Find m/ABD.
D
с
A
20°
B

Applying the definition of exterior angle, the measure of angle B is: c. 33°

When a side of a triangle is extended through an interior angle, the angle formed is called the exterior angle of a triangle.

The angle to the exterior angle of the triangle, when added to the exterior angle will have a sum of 180 degrees, which means their supplementary angles.

Therefore:

4x - 15 + 14x - 21 = 180

4x + 14x - 15 - 21 = 180

18x - 36 = 180

18x = 180 + 36

18x = 216

18x/18 = 216/18

x = 12

m∠B = 4x - 15 = 4(12) - 15 = 33°

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Answer:

its B. 33

Step-by-step explanation:

110 additional miles he will have to drive .

To calculate : additional miles qiang will have to drive

Let the additional no. of miles he has to drive be x .

⇒ Total Distance = 15 + x

    Total Time ( in hrs ) = ( 15 / 30 ) + ( x / 55 ) = ( 1 / 2 ) + ( x / 55 )

The equation becomes ,

[ ( 15 + x ) ] / [ ( 1 / 2 ) + ( x / 55 ) ] = 50

On simplification we get ,

15 + x = 25 + ( 10x / 11 )

x = 110

Therefore , 110 additional miles he will have to drive .

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The equation of the line that passes through the points (-6 , 2) and (-4 , -1) is 3x + 2y = -14 .

In the question ,

two points are given as  (-6 , 2) and (-4 , -1) .

we need to find the equation of the line passing through the given points .

to find the equation First we need to find the slope  ,

slope = (-1-2)/(-4-(-6))

slope = -3/(-4 + 6)

slope = -3/2

So , the equation of the line passing through the point (-6 , 2) with slope -3/2 is  

(y - 2) = (-3/2)(x - (-6))

y - 2 = (-3/2)(x + 6)

y - 2 = (-3/2)x - 9

y = (-3/2)x - 9 + 2

y = (-3/2)x - 7

2y = -3x - 14

3x + 2y = -14

Therefore , The equation of the line that passes through the points (-6 , 2) and (-4 , -1) is 3x + 2y = -14 .

The given question is incomplete , the complete question is

Write the equation for the line that passes through the point (-6, 2) and (-4,-1) , write the answer in fully reduced form .

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the answer is 1 but it could be a I took the test

The length of the garden is:  l ≥ 6225ft.

Area = L multiplied by W. Since you measure the area in square feet, your final number should reflect that.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Let l serve as a symbol for the garden's length.

Let w be the symbol for the garden's width.

The perimeter is 540 feet.

The rectangle's circumference is equal to

2(l + w)2(l + w) = 540 l + w = 270.      (1)

The rectangle's area is equal to its length times its width, which equals 12000.            (2)

Make the variable w the subject of the following equation:

w = 270 - l.   (3)

Substitute equation (3) into equation (2)

(270 - l)(l)   ≤    12000

270l  -  l²  ≤   12000

0   ≤  l²  -  270l +  12000

l²  -  270l  +  1200  ≥  0

Solving the quadratic inequality above:

l  ≥  6225

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Each motorcycle travel a distance of 240 miles for the faster motorcycle and 120 miles for the slower motorcycle.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x = time it took the faster motorcycle to travel

If the faster motorcycle travels 1 hr longer than the slower motorcycle, then the slower motorcycle travels x - 1 hours.

The product of the rate of speed and time is equal to the distance.

Hence, the distance traveled by the faster motorcycle is 80x, while the distance traveled by the slower motorcycle is 60(x - 1).

If the faster motorcycle travels twice the distance of the slower motorcycle, then the distance traveled by the slower motorcycle is 80x/2.

60(x - 1) = 80x/2

Simplify and solve for x.

60(x - 1) = 80x/2

60x - 60 = 40x

20x = 60

x = 3

distance traveled by the faster motorcycle = 80x = 80(3) = 240 miles

distance traveled by the slower motorcycle = 80x/2 = (80)(3)/2 = 120 miles

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=======================================================

Explanation:

The U refers to set union. We combine the elements of set R and set S together in one big set. Toss out any duplicates. Sorting the items is optional, but I recommend it.

R U S = {2, 3, 5, 17, 19, 37} U {3, 5, 7, 11, 13, 37}

R U S = {2, 3, 5, 17, 19, 37,      3, 5, 7, 11, 13, 37}

R U S = {2, 3, 5, 7, 11, 13, 17, 19, 37}

This list of values consist of items in set R, set S, or both.

There are 9 items in set R U S.

This is out of 12 items total in the universal set rectangle.

The probability of randomly selecting something from set R U S is 9/12 = 3/4

The advantages of bankruptcy include the following: e. All of these choices are correct.

In Financial accounting, bankruptcy can be defined as a legal process that is initiated when an individual or business organization (debtors) is relieved of the responsibility to pay their debts, honor its financial obligations to creditors, or protect them while they are trying to repay their debt.

Generally speaking, there are several advantages of bankruptcy and these include the following:

In conclusion, we can reasonably infer and logically deduce that bankruptcy is generally considered as both a friend and foe (enemy).

