Solve for the unknown angle measures of the polygon.
A pentagon has angle measures of 100°, 103°, 111° and 114°. What must the fifth angle measure?
The fifth angle measures

Answer:

400

Step-by-step explanation:

[tex]R(x)=\frac{2000x^2}{x^2+4}[/tex]

Since x represents the number of years since publication, the revenue at the end of the first year would be found by just plugging in 1 into the function.

[tex]R(1)=\frac{2000(1)^2}{(1)^2+4} \\\\R(1)=400[/tex]

It is true. For all rational numbers a and b, a−b = a + (−b).

Given that,
To determine whether the statement, "For all rational numbers a and b, a−b = a + (−b)." is true or false.

In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.

Here,
= a + (-b)
Since in the parenthesis there is a negative value, when we open the parenthesis the sign of the arithmetic operator will change accordingly,
So,
= a - b
So, the condition is true for all rational numbers.

Thus, It is true. For all rational numbers a and b, a−b = a + (−b).

Learn more about rational numbers here:

https://brainly.com/question/17450097

#SPJ1

The length of time that it cost less to move good across town will be more than 2.36 hours.

From the information, ACME movers charges $59 plus $20 per hour to move household goods across town and Hank movers charges $45 per hour.

Let the number of hours be represented by h.

Therefore, the appropriate equation will be:

59 + 20h = 45h

Collect like terms

45h - 20h = 59

25h = 59

h = 59/25

h = 2.36 hours.

Therefore, the length of time that it cost less to move good across town will be more than 2.36 hours.

Learn more about expressions on:

brainly.com/question/25968875

#SPJ1

ACME movers charges $59 plus $20 per hour to move household goods across town. Hank movers charges $45 per hour. For what length of time does it cost less to move good across town?

Answer:

The equation for this line is (P(x,y)----> P'(2h-x,2k-y), hence h=3 and k=1/2

Step-by-step explanation:

P(x,y)----> P'(2h-x,2k-y)

P(-4,-4)---->P'(8,5)

Now comparing the corresponding sides;

2h+4=8

2h=8-4

2h=4

h=2

Again,

2k-y=5

2k+4=5

2k=5-4

2k=1

k=1/2

Now, checking the answer:

P(-4,-4)----->P'{2*2-(-4),2*1/2-(-4)}

=P'(4+4,1+4)

=P'(8,5)

During an isosceles triangle two angles are identical, adding up to a total of 180, and its x value is 78.

Isosceles triangle: what is it?

In geometry, an isosceles triangle is one with at least two sides of equal length. There are two ways to define it: either as having precisely two sides of equal length or at least two sides of equal length, with the equilateral triangle being an exception to the second definition.

The aforementioned claim states that a triangle's total number of angles is 180.

the total of all angles in a triangle is 180.

⟹24+x+x=180

24+2x=180

12+x=90

x=90−12

x=78

To know more about isosceles triangle visit;

https://brainly.com/question/2456591

#SPJ9

Answer:

D. 27,468

Step-by-step explanation:

654

x42

--------

1,308

+26,160

---------

27,468

Answer:

20, 21,22,23

Step-by-step explanation:

Consecutive means in order.  Integers are the set of whole numbers and their opposites: ...-3,-2,-1,0 ,1,2,3...

Let x = the one sibling

Let x + 1 = the second sibling

Let x + 2 = the third sibling

Let x+4 = the fourth sibling.

If you add the four siblings together they equal 86

(x) + (x +1) + (x + 2) + (x+3) = 86  I put the parentheses in so that you can see each sibling, but it is not needed.

x + x+ 1 +x + 2 + x+ 3 = 86  Combine like terms

4x + 6 = 86  Subtract 6 from both sides

4x = 80  Divide both sides by 4

x = 20

The first sibling is 20, then 21, then 22 and finally 23

Check:

20 + 21 + 22 + 23 = 86

Step-by-step explanation:

Given that

To find

So, according to the question

we have,

We know that,

  Probability P(E) = [tex]\frac{possible\;events}{no.\;of\;events}[/tex]

There is,

possible event is 1, and no. of events are 5.

