Need help on solving this math problem!!

Need Help On Solving This Math Problem!!

Answers

Answer 1

Answer:Hello!-47 s the answer :)

Step-by-step explanation:


Related Questions

-2 ( x + 2 ) is greater than 14

Answers

-2x - 4 is not greater than 14

Step-by-step explanation:

I don't understand the question but I hope this helps

(-2 × X) + (-2 × 2)

y=-4x-29
y=-x-11

solve system of equation by substitution .

Answers

Answer:

(-6, -5)

(Don't forget to give me brainiest)

Step-by-step explanation:

1. Make the two equations equal to each other: -4x - 29 = -x - 11

2. Add "X" on both sides: -4x - 29 = -x - 11

                                              +x             +x

                                       = -3x - 29 = -11

3. Add both sides by "29":      -3x - 29 = -11

                                                  +29          +29

                                                   =    -3x = 18

4. Divide both sides by "-3" to isolate "X":     -3x = 18

                                                                         -3         -3

                                                                            x = -6

5. Plug in "-6" to "X" on first equation:  y = -4(-6)-29

                                                                y = 24 - 29

                                                                y = -5

6. Solution is: (-6, -5)

please help me

M is the set of positive three-digit numbers where the first digit is greater than the second by 4 and the third digit is greater than the first by 2

Answers

Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Final answer:

In Mathematics, a set is a group of unique elements. Here, the set M consists of three-digit numbers where the first digit is greater than the second by 4, and the third digit is greater than the first by 2. Examples of such numbers could be 530, 641, 752, etc.

Explanation:

The subject of the question is Mathematics, more specifically, the definition and properties of a set. In Mathematics, a set is a collection of distinct elements. A three-digit number has three digits: the first, second and third digit. In this case we need numbers where the first digit is greater than the second by 4, and the third digit is greater than the first by 2.

For example, let's take 501. Here, 5 is the first digit, 0 is the second and 1 is the third. The first digit is greater than the second by 5, not 4, therefore 501 does not belong to the set. But if we consider 640, here 6 is the first digit, 4 is the second and 0 is the third. The first digit is greater than the second by 2 and the third digit is less than the first by 6. So 640 belongs to the set. Therefore, our set M can include numbers like 530, 641, 752, and so on.

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Solve for x

^ use picture

Answers

Check the picture below.

[tex](x+18)(18)=(24+16)(16)\implies 18x+324=640 \\\\\\ 18x=316\implies x=\cfrac{316}{18}\implies x=\cfrac{158}{9}\implies x=17\frac{5}{9}[/tex]

Let x = the length of one side of the building. Let y = the length of one side of the entrance.

Write an expression to find
1. Volume of the whole box:

2. Volume of the cube that makes the entrance:

3. Volume of the building:​

Answers

The box volume, entrance volume and building volume are 50x², y³ and 50x² - y³ respectively

What is an equation?

An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.

a) The volume of the whole box is:

Volume = length * width * height = x * x * 50 = 50x²

b) The volume of the entrance is:

Volume = length * width * height = y * y * y = y³

c) Volume of building is:

Building volume = volume of the whole box - volume of the entrance

Building volume = 50x² - y³

The building volume is 50x² - y³

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need help with problem 7

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The 90% confidence interval for the difference between the two sample proportions are -0.078 <p₁ - p₂ < 0.003.

How to find confidence interval?

To find the 90% confidence interval for the difference between two sample proportions, use the formula:

CI = (p₁ - p₂) ± z√((p₁(1-p₁)/n₁) + (p₂(1-p₂)/n₂))

where:

p₁ = number of successes in sample 1 / sample size 1

p₂ = number of successes in sample 2 / sample size 2

n₁ = sample size 1

n₂ = sample size 2

z = z-score for the desired confidence level (90% in this case)

Using the given values:

p₁ = 780/820 = 0.9512

p₂ = 795/804 = 0.9888

n₁ = 820

n₂ = 804

z = 1.645 (from standard normal distribution table for 90% confidence level)

Plugging in the values:

CI = (0.9512 - 0.9888) ± 1.645√((0.9512(1-0.9512)/820) + (0.9888(1-0.9888)/804))

= (-0.0376) ± 0.0403

= (-0.078, 0.003)

Therefore, the 90% confidence interval for the difference between the two sample proportions is (-0.078, 0.003).

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On a small town map, where each unit represents 2 miles, the football field is located at (1,−1), the elementary school is located at (1,2), the middle school is located at (−4,2), and the high school is located at (−4,−1). Which statement is true?

Answers

Answer: We can plot the given points on a coordinate plane where each unit represents 2 miles:

 y

 |    E(1,2)

 |      

 | M(-4,2)

 |      

 |      

 |H(-4,-1)   F(1,-1)

 |___________________

           x

Now we can see that the distance between the football field (F) and the high school (H) is 5 units in the x direction and 1 unit in the y direction, which corresponds to a distance of 5 x 2 = 10 miles in the x direction and 1 x 2 = 2 miles in the y direction. Using the Pythagorean theorem, we can find the distance between the two points:

distance = sqrt((10)^2 + (2)^2)

        = sqrt(104)

So the distance between the football field and the high school is approximately 10.198 miles. Therefore, the statement that is true is:

"The distance between the football field and the high school is approximately 10.198 miles."

Step-by-step explanation:

Cuanto Producent 300.00 al 12%

Answers

Answer

La respuesta es 264.00

Find the time it takes for $9,300 to double when invested at an annual interest rate of 20%, compounded continuously.

Answers

It takes apprοximately 3.5 years fοr an investment with an annual interest rate οf 20%, cοmpοunded cοntinuοusly, tο dοuble frοm $9,300 tο $18,600.

What is cοmpοund interest?

Cοmpοund interest is a sοrt οf interest that is calculated using bοth the principal—the initial amοunt invested οr bοrrοwed—and the interest that has accrued οver time. In οther wοrds, the interest fοr the fοllοwing periοd is cοmputed οn the new, larger amοunt after the interest generated during each periοd has been added tο the principal.

Cοmpοund interest can be explained as interest οn interest. The principle grοws οver time at a rising rate as the interest generated in each periοd is added tο it. Because οf this, cοmpοund interest is an effective instrument fοr lοng-term investing and saving.

Fοr instance, if yοu put $1,000 intο an accοunt with a cοmpοund interest rate οf 5%, yοu will receive $50 in interest the first year. Yοur tοtal sum at the end οf the first year will be $1,050 (the initial $1,000 plus $50 in interest). Yοu will receive $52.50 in interest since in the secοnd year the interest is cοmputed οn $1,050 rather than $1,000. This will increase yοur οverall balance tο $1,102.50 by the cοnclusiοn οf the secοnd year, and sο οn fοr succeeding years.

In cοnclusiοn, cοmpοund interest can be a pοtent tοοl fοr lοng-term grοwth οf yοur savings οr investments, but it's critical tο cοmprehend hοw it wοrks and pick assets with cοmpetitive interest rates and lοw expenses.

Tο find the time it takes fοr an investment tο dοuble with cοntinuοus cοmpοunding, we can use the fοrmula:

[tex]t = ln(2) / (r \times ln(1 + r))[/tex]

where:

t is the time it takes fοr the investment to double

r is the annual interest rate as a decimal

In this case, the annual interest rate is 20%, or 0.20 in decimal fοrm. So,

we can plug in the values and sοlve for t:

[tex]t = ln(2) / (0.20 \times ln(1 + 0.20))\\t = 3.5 years[/tex]

Therefore, it takes apprοximately 3.5 years for an investment with an annual interest rate of 20%, compounded continuously, to dοuble from $9,300 tο $18,600.

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Select all the expressions that represent the following:

Mary swam
3/4 miles each day for 8 days

Answers

Answer:

I'm assuming the question is how many miles in total did mary swim.

if this is the case then we just multiply the number of days by the number of miles per day.

Hence,

3/4 × 8 = 6

so 6 miles in total.

make sure to ask if you need any further help

Step-by-step explanation:

Two cars travel at the same speed to different destinations. Car A reaches its destination in 25 minutes. Car B reaches its destination in 35 minutes. Car B travels 4 miles farther than Car A. How fast do the cars travel?

Answers

Step-by-step explanation:

speed = distance / time

distance = speed × time

they both have the same speed.

distanceB = distanceA + 4

so,

distanceA = speed × 25 min

distanceB = distanceA + 4 = speed × 35 min

distanceA = speed × 35 - 4

both distanceA expressions must be equal :

speed × 25 = speed × 35 - 4

subtract 25speed from both sides

0 = speed × 10 - 4

add 4 to both sides

4 = speed×10 min

divide both sides by 10 min

4 miles / 10 min = speed

to get the usual miles per hour, we need to multiply numerator and denominator by the same number, so that the denominator is 1 hour = 60 minutes.

as we cab see, we need to multiply by 6/6 :

4/10 × 6/6 = 24/60 = 24 miles per hour.

PLEASE ANSWER! (+35 points) Solve for y, solution can not be negative

Answers

1.y=6  2. y=3  3. y=9/5   4.y=3/2  5. y=3   6. y= 3

Graph the following functions and determine where F(x) = G(x). Select all that apply.

0.414
-2
-0.101
-7.89
1.586
4.414

Answers

The graph of the two functions is different from each other.

What is a function?

The expression that established the relationship between the dependent variable and independent variable is referred to as a function.

In the function as the value of the independent variable varies the value of the dependent variable also varies.

When we plot the graph of the function [tex]f(x) = \dfrac{x + 2 }{x^2-4}[/tex] and the function g(x) = |(x + 2 )} - 6.

Both graphs are different in nature and shape from each other. The graph of both functions is attached with the answer below.

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PLEASE IT IS TIMED!!!!!!!!! If f(x)=x^3 and g(x)=(x+4)^3 which description represents the graph of function g? A. a vertical transformation of function f 4 units down B. a horizontal transformation of function f 4 units left C. a horizontal transformation of function f 4 units right D. a vertical transformation of function f 4 units up

Answers

Answer:

5175 7 ehsjdjdrusjskskekrirr

Does this represent a function yes no because

Answers

The given data does not belong to the function.

What is the function?

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

A function is defined as a relation between a set of inputs having one output each.

In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and codomain or range.

Since in the given data,

at the different values of y, the value of x is the same. that is the first violation of the rule of function.

Therefore, the given data does not belong to the function.

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reduce 90/135 plss answer

Answers

Answer: 2 over 3

Step-by-step explanation: The GCF of 90 and 135 is 45. So,

divide 90 by 45 = 2

divide 135 by 45 = 3

Answer: 2/3

2/3 is 90/135 reduced

i need the answers asap, please help me.

Answers

The polynomial expressions when simplified are 2g² + 3g - 1, 24c⁵d - 8cd² + 12c³d³ + 4cd, (m² + 5m + 4) ÷ (m + 1) = m + 4.

Others are added below

Simplifying the polynomial expressions

Expression 1

The expression is given as

(14g³ + 21g² - 7g)/7g

Divide the numerator by the denominator

So, we have

2g² + 3g - 1

Expression 2

Here, we have

24c⁵d - 8cd² + 12c³d³ + 4cd

The expression is in its simplified state

Simplifying by long divison

Expression 3

Given that

(m² + 5m + 4) ÷ (m + 1)

By long division, we have

           m + 4

m + 1 | m² + 5m + 4

           m² + m

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

              4m + 4

              4m + 4

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

                0

This means that (m² + 5m + 4) ÷ (m + 1) = m + 4

Expression 4

Given that

(c² - 2c - 15)(c + 3)⁻¹

By long division, we have

           c - 5

c + 3 | c² - 2c - 15

          c² + 3c

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

              -5c - 15

              -5c - 15

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

                0

This means that (c² - 2c - 15)(c + 3)⁻¹ = c - 5

Simplifying by synthetic division

Expression 5

Here, we have

(2y² + 10y + 17) ÷ (y + 3)

By synthetic division, we have

   

-3 | 2  10  17

    |__-6_-12______

      2  4   5

This means that (2y² + 10y + 17) ÷ (y + 3) = 2y + 4 + 5/(y + 3)

Expression 6

Here, we have

(2p³ - p² - 10p + 8)(p - 2)⁻¹

By synthetic division, we have

   

2 | 2    -1   -10    8

    |___4__6__-8____

      2    3   -4     0

This means that (2p³ - p² - 10p + 8)(p - 2)⁻¹ = 2p² + 2p - 4

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Which is the same as dividing a number by 1,000? CLEAR CHECK Move the decimal 3 places to the right. Move the decimal 3 places to the left. Move the decimal 1 place to the right. Move the decimal 1 place to the left.

Answers

Answer:

Moving the decimal 3 places to the left.

Step-by-step explanation:

Take the number 3000 and divide it by 1000 in your calculator.  You will get the answer 3.  Although we do not write it, the decimal in the number 3000 is at the end of the number (after the last zero).  When we divide by 1000, we move the decimal 3 places to the let.  The decimal in the number 3 is at the end or to the right of the 3, we just do not write the decimal.

Helping in the name of Jesus.

Help with math problems

Answers

The inverse function of the given is y^-1=x/2 -4.

What is inverse function?

The domain of the original function becomes the range of the inverse function, and the range of the given function becomes the domain of the inverse function. The inverse function is denoted by the notation f-1 in relation to the original function f. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function. Only when f is both a one-one and an onto function does it have an inverse, indicated by the symbol f-1. Keep in mind that f-1 is NOT f's inverse. The domain value of x is given by combining the function f and the reciprocal function f-1.

Here the given function is,

=> y = 2x+8

Now interchange x and y then

=> x=2y+8

Now simplify the expression with respect to y then,

=> x-8=2y

=> y =x/2 -4

=>y^-1=x/2 -4

Hence inverse function is, y^-1=x/2 -4

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What is the total price of the 50-inch Panasonic Plasma TV?

Answers

The total price of the 50-inch Panasonic Plasma TV is $687.44.

What is tax?

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

Given that, 50-65 inch TV's $150 rebate and delivery charge is $35.

50 inch Panasonic Plasma TV costs $734.95

Rebate is $150

So, cost of TV is 734.95-150

= 584.95

Cost of TV including delivery charge

= 584.95-35

= 549.95

Here, tax is 25%

So, cost of TV including tax

= 549.95+25% of 549.95

= 549.95+25/100 ×549.95

= 549.95+0.25×549.95

= 687.4375

Therefore, the total price of the 50-inch Panasonic Plasma TV is $687.44.

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Brainliest for correct answer

Answers

Answer:

D 40 square feet

Step-by-step explanation:

2×8=16

16÷2=8 is area of one triangle

8+8=16 is area of both triangles

8×3=24 is area of rectangle

24+16=40 square feet

EASY MATH POINTS! Answer from the screenshot :)

Answers

Answer:

The last one

Step-by-step explanation:

First one is a parabola

Second one is an absolute value

Third one is a cubic

Fourth one is a linear

What would help me find the x?

Answers

Answer:

C

Step-by-step explanation:

I think its C because where x is you see those three lines, those mean congruent so in that triangle whatever x is the other two angles are the same thing. If I had to guess what x is, its prob 60.

the answer for this question is C

What are the equations of the tangent lines to circle x ^ 2 + y ^ 2 = 4x + 1 that are perpendicular to line 2x + y = 10​

Answers

Answer:

y = (3a + sqrt(11a^2 - 8b + 41)) / 2

y = (3a - sqrt(11a^2 - 8b + 41)) / 2

Step-by-step explanation:

To find the tangent lines that are perpendicular to the given line, we need to find the slope of the given line and then find the negative reciprocal of that slope. The negative reciprocal will be the slope of the tangent lines we are looking for.

The given line is 2x + y = 10, which can be rewritten as y = -2x + 10. Therefore, the slope of the given line is -2.

The center of the circle can be found by completing the square of the x and y terms. We have:

x^2 - 4x + y^2 = 1

(x - 2)^2 + y^2 = 5

Therefore, the center of the circle is (2,0), and the radius is sqrt(5).