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Answer:

11

Step-by-step explanation:

x = 2(-x) + 33

x = -2x + 33

x + 2x = 33

3x = 33

3/3 x = 33/3

x = 11

The main difference between opinion based and informational essay is that in opinion based you have to share your own opinion reading any topic or something but in case of informative essay to have to provide particular information about the subject.

Generally speaking, an essay is a bit of writing in which the author presents their own arguments; nevertheless, this definition seems ambiguous and includes elements of letters, papers, articles, pamphlets, and short story collections. Essays are divided into two categories: formally and informally. Formal writings are distinguished by their "serious aim, dignity, logical arrangement, and length," whilst informal papers are distinguished by their "personal element."

To express your opinions on a subject and persuade the reader of your point of view, you must write an opinions essay. To accomplish it, you must first present the subject and express your viewpoint. Following that, you should provide three arguments in favor of your viewpoint. Finally, create a closing in which you summarize your case and restate your viewpoint in a new way.

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A 99% confidence interval of what the actual average mileage is for a car before it is junked is;  (153589, 174411)

The formula for confidence interval is;

CI = x' ± z(s/√n)

where;

x' is sample mean

s is standard deviation

n is sample size

z is critical value at confidence level

We are given;

x' = 164000

n = 48

s = 28000

CL = 99%

z-score at confidence level of 99% is 2.576

Thus;

CI = 164000 ± 2.576(28000/√48)

CI = 164000 ± 10410.78

CI = (164000 - 10410.78), (164000 + 10410.78)

CI = (153589, 174411)

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Answer:

Yes

Step-by-step explanation:

(1)-4=3((-2)+1)

-3=3(-1)

-3=-3

The answer is yes because if you substitute x and y for -2 and 1 you can simplify the equation. Then you get the answer -3=-3 which means that the equation is equal.

The required addition of the given fraction is given as 7/6.

Given that, a mixed fraction is given 1 1 /6 we have to determine the simplified fraction.

Fraction is defined as the number of compositions that constitutes the Whole.

Here,
Given fraction = 1 1 /6
This fraction is written as 1 + 1/6
Simplifying the fraction by multiplying the one with 6 and adding the product to the 1 in the numerator,
= [1×6 + 1]/6
= 7/6

Thus, the required addition of the given fraction is given as 7/6.

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By using addition and multiplication, the result obtained is

Kianna saves $3020 this year

What is addition and multiplication?

Suppose there are many numbers. To get the sum total of all the numbers, addition is used

Repeated addition is called multiplication

Addition and multiplication will be used here

Amount of money Kianna saves each month for the first 7 months = $215

Total amount of money Kianna saved in the first 7 months = $215 [tex]\times[/tex] 7

                                                                                                  = $1505

Amount of money she saves each month for the last 5 months = $305

Amount of money she saves in the last 5 months = $305 [tex]\times[/tex] 5 = $1515

Total amount of money Kianna saves this year = $(1505 + 1515)

                                                                              = $3020

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Answer:

x≈-0.0200335+2kπ/5

x≈-0.648352+2kπ/5

Step-by-step explanation:

sin(-5x)=0.1

-sin(5x)=0.1

sin(5x)=-0.1

sin(5x)=1/10

5x=arcsin(- 1/10)

5x=π-arcsin(- 1/10)

5x=π-arcsin(- 1/10)

5x=π-arcsin(- 1/10)+2kπ

5x=π-arcsin(- 1/10)+2kπ

x=arcsin (1/10)/5 + 2kπ/5

x=arcsin (1/10)/5 + 2kπ/5

x≈-0.0200335+2kπ/5

x≈-0.648352+2kπ/5

The value of angle ∠5 will be equal to 120°.

Straight lines with little depth or width are present. You will learn about a variety of lines, including transversal, intersecting, and perpendicular lines.

A figure called an angle is one in which two rays originate from the same point. In this area, you might also encounter contrasting and related viewpoints.

Given that In the given figure, l ∥ m and n are transversal and the angles are ∠1=80° and ∠5=100°.

First, calculate angle 2,

∠1 = ∠2  = 80 ( By alternate interior angles)

Calculate the angle ∠4,

∠4 = 180 - 80 - 40

∠4 = 180 - 120

∠4 = 60°

Calculate the angle ∠5,

∠5 = 180 - 60

∠5 = 120

Therefore, the value of angle ∠5 will be equal to 120°.

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The percentage decrease in the number of students in the school was 10%.

The percentage refers to the ratio or proportion of students that reduced the number of the school population for the present year in comparison to last year's.

We can compute the percentage by finding the decrease in population and taking the result as a numerator of the total number in the last year and multiplying the result by 100.

Percentages represent fractional values and are usually depicted by the percentage sign (%).

The total number of students in the school last year = 1,200

The total number of students in the school this year = 1,080

The decrease in the number of students = 120 (1,200 - 1,080)

The percentage decrease = 10% (120/1,200 x 100)

Thus, we can conclude that the school population decreased by 10%.

