumers to keep buying new things and maintain their sales.

Find the value of x.

Answers

The triangles are similar triangles. Then the value of the variable 'x' will be 6.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Similar triangles are shown below.

We know that the ratio of the corresponding sides of similar triangles remains constant. Then the equation is given as,

(6x - 1) / 15 = 14 / 6

Simplify the equation, then we have

(6x - 1) / 15 = 14 / 6

(6x - 1) / 5 = 7

6x - 1 = 35

6x = 36

x = 6

The triangles are comparable triangles. Then, at that point, the worth of the variable 'x' will be 6.

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10. The table represents the relationship between the base length and the height of some parallelograms, Both measurements are in inches. What is the relationship between the base length and height of these parallelograms?

Answers

The relation between base length and height is: f(x) = 48/x

What is parallelogram?

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two pairs of parallel sides. A parallelogram has opposite sides that are facing one another and opposite angles that are of equal size.

By the values given in the table, for base length and height of the parallelograms, you can notice that base length increases 1 units, so you have 1, 2, 3, 4, 5.

For height you can notice that while base length increase 1 unit, height decreases by a factor of 1/x, just as follow:

1 - 48

2 - 24

3 - 16

4 - 12

5 - 8

The relation between base length and height is:

f(x) = 48/x

where f(x) is the height and x is the base length. In fact, you have:

f(1) = 48/1 = 48

f(2) = 48/2 = 24

f(3) = 48/3 = 16

f(4) = 48/4 = 12

Hence, the relation between base length and height is: f(x) = 48/x.

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Casey inherited $70000, and decided to invest some of the money in a savings account earning 1% interest per year, and the rest in a certificate of deposit earning 2% interest per year. If the interest from the certificate of deposit was $800 more than the interest from the savings account, how much did Casey invest in each account?

Savings:


Certificate of Deposit:

Answers

The amount that Casey invested in the savings account is $10,000 and the amount Casey invested in the certificate of deposit is $60,000.

How much was invested in the savings account and the certificate of deposit?

0.01c -  0.02s = $800 equation 1

c + s = $70,000 equation 2

Where:

c = amount invested in the certificate of deposit s = amount invested in the savings account

Multiply equation 2 by 0.01:

0.01c + 0.01s = 700 equation 3

Subtract equation 3 from equation 1:

0.01s = 100

Divide both sides of the equation by 0.01:

s = 100 / 0.01

s = 10,000

Substitute for s in equation 2:

c + 10,000 = 70,000

c = 70,000 - 10,000

c = 60,000

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5+5p=5p +5 is what property

Answers

Answer:

Commutative Property Addition

Rewrite the following scientific notation numbers into standard form. (Be sure to use commas)
a. 3.23x10 -3
b. 7.45x10 5 =

Answers

Answer:

a. 0.00,323

b. 745,000

Step-by-step explanation:

a) move the decimal 3 places to the left

b) move the decimal 5 places to the right.

Owen paid a landscaping company $108 for an initial lawn treatment,
then $74 per month thereafter.
The function p(t) = 108 + 74t represents the total amount of money he will
have paid after t months.
Find p(12).

Answers

The value of p(12) is $996

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

"Find p(24)" also means "Find the amount of money Owen pays for lawn service after 12 months" as we're given 12 for t. As such, rewrite the given function as p(12) = 108 + 74(12)

p(12) = 108 + 74(12)

p(12) = 108 + 888

p(12) = $996

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If 3x – y = 5 and 2x + y = 15, evaluate x^2 + 2y

Answers

If 3x – y = 5 and 2x + y = 15  then evaluation of  x^2 + 2y is equal to 72.

What is evaluation ?

Finding the value of an algebraic expression when a given number is used to replace a variable is known as evaluating the expression. When evaluating an expression, we change the variable in the expression to the given number and then use the order of operations to simplify the expression.

3x-y=5 and 2x+y= 15

Add the two equations together to eliminate y

3x-y=5

2x+y= 15

---------------------

5x = 20

Divide by 5

5x/5 = 20/5

x = 4

Now we can find y

2x+y = 15

2(4) +y = 15

8+y =15

Subtract 8 from each side

8+y-8 = 15-8

y =7

We want to find

x^2+2xy

(4)^2 +2(4)(7)

16+56

72

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Please help, this is geometry and I need to find the measure of the missing angle

Answers

The measure of missing angle is 145°.

Define linear pair theorem.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.

Given

Missing angle = x°

Opposite angle = 100°

Exterior angle = 35°

x and exterior angle are linear pair

Sum of linear pair is 180

x + 35 = 180

x = 180 - 35

x = 145

The measure of missing angle is 145°.

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PLS HELP THANK YOU SO MUCH

Answers

Answer :

y = 202°

Solution :

As we know that, while finding any angles on a line, the full angle is 360°.

Now we have three angles in the image and their sum will be 360°, and the angles are :

68° 90° y

Now, 68° + 90° + y = 360°

=> 158° + y = 360°

=> y = 360° - 158°

=> y = 202°

Hence, y = 202° is the answer.

i only need 12 and 17, first good response i will give brainliest please i’m desperate

Answers

Answer:

[tex]\textsf{12.} \quad y = 6x - 5[/tex]

[tex]\textsf{17.} \quad y=-\dfrac{1}{4}x-2[/tex]

Step-by-step explanation:

Question 12

Find the slope of the line by substituting two points from the given table into the slope formula.

Define the points:

Let (x₁, y₁) = (2, 7)Let (x₂, y₂) = (3, 13)

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{13-7}{3-2}=\dfrac{6}{1}=6[/tex]

Substitute the found slope and point (2, 7) into the point-slope formula to create an equation of the line:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-7=6(x-2)[/tex]

[tex]\implies y-7=6x-12[/tex]

[tex]\implies y=6x-5[/tex]

Question 17

Given:

f(4) = 3f(0) = -2

Therefore, two points on the line are:

(4, -3)(0, -2)

The y-intercept is the y-value when x = 0.

Therefore, the y-intercept of the line is -2.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Substitute the y-intercept and the point (4, 3) into the slope-intercept formula and solve for m to find the slope:

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

[tex]\implies -3=m(4)-2[/tex]

[tex]\implies -1=4m[/tex]

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

Therefore, the equation of the line is:

[tex]y=-\dfrac{1}{4}x-2[/tex]

Which equation is equivalent to the given equation?
x² - 6x = 8

Answers

Answer:

(x-3)^2=17

Step-by-step explanation:

i took dis test b4

i’ll give brainliest!!!!

Answers

Answer:

Lyric ran faster.

Step-by-step explanation:

When you plot y = 5x, you can trace a certain point to see which value is higher.  When I plotted y = 5x and chose the point when x = 8, y = 40 for Kira, and for Lyric, at x = 8, y = 80.  Since the y coordinate (distance) is higher, Lyric ran faster.

Answer:

Lyric ran faster than Kira, since they were travelling a longer distance when comparing to Kira in the same period of time.

Step-by-step explanation:

You may use the following logic to analyze this situation. Theoretically, the faster runner will have traveled a longer distance at any given point in time different than 0 when comparing to the other runner. Therefore, let's randomly pick a point in time to see who had traveled the longer distance.

The time we'll evaluate will be 4 seconds.

1. Evaluating the function to find Kira's traveled distance at 4 seconds.

For this, simply substitute the "x" by the number "4" in the given equation for Kira:

[tex]y=5(4)\\ \\y=20[/tex]

Conclusion: Kira had traveled a total distance of 20 yards, 4 seconds after starting the race.

2. Evaluating the function to find Lyric's traveled distance at 4 seconds.

To evaluate the graph, we'll have to draw a line where x=4 sits and then find the value of "y" the function returns. Check the attached images in order to see this process.

Conclusion: Lyric had traveled a total distance of 40 yards, 4 seconds after starting the race.

3. General conclusion.

After 4 seconds Kira traveled 20 yards;

After 4 seconds Lyric traveled 40 yards.

Conclusion: Lyric ran faster than Kira, since they were travelling a longer distance when comparing to Kira in the same period of time.

What is the equation in point-slope form of the line that passes through the points (-3, -1) and (2, 9)?
y-1 = 2(x+3)
y-9=2(x-2)
y+9=2(x-2)
y-1= 2(x-3)

Answers

Answer:

[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Given points:

(-3, -1)(2, 9)

Substitute the given points into the slope formula to find the slope of the line:

[tex]\implies m=\dfrac{9-(-1)}{2-(-3)}=\dfrac{10}{5}=2[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and point (-3, -1) into the point-slope formula:

[tex]\implies y-(-1)=2(x-(-3))[/tex]

[tex]\implies y+1=2(x+3)[/tex]

Substitute the found slope and point (2, 9) into the point-slope formula:

[tex]\implies y-9=2(x-2)[/tex]

Therefore, the correct answer option is:

[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]

Bobby and Garnetta thought of four consecutive odd intergers such as five times the sum of the first and the third was 22 greater than the product of 8 and the sum of the second and the fourth. Find the numbers.

