The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four
times the measure of the first angle. The third angle is 12 more than the second. Let x, y, and z represent the measures of
the first, second, and third angles, respectively. Find the measures of the three angles.

Answers

Answer 1

Answer:

x = 36°

y = 66°

z = 78°

Step-by-step explanation:

General outline:Setup equations for each sentenceSolve the resulting system

Setup equations:

Allowing the first angle to be x, the second to be y, and the third to be z, the three sentences describing the relationships between angle measures are given below:

Eq1:  x + y + z = 180°Eq2:  y + z = 4xEq3:  z = y + 12°

Solve the system

Substituting equation 3, into equations 1 and 2

Eq1:  x + y + z = 180°

x + y + (y+12°) = 180°

x + 2y + 12° = 180°

x + 2y = 168°

x = 168° - 2y

Eq2:  y + z = 4x

substituting the result from equation 1, and Equation 3...

y + (y+12°) = 4*(168° - 2y)

2y + 12° = 672° - 8y

10y = 660°

y = 66°

Substituting back into Equation 3...

Eq3:  z = y + 12°

z = (66°) + 12°

z = 78°

Substituting both y, and z into Equation 1...

x + y + z = 180°

x + (66°) + (78°) = 180°

x + 144° = 180°

x = 36°

So, the three angle measures are:

x = 36°

y = 66°

z = 78°

Verification

"The sum of the measures of the angles of a triangle is 180."

x + y + z = 180°

36° + 66° + 78° = 180°

True

"The sum of the measures of the second and third angles is four times the measure of the first angle"

y + z = 4x

66° + 78° = 4*(36°)

144° = 144°

True

"The third angle is 12 more than the second"

z = y + 12°

78° = 66° + 12°

True


Related Questions

Andrew has a new job at the local pizza store as a delivery boy

Answers

The distance of the entire trip is 15 minutes and  distance far away from the house to the pizza store is 9 blocks away.

Distance

a. The entire trip based on the given graph is 15 minutes.

b.  Distance:

Distance=10-1

Distance=9 block away

c.  Andrew stopped for 3 minutes for 1 minutes between third minutes and fourth minutes.

d. Distance:

Distance=10-2

Distance=8

Distance=15-8

Distance=7 minutes

Distance=5-1

Distance=4 minutes

Therefore the distance of the entire trip is 15 minutes and  distance far away from the house to the pizza store is 9 minutes.

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Otto has some whipping cream that is 30%, butterfat, and some milk that is 2%, butterfat. He wants to make a 500 ML mixture of them that is 12%, percent butterfat.

What does point K represent in this context?

Answer:
CORRECT (SELECTED)
The mixture has the intended volume and has the intended percent of butterfat.

Explanation: Point K is on line b, so it represents a scenario where the mixture has a volume of 500 \,\text{mL}500mL500, start text, m, L, end text. Point KKK is on line aaa, so it represents a scenario where the mixture has 12\%12%12, percent butterfat.

Answers

The inference illustrates that the point K in this context represents that the mixture has the intended volume and has the intended percent of butterfat.

How to illustrate the information?

It should be noted that an inference simply means the conclusion that can be deduced based on the information given.

In this case, the inference illustrates that the point K in this context represents that the mixture has the intended volume and has the intended percent of butterfat.

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Answer: It The mixture has less than the intended volume and has more than the intended percent of butterfat.

Step-by-step explanation:

Volume and surface area

Answers

By applying the volume formulae for composite figures, cones and hemispheres, we obtain that the volume is approximately equal to 558.9 cubic centimeters.

How to determine the volume of a composite figure

The volume of the composite figure is the sum of the volumes of the two figures: (i) a cone, (ii) a hemisphere. The volume formula of the figure is shown below:

[tex]V = \frac{2\pi}{3} \cdot r^{3} + \frac{\pi}{3}\cdot r^{2}\cdot h[/tex]      

If we know that r = 5.3 cm and h = 8.4 cm, then the volume of the composite figure is:

V = (2π/3) · (5.3 cm)³ + (π/3) · (5.3 cm)² · (8.4 cm)

V ≈ 558.900 cm³

By applying the volume formulae for composite figures, cones and hemispheres, we obtain that the volume is approximately equal to 558.9 cubic centimeters.

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Glenn, the owner of a hardware store, originally paid $54.60 for 15 tool sets. At his year-end clearance sale, he sold the last tool set for 24.00 How much money did he lose on the last tool set.

Answers

The amount of money he lose on the last tool set is: $30.60.