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The algebraic proof that 10+n²-(n - 2)² is always an even number is 2(5+(2n-2))

To show that this will always give an even number, we need to express in a form that it is 2 multiplied by some positive integer

Given: n is an integer greater than 1, prove 10+ n² - (n - 2)² algebraically

10+ n² - (n - 2)² = 10+ ( n² - (n - 2)² )      (factorize difference of two squares)

                     = 10+(n-(n-2))(n+(n-2))      

                     = 10+(n-n+2)(n+n-2)         (simplify)

                     = 10+(2)(2n-2)                  (factorize)

                     =  2(5+(2n-2))

Therefore, due to the factor of 2, the given expression is always even for integer n

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Answer:

Step-by-step explanation:

The line perpendicular to y = 4 will be a vertical line through the point (−2, 1). The equation of the vertical line is x = −2.

Step-by-step explanation:

common factor= x and y

remaining factor = x , 2 , 3

L.C.M = 6 x sq. y

Answer:

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

Find the total cost to produce 3575 chairs. It includes the fixed costs as well as the variable cost per chair.

Add the profit we want to have

This is the minimum amount to be made from sale.

Find minimum sales price per chair:

This is matching the first answer choice.

A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, then the value y is -2.8889

The general cosine function is given by

f(x)= A cos (B x -C) +D

where A= 1/3 is the amplitude,

period =  2π /B

π/3 =2π/B

B= 2/3

C= -2π is the horizontal shift and  D= -3s a downward vertical shift.

If we substitute all these values into the formula we obtain;

f(x)= 1/3 cos (2/3 x +2π ) -3

if x= π then we have to calculate y

y= 1/3*0.3333 -3

y= -2.8889

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Balck car can overtake the red car in 2 hrs  

The Relationship between Speed, Distance & Time can be understood by the following formulas

Speed = Distance/Time  

Time = Distance / Speed

Distance = Speed X Time  

Constant speed is also called the uniform rate which involves something traveling at a fixed and steady pace or something moving at some average speed.

Here we have

Two cars are traveling in the same direction along the same route.  

The speed of the Red car = 40 miles per hr

The speed of the Black car = 50 miles per hr  

From above data

The difference between speeds of cars = 50 - 40 = 10 miles per hr

Which means the Black car is chasing the Red car at 10 miles per hr

Given that distance between two cars = 20 miles  

The time taken by the Black car to cover 20 miles

=> Distance/ speed = 20/10 = 2hrs

Balck car can overtake the red car in 2 hrs  

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Answer:

A. y = -4x

B. y = 20

Step-by-step explanation:

A. y = xk

Where k is constant

Substitute y for -8 and x for 2

-8 = 2k

Divide both sides by 2

-8/2 = 2k/2

-4 = k

k = -4

y = x(-4)

y = -4x

B. y when x = 5

y = 5(-4)

y = 20

The velocity of the sign are given as follows:

a) Relative to the car: 60 kilometers an hour.

b) Relative to the ground: 0 kilometers an hour.

The relative speed of one object towards another is given by the rate of change in the position of each these objects relative to each other in regard to time.

Relative to the car, the sign gets 60 kilometers closer every hour, hence the relative speed of the sign will be of 60 kilometers. an hour.

Now, for the ground, the distance between the sign and the ground will always be the same, that is, there is no change in the distance. Hence, the velocity of the sign relative to the ground is of 0 kilometers and hour.

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Answer: Your question is too long for me to answer

Step-by-step explanation:

A function rule for the table:  f(x) = 2x

In this question, we have been given a table.

We need to write  a function rule for the table.

x         ƒ(x)

-3        -6

-2       -4

-1        -2

0         0

We can observe that f(x) = 2x

Therefore, a function rule for the table:  f(x) = 2x

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Our elevation is 178 feet when the elevation of a sunken ship is 120 feet.

Given, The elevation of a sunken ship is 120 feet.

Your elevation is 58 of the ship elevation.

as it is given that the elevation of a sunken ship is 120 feet and our elevation is 58 of the ship elevation.

So, on using the concept of application of trigonometry we can conclude that our elevation is 58.

As, it is given that our elevation is 58 of the ship elevation.

So, our elevation is 120 + 58 = 178 feet.

Hence, our elevation is 178 feet when the elevation of a sunken ship is 120 feet.

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Using mathematical operations, Betsie should buy the 250 envelopes from Letters2go Shop at a total cost of £319.

To determine the total cost, we first determine the unit cost of an envelope at each shop.

The unit cost is multiplied by the number of envelopes required less the cost of free envelopes at Value World.

The mathematical operations used include division and multiplication.

Deals:

Letters2go

Pack of 25 envelopes for £3.19

Value World

Pack of 10 envelopes for £1.99

Buy 2 packs get 1 pack free

                                              Letters2go         Value World

Cost per pack                           £3.19                     £1.99

Cost per envelope                   £0.1276                £0.199

The number of envelopes         250                     250

The number of packs                 10 (250/25)        25 (250/10)

Cost of free envelopes                                         £24.875 (25/2 x £1.99)

Total cost of envelopes        £319 (£3.19 x 10)    £472.63 (£1.99 x 250 - $24.875)                    

Thus, using mathematical operations, the total cost of 250 envelopes at Letter2go is less than the total cost at Value World.

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