Answers

An integer is a whole number  x=-11.

What are Integers?The Latin term "Integer," which implies whole or intact, is the source of the English word "integer." A particular category of numbers called integers includes zero, positive numbers, and negative numbers.Symbol

The symbol "Z" stands for an integer.

Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}

Example :

Let the numbers be x, x + 2, x + 4, x + 6...

5(x+x+4)=8(x+2+x+6)+22

5(2x+4)=8(2x+8)+22

10x+20=16x+64+22

The integers are -11,-9,-7,-5,

10x-16x=64+22-20 -6x=66/-6

x=-11.

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help please and thanks so much

Answers

Answer:

Option 2

Step-by-step explanation:

The greater than sign with the line under it means greater than/less than or equal to. So -2.4 is less than or equal to -2.40.

-Hope this helped

how many 3/4 cups serving aare in 5 1/2 cups of yogurt

Answers

Answer:

Below

Step-by-step explanation:

5 1/2 = 11 / 2

11/2  ÷  3/4   = 11/2  x 4/3  = 44/6 = 7  1/3

Other Questions
most nerve impulses from our senses are routed through the Find the domain and solve.(d) log(1+x)=0.25 Determine whether the statement is true or false. If f has an absolute minimum value at C, then f'(c) = 0. True False in 2016, a 1952 Willie Mays rookie card from Topps sold for $478,000! Currently, a toaster may cost $25. How many toasters could you buy with the money spent on the willie Mays rookie card? An acellular entity composed of a small circular RNA molecule without a capsid and capable of replicating its genome is known as which of the following? A) prion B) virion C) viroid D) virus suppose the continuous random variable, x, is uniformly distributed between 2 and 10. what is the probability that x is either less than 3 or greater than 8? A force of 100 newtons is applied to a box at an angle of 36 with the horizontal. if the mass of the box is 25 kilograms, what is the horizontal acceleration of the box? a. 1.52 meters/second2 b. 3.24 meters/second2 c. 5.48 meters/second2 d. 6.87 meters/second2 e. 7.15 meters/second2 How much of the 30 year increase in life expectancy since 1900 can be attributed to public health?. A polygon has vertices at (-5, 3), (-1, 3), (1, 0), and (-3, 0). Which represents a geometric translation of the givepolygon 4 units to the right and 5 units down? Arrange the steps in the correct order to solve the equation,3(22-5) - 4 = 10Add 4 to each side of theequation:3/22 - 5) = 14Use the Exponential Property andwrite in decimal form:(2 - 5)log2 = log4. 67log4. 67Find the value of Togaand substitute2-5 = 2. 23Simplify23. 625Take the log of each side:log(22+ - 5) = log('9). 2 - 5 - 1034. 87Divide each side by log 2Tog?Add 5 to each side of theequation2+ = 2. 23 +5Divide both sides of the equation Vincent is completing his math homework about the process of Completing the Square to solve quadratic equations. His work is shown below.solve: x-3x+7=0step 1: x-3x = -7step 2: x-3x+9=-7 +9step 3: (x-3) = 2step 4: X-3= = 2 x=3 = 2Did Vincent make a mistake as he solved the quadratic using Completing the Square? If so, in whatstep did he first make a mistake? (Step numbers are labeled in blue on the left) Watch help videoWrite an explicit formula for an, the nth term of the sequence 48, 12, 3, .... What is the equation of the blue line What percentage of the area under the normal curve lies to the left of A 4-person grievance committee is to be selected out of 2 how many ways can the following committees be selected? Complete parts (A) through (E) below. (A) 3 from A and 1 from B A and B, with 11 and 30 people, respectively. in (B) 2 from A and 2 from B (C) All from A (D)4 people regardless of department (E) At least 3 from department A I need help on this two column proof. a paper company needs to ship paper to a large printing business. the paper will be shipped in small boxes and large boxes. the volume of each small box is 7 cubic feet and the volume of each large box is 14 cubic feet. a total of 21 boxes of paper were shipped with a combined volume of 252 cubic feet. write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. define the variables that you use to write the system. how do you think if density of the liquid will change if you increase their concentrationAn Quailty Assurance Answer Please n international manager can best develop an understanding of a particular culture by . a. creating a cultural profile for that country or region in which the firm does business b. assuming that his or her own cultural styles and practices can be successfully followed in the host country c. using stereotypes to develop cross-cultural understanding in a business setting d. hiring locals rather than expatriates for management positions in overseas subsidiaries if the mpc is 0.50 and the equilibrium gdp is $100 billion below the full-employment gdp, then the size of the recessionary expenditure gap is