So, we can say that

   [tex]P(E) = \frac{1}{5}[/tex]

Answer:

To learn more about probability, please click on the link:

https://brainly.com/question/28168108

#SPJ9

The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.

The catering cost was determined if the cost per person is R 225,00.​

The cost per person = 225,00 R

To calculate the cost per unit, add all of your fixed costs and all of your variable costs together and then divide this by the total amount of units you produced during that time period.

Let us assume,

Suppose you can find the cost for 50 people.

Then,

We can write,

Catering cost = x

x = 225,00 * 50

x = 1,125,000 R

Therefore,

The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.

To learn more about cost problems visit : brainly.com/question/14303724

#SPJ9

Step-by-step explanation:

cross multiply both sides

2(6x+1)=3(5x–2)

12x+2=15x–6

collect like terms

+2+6=15x–12x

8=3x

divide both sides by 3

8\3=3x\3

therefore, the final answer is

8\3

thank you

please mark as the brainliest

42 bologna sandwiches were made

The ratio is given as

Cheese : Bologna : Peanut butter = 5 : 7 : 8

Also, we have

Total = 120 sandwiches

The number of bologna sandwiches made is calculated using

Bologna = bologna ratio/total ratio * 120

So, we have

Bologna = 7/(5 + 7 + 8) * 120

Evaluate

Bologna = 42

Hence, 42 bologna sandwiches were made

Read more about ratio at:

https://brainly.com/question/2784798

#SPJ1

Answer:

a = 3

Hope this helps :)

Explanation and Check part below.

Step-by-step explanation:

1. Isolate the variable by doing the inverse operation which is in this case subtracting 2 on both sides of the equation.

a + 2 = 5

- 2 - 2

a = 3

Check:

1. Substitute a with the solution 3.

3 + 2 = 5

5 = 5 ✓

The rate unit of the cost of the juice bought by Megan is  $1.28 per quart.

For the given question;

The price of 2-quart bottle of juice bought by Megan = $2.56.

For calculating the price of 1 bottle, simply divide the total cost by number of bottles.

Price of a single quart bottle = $2.56/2.

Price of a single quart bottle = $1.28 per quart.

Thus, the price of single quart bottle of juice is 1.28 per quart.

To know more about unitary method, here

https://brainly.com/question/8083231

#SPJ9

As a result, 95% of the students had grade point averages ranging from 1.83 to 3.39.

A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end.

The normal distribution is also known as the bell curve because the probability density graph resembles a bell. It is also known as the Gaussian distribution, after German mathematician Carl Gauss, who described it initially.

A bell-curve distribution is a normal Distribution.

Let X be the grade point averages of undergraduate students at one university.

X ~ Normal Distribution(2.61,(0.39)2)

P(1.83 < X < 3.39)

= P(X < 3.39) - P(X < 1.83)

= P((X - μ)/σ < (3.39 - 2.61)/.39) - P(((X - μ)/σ)< (1.83 - 2.61)/039)

= P(z < 2) -P(z < -2)

= P(-2 < z < 2)

Thus, given a regular normal distribution (μ=0, σ =1), z is between 2 standard deviations away from the mean.

According to the Empirical Rule, 95% of the data obtained after a normal distribution is within two standard deviations of the mean.

To know more about normal distribution visit:

https://brainly.com/question/15103234

#SPJ9

The line of reflection of the given congruent angles is the y-axis.

A line of reflection is defined as a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image

Now, from the attached image, we see that the two given congruent triangles are; ΔAHJ and ΔADB

Now, we see that the coordinates are transformed as folllows;

D(5, 2) → H(-5, 2)

B(3, 0) → J(-3, 0)

Now, this type of transformation follows the transformation rule; (x, y) → (−x, y). This means it was reflected over the y-axis.

This the line of reflection of the given congruent angles is the y-axis.