Amount lose

Using this formula

Amount lose=Original amount paid -Selling price

Where:

Original amount paid=$54.60

Selling price=$24.00

Let plug in the formula

Amount lose=$54.60-$24.00

Amount lose=$30.60

Therefore the amount of money he lose on the last tool set is: $30.60.

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Find the area under the standard normal curve to the left of z=2.63. Round your answer to four decimal places, if necessary.

Answers

The area under the standard normal curve to the left of z = 2.63 is given by calculator will be 0.995.

What is a normal distribution?

The Gaussian distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The area under the standard normal curve to the left of z = 2.63 is given by calculator will be

Area = 0.995

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What is the best approximation for the perimeter of polygon ABCDE? A. 11.0 units B. 17.0 units C. 24.3 units D. 22.1 units

Answers

TheThe best approximation for the perimeter of polygon ABCDE is: C. 24.3 units.

Perimeter of polygon

Coordinate:

A=(-2,3)

B=(0,6)

C=(5,4)

D=(4,-1)

E=(-1,-2)

Distance AB=√(0+2)²+(6-3)²

Distance AB=√4+9

Distance AB=√13

Distance BC=√(5-0)²+(4-6)²

Distance BC=√25+4

Distance BC=√29

Distance CD=√(4-5)²+(-1-4)²

Distance CD=√1+25

Distance CD=√26

Distance DE=√(-1-4)²+(-2+1)²

Distance DE=√25+1

Distance DE=√26

Distance EA=√(-2+1)²+(3+2)²

Distance EA=√1+25

Distance EA=√26

Perimeter of pathogen ABCDE

=AB+BC+CD+DE+EA

=√13+√29+√26+√26+√26

=√13+√29+3√26

=24.2877 units
= 24.3 units (Approximately)

Therefore the correct option is C.

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Answer: 24.3 units

Step-by-step explanation:

triangle abc is equal to triangle pqr, angle p=8x+4, angle a=5x+16 , and angle q=10x+2. find angle r
a. 36
b.not enough info
c. 42
d. 102

Answers

Answer: b.not enough info

Step-by-step explanation:

Corresponding angles of congruent triangles are congruent, so [tex]\angle A =\angle P[/tex]

However, we don't have all 3 interior angles of either triangle, so we cannot conclude anything.

Using an Algebraic Expression to Represent a Problem
CAR
WASH
Fundraiser !!!
Raising money
The science club sponsors a car
wash every year to raise money for
the state robotics competition.
This year, the club raised $20 more
than twice what it raised last year.
Answer these questions to write an algebraic expression for the car wash problem.
Check Your Understanding- Question 1 of 3
Attempt 1 of 2
What missing piece of information would help you write an algebraic expression to
represent the amount of money raised this year?
A. The number of cars that were washed
B. The number of club members going to the robotics competition
C. The price of each car wash
D. How much the science club raised during last year's car wash

Answers

Answer:

x= what they raised last year

2x+20= what they raise this year or y

d

Hope This Helps!!!

Suppose we write down the smallest (positive) $2$-digit, $3$-digit, and $4$-digit multiples of $7$.

What is the sum of these three numbers?

Answers

Step-by-step explanation:

Smallest two digit number which is multiple of 7 = 14 (7*2)

Smallest three digit number which is multiple of 7 = 105 (7*15)

Smallest four digit number which is multiple of 7 = 1001 (7*143)

Sum = 14+105+1001 = 1120.

If Jonathan has 2 times as many dimes as quarters and they have a combined value of 360 cents, how many of each coin does he have?

Answers

Answer:

16 dimes8 quarters

Step-by-step explanation:

When ratios of quantities are given, it is often convenient to consider a group of objects in which the objects have that ratio.

How many groups?

Here, we have 2 dimes for each quarter, so a group of 2 dimes and 1 quarter is a useful group for this problem. Its value is 2×$0.10 +0.25 = $0.45.

The total value of all of the groups is $3.60, so there must be ...

  $3.60/($0.45/group) = 8 groups

The 8 groups of coins will have 16 dimes and 8 quarters.

Giselle works as a carpenter and as a
blacksmith.
She earns $20 per hour as a carpenter and
$25 per hour as a blacksmith. Last week,
Giselle worked both jobs for a total of 30
hours, and earned a total of $690.
How long did Giselle work as a
carpenter last week, and how long did
she work as a blacksmith?
Giselle worked as a carpenter for
hours and as a blacksmith for
hours last week.

Answers

Answer:

12 hours as a carpenter and 18 as a blacksmith.

Step-by-step explanation:

So she earns 20$ per hour as a carpenter. c can represent the amount of hours she worked as a carpenter, and the coefficient will be 20 (salary)

So she earns 25$ per hour as a blacksmith, b can represent the amount of hours she worked as a blacksmith, and 25 will be the coefficient (salary)

So we have the two equations:

c + b = 30

20c + 25b = 690

Now we can solve for c in terms of b and substitute that into the second equation:

Original equation:

c + b = 30

Subtract b from both sides

c = -b + 30

Original equation:

20c + 25b = 690

Substitute -b + 30 as c

20(-b + 30) + 25b = 690

Distribute the 20

-20b + 600 + 25b = 690

Simplify the equation

600 + 5b = 690

Subtract 600 from both sides

5b = 90

Divide both sides by 5

b = 18

Now plug this into either of the original equations to solve for c, but the first equation b + c = 30 is the easiest, so I'll use that equation

Original equation

b + c = 30

Substitute 18 as b

18 + c = 30

Subtract 18 from both sides

12 = c

PLEASEEE HELP !!!
Review the graph of a piecewise function.

On a coordinate plane, a curve goes through closed circle (negative 3, negative 1) and curves up and approaches x = negative 1 in quadrant 1. A line starts at closed circle (negative 1, negative 3) and goes to open circle (1, negative 1). It then goes to open circle (3, negative 1). A horizontal line starts at open circle (3, negative 3) and goes to (5, negative 3). A closed circle is at (3, negative 4).

For which value of x is the function continuous?

Answers

Using the continuity concept, it is found that the function is continuous at x = -3.

What is the continuity concept?

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

In this problem, the function is continuous at x = -3, as:

f(3) = -1.[tex]\lim_{x \rightarrow -3^-} f(x) = -1[/tex].[tex]\lim_{x \rightarrow -3^+} f(x) = -1[/tex].

At x = -1, we have that [tex]\lim_{x \rightarrow -1^-} f(x) = \infty[/tex], hence it is not continuous.

The function is not defined for x = 1, and at x = 3, the lateral limits are different.

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the length of the flagpole is ?

Answers

The length of the flagpole is x - 5 yards

Area of a square

The formula for calculating the area of the flagpole is expressed as:

A = L²

Given that;

A = x² - 10 + 25

Factorize

A = x² - 5x - 5x + 25

A =(x - 5) - 5(x - 5)

A = (x-5)²

Compare

L = x - 5 yards

Hence the length of the flagpole is x - 5 yards

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The principal P is borrowed at a simple interest rate r for a period of time t.

Answers

Answer:

simple interest of the given question is 495

Step-by-step explanation:

SIMPLE INTEREST=P*T*R/100

Bobby is at a county fair and is participating in "The Height Game". To play, the booth owner attempts to guess a participant's height. If the owner's guess is no more than 1 inch from the actual height, the owner wins the participant’s money. Otherwise, the participant wins a prize. If Bobby's height is 75 inches, what inequality would give the range of values that the owner could guess (g) in order to for Bobby to win a prize?

Answers

The required range for the owner to win the participant's money is given by
g ≤ 76 inches.

In the game of the Height, there is a participant named bobby and the guess maker a booth owner, if the booth owner makes the right guess than  he will get the money of the participant who are participating in the game.

What is range?

Range, it is the set of the values that come out to an outcome for certain mathematical operation.

As per the condition, the booth owner can guess the height of the participants more than 1 inches of the actual height.
so the range (g) ≤ 76, so the booth owener wins the money

Thus, the required inquility for the condition is given by (g) ≤ 76.

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Please solve this for me thank you!

Answers

Answer:

620.14

Step-by-step explanation:

Original Equation:

[tex]\frac{4y}{1.025^4}+y-2y(1.05)^2=1500[/tex]

Calculate exponents

[tex]\frac{4y}{1.103812890625}+y-2y(1.1025)=1500\\[/tex]

Simplify:

[tex]3.6238025791990193084270042653997y + y - 2.205y = 1500[/tex]

Add like terms

[tex]2.4188025791990193084270042653997y \approx 1500[/tex]

Divide both sides by 7.012

[tex]y\approx 213.91[/tex][tex]y\approx620.14[/tex]

Answer:

y = $620.14 (nearest cent)

Step-by-step explanation:

Given equation:

[tex]\dfrac{4y}{1.025^4}+y-2y(1.05)^2=\$1,500[/tex]

Factor out y from the left side:

[tex]\implies y\left(\dfrac{4}{1.025^4}+1-2(1.05)^2\right)=\$1,500[/tex]

Carry out the arithmetic operations inside the parentheses by following the order of operations PEMDAS:

Calculate the exponents:

[tex]\implies y\left(\dfrac{4}{1.103812891...}+1-2(1.1025)\right)=\$1,500[/tex]

Carry out the multiplication and division from left to right:

[tex]\implies y\left(3.623802579...+1-2.205\right)=\$1,500[/tex]

Carry out the addition and subtraction from left to right:

[tex]\implies y\left(4.623802579...-2.205\right)=\$1,500[/tex]

[tex]\implies y\left(2.418802579...\right)=\$1,500[/tex]

Finally, divide both sides by the coefficient of y to isolate y:

[tex]\implies \dfrac{y\left(2.418802579...\right)}{2.418802579...}=\dfrac{\$1,500}{2.418802579...}[/tex]

[tex]\implies y=\$620.141558...[/tex]

Therefore, y = $620.14 (nearest cent)

the arc corresponding to the central angle of 35 degrees in a circle of radius 10 feet measures __feet. Round your answer to two decimal places.

Answers

Answer:

[tex]\huge\boxed{\sf Arc \ length = 6.11 \ ft.}[/tex]

Step-by-step explanation:

Given data:

Theta = θ = 35°

Radius = r = 10 ft.

Required:

Arc length = ?

Formula:

[tex]\displaystyle Arc \ length = 2 \pi r(\frac{\theta}{360} )[/tex]

Solution:

Put the givens in the above formula

[tex]\displaystyle Arc \ length = 2 (3.14)(10)(\frac{35}{360} )\\\\Arc \ length = 2(3.14)(10)(0.097)\\\\Arc \ length = 6.11 \ ft.\\\\\rule[225]{225}{2}[/tex]

What is the final transformation in this sequence of transformations mapping pre-image VWXYZ to final image V''W''X''Y''Z''?
a translation up and to the right
a reflection across point Z'
a rotation 90° about V'
a rotation 180° about Z'

Answers

Polygon ABCD was rotated 270° about point Z to form polygon A"B"C"D"

What is a transformation?

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

Polygon ABCD was rotated 270° about point Z to form polygon A"B"C"D"

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Answer:

It's D

Step-by-step explanation:

Got it right

Type the correct answer in each box. Use numerals instead of words. A group of students were surveyed about what they want to be when they grow up. The table provided shows the choices that the students made. Use the information in the table to answer the following questions. Round all answers to the nearest whole number. Teacher Doctor Athlete Boys 24 28 56 Girls 45 31 26 The marginal relative frequency of boys and girls who want to be a teacher is %. The joint relative frequency of girls who want to be an athlete is %. The conditional relative frequency of students that selected doctor, given that those students are boys is %.

Answers

The marginal relative frequency of boys and girls who want to be a teacher is 32 %. The joint relative frequency of girls who want to be an athlete is 25.4%. The conditional relative frequency of students that selected doctor, given that those students are boys is 51.85 %.

according to the question, the table given is
          Teacher - Doctor - Athete
boys
       24            28        56                     Total boys = 108

girls           45            31          26                  Total girls = 102

What is average?

Average of the values is the ratio of total sum of values to the number of values.


Conditions

1) for boys and girls whom opt for teacher,
   [tex]=\frac{69}{210} \\[/tex]

=     32%

2) for the girls who opt for athlete relative to girls,
   [tex]=\frac{26}{102}[/tex]
 =    25.4%

3) for the boys whom opt for doctors in boys
  =  [tex]\frac{28}{108}[/tex]
 =   25.9%

Thus, The required values of conditions 1,2,3 is  32%, 25.4%, 25.9% respectively

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Answer:

the answer is 33.       12.         and 26

Step-by-step explanation:

At the beginning of the year (January 1), a company has $11,000 of common stock outstanding and retained earnings of $7,900. During the year, the company reports net income of $8,200 and pays dividends of $2,900. In addition, the company issues additional common stock for $7,700.

Answers

The preparation of the statement of stockholder's equity at the end of the year (December 31) is presented below in the form of table.

How to find the stockholder's equity?

The preparation of the statement of stockholder's equity at the end of the year (December 31) is presented as:

                                   Statement of stockholder's equity        

Particulars Common stock Retained earnings    Total stockholder  

                                                                                          Equity

Beginning

balance        $11,000                  $7,900                     $18,900

Add: Additional

common stock $7,700                                                   $7,700

Add: Net income                           $8,200                    $8,200  

Less - dividend                            -$2,900                    -$2,900

Ending balance  $17,000              $5,300                 $5,300

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use the interactive expression equivalent to 4x-4-2x+3. ​

Answers

Answer: x = 1/2

Step-by-step explanation:

4x - 2x - 4 + 3

2x - 1

x = 1/2

-. A medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the test is 0.95. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 4% of the population who take this test have the disease .If the test administered to an individual is positive, what is the probability that the person actually has the disease? Suppose 20% of the people who were referred to a clinic for the test did in fact have the disease. If the test administered to an individual from this group is positive, what is the probability that the person actually has the disease?​

Answers

Answer:

TV focusing urgency hangs amateur ushers sex tendency yachting

Please help me with this asap

Answers

Answer:

18

Step-by-step explanation:

So since the two lines are parallel, 3x is congruent to the angle to the left of 6x+18 and since the two angles together are a straight line it's equal to 180 degrees. So

6x + 18 + 3x = 180

9x + 18 = 180

9x = 162

x = 18

Whats the correct answer answer asap for brainlist

Answers

Answer: mountains
Explanation: The snow melts into the rivers

The population of Kenya is 50 000 000. The population of Pakistan is 4 times greater than the population of Kenya. What is the population of Pakistan?

Answers

Answer:

Step-by-step explanation:

Comment

I would think Pakistan should be more than just 4 times as large as Kenya. However if you are given that Kenya is 50 000 000 then Pakistan will be 4 times the size of Kenya.

Pakistan = 4 * Kenya

Pakistan = 4 * 50 000 000

Pakistan = 200 000 000

Answer: Pakistan = 200 000 000

How many significant figures are in the measurement 1.050 l? a. 1 b. 2 c. 3 d. 4 please select the best answer from the choices provided a b c d

Answers

There are 4 significant figures in the measurement 1.050 (Option d)

What are significant figures?

Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. We can determine how many significant figures in a given numbers by counting the number of digits that are significant to indicate the quantity or value of something.

How the measurement 1.050 has 4 significant figures?

Since the quantity 1.050 starts with 1, that is a non-zero digit, we start counting the significant figures starting from this digit. Thus, 1 is the first significant digit here. 0, 5, and 0 are the second, third, and fourth significant digit respectively.

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Answer:

option D

Step-by-step explanation:

just took the test

A social security number is a sequence of nine digits. Determine the number of social security numbers that satisfy the following conditions:
a. There are no restrictions.
b. The digit 8 is never used.
c. The sequence does not begin or end with 8.
d. No digit is used more than once.

Answers

Answer:

765314290

Step-by-step explanation:

doesn’t use 8

Not start with 8

Digits used only 1’cd

•Mr. Jones and Mr. Thomas
entered into partnership
I with capital of $12600
and $19200 respectively.
after 3 months they!
were joined by Mr.Forson with a capital of $ 16200.It is agreed that the profit should be shared in proportion to their capitals.During the first 3 month of the year,………..

Answers

The profit should be shared in proportion to Mr Jones, Mr Thomas and Mr forson capitals in the ratio 21 : 32 : 27 respectively.

Proportion

Mr Jones capital = $12600Mr Thomas capital =$19200Mr forson capital = $16200

Total capital = $12600 + $19200 + $16200

= $48,000

Mr Jones proportion = $12600 / $48,000

= 21/80

Mr Thomas proportion = $19200 / $48,000

= 32/80

Mr forson proportion = $16200 / $48000

= 27/80

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match each equation to one of the graphs

Answers

Can you show us all the graphs

Answer:

I can only see one graph in that screenshot, so I graphed all of them. The one on your screenshot was B.

The price p (in dollars) and the demand X for a particular clock radio are related by the equation X = 3000 -10p. Find and answer A - D

Answers

The price p based on the equation given is p = 3000 - 0.1x.

How to express the price?

The equation given in the question is x = 3000 - 10p. The price(p) will be:

x = 3000 - 10p.

Make p the subject of the formula

x + 10p = 3000

10p = 3000 - x

p = (3000 - x)/10

p = 3000 - 0.1x

The revenue will be price multiplied by quantity. This will be:

= (3000 - 0.1x) × x

= 3000x - 0.1x²

The marginal revenue will be calculated after differentiating. This will be:

= 3000x - 0.1x²

= 3000 - 0.2x

The demand which is the quantity based on the information will be:

3000 - 0.2x = 0

0.2x = 3000

x = 1500

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Other Questions
Which directly results in a consequence?O reflecting on selfish choicesO wishing to demonstrate more tolerant behaviorsO reading a novelO making a decision In what two ways did the Soviets stray from the ideas about communism advanced by Karl Marx?Oby not giving power to the workersby attending the Yalta conferenceOby not opposing capitalismby supporting Mao ZedongOby curbing civil rightsResetNext C++ code onlyInventory Items:We're going to do an inventory management system. In the real world, this would use a database, not a file. A single inventory item contains:item names (or description), like "socks, - red" or "socks - blue". This has to be a character string that WILL include spaces.item numbers that are unique to the item, similar to UPC codes, like 121821 or 128122. Even though they look like numbers, they are really character strings.a price, like 4.99, a double.a quantity on hand, like 13, an integer.Your program will need to manage arrays of these items.-----------------------------------------------------------------------------------Menu:Your code need to have the following features, all accessible from a menu.Add a new inventory item to the data into the array in memory. You'll type in the inventory number, description, quantity and price. This will also update the number of items on the menu screen.List the inventory (in the array in memory) on the screen in neat columns. Display it in chucks of 15 items with a pause in between.Search the inventory (in the array in memory) for an item by inventory number. If found, print the stored info, otherwise print 'not found'.Calculate the total value on hand of the inventory (in the array in memory). The sum is the accumulation of all the (quantities * prices).Save the array in memory to a disk file. It can then be loaded later.Read from a disk file to the array in memory. This will overwrite the array in memory with new information from the disk. If you data isn't saved, it will be lost. That how is SHOULD work!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Menu Sample:56 items stored1) Add an item to memory2) Search memory for an item3) List what's in memory4) Total value on hand5) Save to a file6) Read in from a file0) Exit ProgramEnter Choice:-------------------------------------------------------------------------------------------------------------------How to store the arrays: Parallel Arrays OptionYou can maintain 4 arrays, one for each type. You will need to be careful to keep the items in the same position.string descriptions[1000];string idNumbers[1000];float prices[1000];int quantity[1000];In this scenario, an item will be spread over the 4 arrays, but all at the same index.------------------------------------------------------------------------------------------------------------------------------How to store the data on the disk:You are required to use the following text based formatSocks - Blue (in the inventory file)746272046515384.9927Yellow Socks254355674567234523457.9927Each individual item is stored in 4 separate lines. Records follow each other directly. given the function f(c)=4|x-5|+3, for what values of x is f(x)=15? What is NOT one of the reasons for the Fall of the Roman Empire?Series of earthquakes and natural disastersThe empire was divided into East and Westconstant invasion by Germanic tribes and the Huns from the Eastthe army had little loyalty to Rome The Centers for Medicare and Medicaid Services (CMS) inspects and approves hospitals that provide care for: Calculate the heat released when 12.5g of water, at its freezing point, freezes.16700 J8350 J4170 J12543 J Men are more likely than women to engage in sexual harassment, just as most victims of this offense are women. This is true primarily because men _______. Find the area of this circle.A = r2A = [?]Hint: First, plug in the valueof the radius into theformula for r.5 inEnter A television game show has 12 doors, of which the contestant must pick 3. Behind 3 of the doors are expensive cars, and behind the other 9 doors are consolation prizes. The contestant gets to keep the items behind the 3 doors she selects. Determine the probability that the contestant wins at least one car. A distance travaled by train in three hours with a constant speed of r miles per hour A motor hoists a mass m = 60 kg crate at a constant velocity to a height of h = 5 m in 2 s. If the indicated power of the motor is 3.2 kW, determine the motor's efficiency. Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is either in the circle or in the trapezoid. What is the angular displacement (in rad) of an object that starts from rest and accelerates at a rate of 4 rad/s2 for a time of 4 seconds? (Please leave your answer with one decimal places with no units) Put the following noun in the plural: la vez las vezs las vess las vezes las veces An arithmetic sequence has this recursive formula:a1= 5an= an-1-4 An industrially developing country called Moonopia has recently begun trading at an international level. How would the United Nations classify Moonopia's stage of economic development? What is endocrine system disease Which relation is also a function{(2,0),(3,2),(2,3)} How can gamma rays be harmful?OA. They consist of high-energy radiation that can travel through mostmaterials.B. They are large particles that can break apart other particles.C. They are fast-moving particles that can penetrate the skin.D. They are small, slow particles that can cause uncontrolled chainreactions.