Now, we can find the equation of the tangent lines. Let (a,b) be the point where the tangent line intersects the circle. Since the tangent line is perpendicular to the given line, its slope is the negative reciprocal of -2, which is 1/2. Therefore, the equation of the tangent line passing through (a,b) is:

y - b = (1/2)(x - a)

To find the points of intersection of this line and the circle, we substitute y = -2x + 10 into the equation of the tangent line and solve for x:

(x - a)^2 + (-2x + 10 - b)^2 = 5

Expanding and simplifying this equation, we get:

5x^2 - 4ax + 4a^2 + 4bx - 40b + 84 = 0

This is a quadratic equation in x, so we can solve for x using the quadratic formula:

x = [4a ± sqrt(16a^2 - 4(5)(4a^2 + 4b - 84))] / 10

Simplifying this expression, we get:

x = [2a ± sqrt(11a^2 - 8b + 41)] / 5

Now we can substitute these values of x into the equation of the tangent line to find the corresponding values of y:

y = -2x + 10

y = -a + b + (1/2)(2a ± sqrt(11a^2 - 8b + 41))

This gives us two equations for the tangent lines passing through (a,b), one for each value of x. We can simplify these equations to get:

y = (3a ± sqrt(11a^2 - 8b + 41)) / 2

Therefore, the equations of the tangent lines that are perpendicular to the given line are:

y = (3a + sqrt(11a^2 - 8b + 41)) / 2

y = (3a - sqrt(11a^2 - 8b + 41)) / 2

where (a,b) is any point on the circle (x - 2)^2 + y^2 = 5.

A sofa regularly sells for $570. The sale price is $541.50. Find the percent decrease of the sale price from the regular price.

Answers

Answer:

5%

Step-by-step explanation:

So how I figured this out was I subtracted 570 and 541.50 to find how much of a difference there was. I got 28.50 so now I know thats how much the sale took off. I'm sure there was a better way of figuring out this next part but this is how I did it, I took 570 and multiplied it by 0.10 to see what that would be. It ended up being 57 and thats not 28.50 so I multiplied 570 by 0.05 and ended up with 28.50. You coulda also divided the 57 by two to figure out is 0.05 which equals 5%.

Look at the picture and solve it guys!!!!!! Right answers only!

Answers

Answer:x=7,1

Step-by-step explanation:

Identify the relationship between the angles

Answers

Answer:

∠x and ∠y are congruent or equal

Step-by-step explanation:

∠x and ∠y are congruent or equal because their vertical angles are alternate interior angles.

OR vertical angle of ∠x is congruent with ∠y because they are both corresponding angles

OR vertical angle of ∠y is congruent with ∠x because they are both corresponding angles

Tammy's home cost her $184,000. She lives in an area with a lively real estate market, and her home increases in value by 3.5% every year. If Tammy sells her home after thirteen years, how much profit will she have made, to the nearest hundred dollars?

Answers

In linear equation, Tammy will have made a profit of $103,768.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Let x be the number of years after Tammy purchased her home.

We have been given that Tammy’s home cost her $184,000. She lives in an area with a lively real estate market, and her home increases in value by 3.5% every year.

We can see that value of house will increase exponentially as the value of increases 3.5% per year.

Since an exponential function is in form

           y = a * bˣ

a = Initial value,

b = For growth b is in form (1+r) where r represents growth rate in decimal form.

Let us convert our given growth rate in decimal form.

   3.5% = 0.035

Upon substituting our values in exponential form of function we will get the value (y) of Tammy's home after x years as

  y = 184000(1 + 0.035)ˣ

 y =  184000(1.035)ˣ

  Therefore, the function   y =  184000(1.035)ˣ represents value of Tammy's home after x years of purchase.

Let us find the value of home after 13 years by substituting x=13 in our function.

     y =  184000(1.035)¹³

     y =  184000 * 1.56395606

  y = 287767.915

  Let us subtract cost of the home from the value of home after 13 years to find the amount of profit.

   The amount of profit, if tammy sells her home after 13 years = 287767.915  - 184000  

 The amount of profit, if tammy sells her home after 13 years = 103767.915 - 103,768

Therefore, Tammy will have made a profit of $103,768.

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If 6+2=8, does 6+2+3=8+3? Why or not

Answers

Answer: Yes

Step-by-step explanation:

Well, since 6+2, 6+2+3 does equal 8 plus 3 because 6+2+3 is basically saying 8+3, but just broken up.

How do I solve
4(x-1) =2(6-2x)​

Answers

Answer:

x=2

Step-by-step explanation:

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describe the abundance of silicate minerals and list commom rock forming silucate minerals what can you to do change the climate (supportive or defensive) of an existing relationship ? The momentum of a car traveling in a straight line at 20 m/sec is 24,500 kg times m/sec. What is the cars mass? It would be better to calculate percentage change on mass rather than change in mass why is this a more valid method??????PLS I NEED THIS ANSWER ASAP If you had three wishes what would them be and why? Choose wisely and please be honest! Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = 3 + 8 x = 1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = 1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = 3 1.What is the cell composition for the epidermal layer?2.What CT proper types compose the dermal layer?3.What CT proper types compose the dermal layer? Mandla, a farmer, wants to buy a new tractor. The tractor costs R160 000 excluding VAT He can pay a deposit of R20 000. He decides to buy the tractor on hire purchase over 60 months at a simple interest rate of 10 % a. What will his instalment be? b. How much interest will he pay? c. How much will he pay in total for the tractor over 60 months? Given the graph of the quadratic function, determine the features. what is the surface area of the cone? Work out the net present value of the following investments. The risk-free rate is 3%, and the average return on the market index is 7%You invest 1,000 in cash in a 0.8-beta project. The project uses a machine you already own, costing 500 last year. You can sell the machine this year for 300. The cash flow from the project is 400 annually in years one through four. The machine is worthless in year four For f(x)=6x+8 and g(x)= 5x, find the following composite functions and state the domain of each (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = _____ (Simplify your answer.) regla general de las siguientes secuencias -2,1,6,13,22,33... What is the value of x in the rational equation x5=618 What is the main difference between federal and confederal systems of government Question THREEa) Why is finance described as the most important activity in any organization? Use relevant examples to support your answer (5 marks)b) Discuss the merit and demerits of debt finance (5 marks) 3. Consider the utility function u(x, y) = -(1/ x+2y+z) (a) Find the equation for the marginal utility for x and one for marginal utility of y. (b) Find an equation of the form y = f(x) that describes the indifference curve for utility equal to -1/2. (c) Argue that the utility values all lie in the interval [-1,0] (d) Does the utility function v(x,y) = x + 2y represent the same preferences as u(x,y)? (e) Does the utility function w(x, y) = x + y represent the same preferences as u(x,y)? Read the excerpts from The Princess and theGoblin by George MacDonald and Rip Van Winkle byWashington Irving. Then, use the archetypes chart toanswer the question.The Princess and the Goblin by George MacDonaldLootie was very glad to please the princess. She gother hat and cloak, and they set out together for a walkup the mountain, for the road was so hard and steepthat the water could not rest upon it, and it was alwaysdry enough for walking a few minutes after the rainceased. The clouds were rolling away in brokenpieces, like great, overwoolly sheep, whose wool thesun had bleached till it was almost too white for theeyes to bear. Between them the sky shone with adeeper and purer blue, because of the rain. The treeson the road-side were hung all over with drops, whichsparkled in the sun like jewels.How do the authors use the archetype of the mountaindifferently?In the first excerpt, Lootie and the princess arehappy to be going on a walk up the mountain. Inthe second excerpt, Rip is upset to find himself sofar from home.In the first excerpt, Lootie and the princesspurposefully set off to walk up the mountain. In thesecond excerpt, Rip finds himself at the top of themountain without having meant to travel so far.In the first excerpt, Lootie and the princess findtheir trip up the mountain to be beautiful. In thesecond excerpt, Rip does not pay attention to thescenery around him.In the first excerpt, Lootie and the princess arerunning away from something when they head A bubble of helium gas has a volume of 0.650 mL near the bottom of a large aquarium where the pressure is 1.54 atmand the temperature is 12C.Determine the bubble's volume upon rising near the top where the pressure is 1.0l atm and116 Find the determinant of the triangular matrix.376057003