Read more about Line of Reflection at; https://brainly.com/question/22342234

#SPJ1

Step-by-step explanation:

a1 = 2

a2 = a1 + 9 = 2 + 9 = 11

a3 = a2 + 9 = 20

a4 = a3 + 9 = 29

a5 = a4 + 9 = 38

a6 = a5 + 9 = 47

Answer:2

Step-by-step explanation:

Answer:

Per acre will cost 6200

70 acres will cost 434,000

Step-by-step explanation:

you’re buying 60 acres Of farmland at a cost of 372000

1) What is the cost per acre

In order to find the cost per acre we divide the values which is;

➟ 372000 ÷ 60

➟ 6200

∴ it will cost 6200 per acre

2) What would be the cost for 70 acres

to find how much it will cost for 70 acres we will multiply the value per acre by 70 which is;

➟ 6200 × 70

➟ 434,000

∴ it will cost 434,000 for 70 acres

Answer:

39

Step-by-step explanation:

1) Remove parentheses.

18 + 21

2) Simplify.

39

Thanks,
Eddie

Quick hint:

When there is a number and then a - sign outside the parenthesis and on the inside, then it creates a figure similar to the plus sign, that is when you just make it one.

Add the two numbers (both are always positive in this instance),

and there's your answer!

Equation of the line in point slope form passing through (-10,8) for the given coordinates (-10,8), (-5, 7) , (10,4), (15,3) of linear equation  is

(y - 8)=(-1/5)(x+ 10).

As given,

Given points of linear equation: (-10,8), (-5, 7) , (10,4), (15,3)

Consider (x₁, y₁)=(-10,8) and (x₂ ,y₂)=(-5,7)

Slope 'm'=(y₂-y₁)/(x₂-x₁)

                =(7-8)/(-5+10)

                =-1/5

Equation of line passing through (-10,8) in point slope form:

y-y₁=m(x-x₁)

⇒(y -8)=(-1/5)(x+10)

⇒y=1/5(-x+30)

Therefore, equation of the line in point slope form passing through (-10,8) for the given coordinates (-10,8), (-5, 7) , (10,4), (15,3) of linear equation  is

(y - 8)=(-1/5)( x + 10).

Learn more about slope here

brainly.com/question/3605446

#SPJ1

The area of the rectangle is 10x² - 13x - 3.

It should be noted that the area of a rectangle is the length multiplied by the width.

Here, the dimensions of a rectangle are 2x-3 and 5x+1.

The area will be:

= (2x - 3)(5x + 1)

= 10x² + 2x - 15x - 3

= 10x² - 13x - 3

Learn more about area on:

brainly.com/question/25292087

#SPJ1

Answer:

B. The airplane starts its descent from an altitude 500 feet higher

Step-by-step explanation:

f(x) = −300x + 30,000

the function itself represents the airplane's altitude. the y intercept, 30,000 ft, then represents the initial starting position of the plane.

when it changes

g(x) = −300x + 30,500

only the y intercept changes. it's now 30,500 ft, which is 500 more than before. that means the plane initial position is 500 feet higher.

since the term with x doesn't change, the rate will not be affected. the answers with slower or faster talks about rate, which isn't what changed.

The interval notation that expresses the statement is (-∝, 1]

The statement is given as:

The set of all numbers less than or equal to 1

The above can be represented as:

<= 1

Represent the set with variable x

So, we have

x <= 1

As an interval notation, we have (-∝, 1]

Hence, the interval notation that expresses the statement is (-∝, 1]

Read more about interval notation at

https://brainly.com/question/24424191

#SPJ1

a) A minimum of number of dogs that could have a mass of more than 24 kg is 6.

b) The maximum number of dogs that could have a mass of more than 18 kg is 20.

Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.

The minimum of the values present in the interval 20 to 40 is 6

The maximum of the values present in the interval 20 to 40 is (12+6) = 18

To to learn more about minimum and maximum values from given link

https://brainly.com/question/14993153

#SPJ1

Answer:

Step-by-step explanation:

Let the hours of actual work be x and total charge be y.

Total amount of charge is:

Total amount of charge is:

Since y is same for both companies, set the equation and solve for x:

Answer:

10 분

Step-by-step explanation: