Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified, exact value in terms of PI (no approximations). The figures are based on semicircles or quarter circles, and problems (b), (c), and (d) involve portions of a square. Calculate area and perimeter

Find The Area And The Perimeter Of The Shaded Regions Below. Give Your Answer As A Completely Simplified,

Answers

Answer 1

Check the picture below.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{triangle}{\cfrac{1}{2}(6)(6)}~~ + ~~\stackrel{semi-circle}{\cfrac{1}{2}\pi (3)^2}}\implies \boxed{18+4.5\pi} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{pythagorean~theorem}{CA^2 = AB^2 + BC^2\implies} CA=\sqrt{AB^2 + BC^2} \\\\\\ CA=\sqrt{6^2+6^2}\implies CA=\sqrt{6^2(1+1)}\implies CA=6\sqrt{2} \\\\\\ \stackrel{\textit{\Large Perimeters}}{\stackrel{triangle}{(6+6\sqrt{2})}~~ + ~~\stackrel{semi-circle}{\cfrac{1}{2}2\pi (3)}}\implies \boxed{6+6\sqrt{2}+3\pi}[/tex]

notice that for the perimeter we didn't include the segment BC, because the perimeter of a figure is simply the outer borders.

Find The Area And The Perimeter Of The Shaded Regions Below. Give Your Answer As A Completely Simplified,

Related Questions

Prepare an amortization schedule for the first three months on a loan of $87,000 at 6% for 20 years.

Answers

Answer:

  see attached

Step-by-step explanation:

An amortization schedule is conveniently prepared using a spreadsheet. It has the formula built in for computing the payment value.

__

The amount of the payment going to interest is the product of the outstanding balance and the monthly interest rate (=6%/12). In the attached, the amount of interest due is rounded to cents. The remaining amount of the payment reduces the outstanding balance.

The attachment shows the payment calculation and the amortization schedule for the first 5 payments.

Dulce got a $25 gift card to a clothing store. She
uses the gift card to buy a shirt for $14.99. She also
wants to use the gift card to buy some socks. Each
pair of socks costs $2.49.
Which of these inequalities describe this situation,
where s is the number of socks Dulce can buy?
A) 14.99 + 2.49s < 25
B) 14.99 + 2.49s > 25
C) 14.99
2.49s < 25
D) 14.99 – 2.49s > 25

Answers

Answer:

A.

Step-by-step explanation:

Answer A. It works because the pairs of socks for 2.49 each and the 14.99 shirt need to be less than 25.

what is the GCF of the terms 5x2 -15x

Answers

Answer:

it would be 5x

Step-by-step explanation:

5x^2-15x

would be 5x because dividing by 5x you would get 5x(x-3)

but if its 5*2-15x, I don't know

Francis bought a new dress that was discounted by 21%. She used the following expression to find the price of the dress after the discount was applied.

d - (0.21)d

Which of the following is another expression that could be used to get the same results?
A.
79d
B.
d - 21
C.
d - 0.21
D.
0.79d

Answers

Answer:

D

Step-by-step explanation:

D .  .79 d would be the same

d- .21d =   (1-.21) * d= .79 d

Write the exponential function y = 22(1.35)' in the form y = aekt.
(a) Once you have rewritten the formula, give k accurate to at least four decimal places.
k%3D
help (numbers)
If t is measured in years, indicate whether the exponential function is growing or decaying and find the annual and
continuous growth/decay rates. The rates you determine should be positive in the case of growth or decay (by choosing
decay the negative rate is implied).
(b) The annual? rate is
% per year (round to the nearest 0.01%).

Answers

Answer:

y = 22·e^(0.3001t), growingannual rate: 35%continuous rate: 30.01%

Step-by-step explanation:

When an exponential function is in the form ...

  y = ab^t

the factor 'b' is called the growth factor. When t is in years, it is related to the annual growth rate (r) by ...

  b = 1 +r

In the alternate form, this can be written ...

  y = a·e^(kt)

Comparing the forms, we see that ...

  b = e^k   ⇒   k = ln(b)

__

(a)

  y = 22·1.35^t

  k = ln(1.35) ≈ 0.3001

  y = 22·e^(0.3001t)

The growth factor is greater than 1, so the function is growing.

__

(b)

The annual growth rate is ...

  r = 1.35 -1 = 0.35 = 35.00%

__

(c)

The continuous growth rate is ...

  k = 0.3001 = 30.01%

Write an equation of the line that passes through (-1,3) and is parallel to the line y=2x+2 .

Answers

Answer:

y = 2x + 5

Step-by-step explanation:

REMEMBER:

The new line will be parallel to the line represented by y =2x +2

⇒ The equation y = 2x + 2 is written in slope- intercept form (i.e. y=mx + b) where m represents the slope.  So the slope of this line is 2.   A line parallel to y = 2x + 2 will have the same slope.  This means the slope of the new line will also be 2.  

To determine the equation of the new line, we can use the given point  to find the y intercept of the new line:
⇒ y = 2x + b

Use x = -1 and y =3 to find b (or the y intercept ) of the new line:

⇒ 3 = 2 * (-1) + b

⇒ 3= -2 + b

⇒ b=5

Therefore, the equation of the line passing thru (-1,3) with the same slope as that of y = 2x + 2 will be:

⇒ y = 2x + 5

Answer:

y = 2x + 5

Step-by-step explanation:

Given line equation 2x - y + 2 = 0

Equation of line parallel to this line will be of form

=> 2x - y + k = 0 ( where 'k' is a constant )

Now this line passes through (-1,3)

=> 2(-1) - (3) + k = 0

=> -2 - 3 + k = 0

=> k - 5 = 0

=> k = 5

Therefore the required line equation is 2x - y + 5 = 0 or y = 2x + 5

Hope you've understood the solution.

Jose has scored 330 points on his math tests so far This semester. To get an for the semester he must score at least 425 points. Write and solve an inequality to find the minimum number of points he must score on the remaining tests,n, to get an A.

Answers

Answer:

(425-330)/n=A

Step-by-step explanation:

Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundred. Radius is 4 height is 10​

Answers

[tex]\bold{ANSWER:}[/tex]
167.47 unit^3

[tex]\bold{EXPLANATIONS:}[/tex]

What is the lateral surface area of the triangular prism?



Round to the hundredths place.

Answers

Answer:

The answer is

→ [tex]A_L = 60[/tex]

Step-by-step explanation:

a Base side is 4cm

b Base side is 5cm

c Base side is 11cm

h Height is 3cm

I ran into a problem when inputing the c Base side. It won't allow me to go over 8cm, for some reason. But hold on. I found a solution! :)

a Base side is 4cm

b Base side is 5cm

c Base side is 8cm ← (Don't mind this, I'll explain it below.)

h Height is 3cm

With c Base side being 8cm, the result is [tex]A_L = 51[/tex]. This is clearly incorrect and is not supposed to be like that. But hold on! Let me explain what I did to fix the problem. Since 8cm was the maximum amount, I did this to fix the problem:

51 + 3 = 54 (9cm)

51 + 6 = 57 (10cm)

51 + 9 = 60 (11cm)

Hope this is easy for you to understand...

Hope this helped! :^)

⭐Brainliest will be appreciated!⭐

✉️Message me if you have any more questions!✉️

- ✨7272033Alt

Submitted on 4/16/2022 at 10:20 PM

(To avoid plagarism, by users whom decide to copy.)

Please give me the answers to all three I will mark u brilliant

Answers

Answer:

First know the formula for the area of a circle;

A = π[tex]r^{2}[/tex]

Where 'π' represents pi(3.14 or 22/7), and 'r' stands for the radius being squared.

For the first problem, we can see that 12 is our diameter.

And to find the radius, we need to find 1/2 of the diameter (half of the diameter), so;

D/2 = R

Replace with actual values;

12/2 = 6, 6 is our radius.

Now we plug this into our formula:

A = π[tex]r^{2}[/tex]

A = 3.14(6^2)

A = 3.14(36)

A = 113.04 centimetres is the area of the circle.

For the second problem, we can see that 18 is our diameter.

And to convert the diameter into the radius, we do what we did to the past problem, find 1/2 of the diameter.

So;

D/2 = R

18/2 = 9, 9 is our radius.

Now we plug this into our formula:

A = π[tex]r^{2}[/tex]

A = 3.14(9^2)

A = 3.14(81)

A = 254.34 inches is the area for this circle.

For the third problem, we can see that our radius is already given, 5.

So now we just simply and easily plug this into our formula;

A = π[tex]r^{2}[/tex]

A = 3.14(5^2)

A = 3.14(25)

A = 78.5 meters is the area for this circle.

in a deck of 52 how many card combinations are greater then 16?

Answers

need pic pls so I can answer your questions

Which is the graph of the equation y-1=2/3(x-3)

Answers

Answer:

Step-by-step explanation:

evaluate the expression 120n+160,500 when n=32 WILL MARK BRAINLIEST

Answers

Answer:

164,340

Step-by-step explanation:

[tex]120n+160500\\120(32)+160500\\3840+160500\\164340[/tex]

120n+160500

Put n=32

120(32)+1605003840+160500164340

The difference between two positive integers is2. If the smaller is added to the square of the larger the sum is 40. Find the integers

Answers

Answer:

4 and 6

Step-by-step explanation:

first you must write your let statements

let x = smaller integer

let y = bigger integer

y - x = 2

x + y^2 = 40

then you use substition to find your anaswer

x = y - 2

y - 2 + y^2 = 40

y^2 + y - 42 = 0

then find the numbers that add up to 1 and multiply to -42

-6 and 7

y^2 + 7y - 6y - 42

y(y + 7) - 6(y + 7)

(y - 6)(y + 7)

set both sides equal to 0

y = 6, -7

y must be positive so it is 6

then plug y into one of the equations to get your answer

6 - x = 2

x = 4

your answer is 4 and 6

"In order to pass your final assessment, you must answer 75% of the questions correctly. There are 84 questions." “Then, I must get __________ correct to pass.”

Answers

Answer: 63 questions

Step-by-step explanation: to find 75% of 84, multiply 84 by .75

Determine the radius in metres Diameter=2230mm height=3130mm​

Answers

Answer: 1.115 metres

Step-by-step explanation:

     The radius is half the diameter.

2,230 mm / 2 = 1,115 mm

     To turn mm into metres, we divide the length by 1,000.

1,115 mm / 1,000 = 1.115 metres

Answer:

1.115m

Step-by-step explanation:

[tex]radius = \frac{diameter}{2} \\ = \frac{2230}{2} \\ = 1115mm \\ = from \: mm \: to \: m \\ = \frac{1115}{1000} \\ 1.115m[/tex]

Please rate brainliest if you think I deserve

Super easy, find the area! 7th grade math

Answers

4.5 cm²

[tex] \: [/tex]

Step-by-step explanation:

It is given that, the height of a triangle is 3cm, and its base is 3cm and we are to find the area of triangle.

[tex] \: [/tex]

To find the area of the triangle, we have to know this formula :

[tex]\\ {\longrightarrow \pmb{\frak {\qquad Area_{(Triangle)} = \: \frac{1}{2} \times Base \times Height \:}}} \\ \\ [/tex]

Now, substituting the values in the formula :

[tex]{\longrightarrow \pmb{\sf {\qquad Area_{(Triangle)} = \: \frac{1}{2} \times 3 \times 3 \:}}} \\ \\ [/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad Area_{(Triangle)} = \: \frac{1}{2} \times 9 \:}}} \\ \\ [/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad Area_{(Triangle)} = \: \frac{9}{2} \:}}} \\ \\ [/tex]

[tex]{\longrightarrow \pmb{\frak {\qquad Area_{(Triangle)} = \: 4.5 \:}}} \\ \\ [/tex]

Therefore,

The area of the triangle is 4.5 cm² .

Answer:

4.5cm^2

Step-by-step explanation:

Find area of a square 3*3=9

Half of a square is 9/2=4.5

In Houston, 9 bats ate 50 grams of insects in one night. At this rate, how many grams of insects could 81 bats eat in one night?

Answers

Answer:

Step-by-step explanation:

Remark

Using Algebra, this is a proportion question. A proportion is 2 equal ratios

If the of the 2 ratio parts are known, it is possible to solve for the 4th one.

Formula

9_bats/50_grams::81_bats/x grams insects

Solution

Put the three knowns in and solve for the 4th which is not known

9 bats/ 50 insects = 81 bats /x insects.         Cross multiply

9 * x = 50 * 81                                                  Combine

9x = 4050                                                       Divide by 9

9x/9 = 4050/9

Answer: x = 450 grams

Will someone please help <3

Answers

Answer:

area of base is 9pi

circumference of base is 6pi

lateral surface 24

surface area is 42

Step-by-step explanation:

please help I'll mark brainliest ​

Answers

Answer:

The answer is D

Step-by-step explanation:

A statistical question is a question that can be answered by collecting data that vary.

A statistical question is one that can be answered by collecting data and where there will be variability in that data

The only one that can have a variety of answers is the last one.

A, B, and C are countable and do Not Vary or change in amount they remain the same. There will always be 12 months in a year. 3 wheels on a tricycle and the amount of stripes in the flag will not change. If the question ask something that can change or vary it is a Statistical question. Like for example "How many minutes do 6th grade students typically spend on homework each week?" and  “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question.

A Good Statistical Question Produces Data with Variability

A statistical question is one that requires the collection of data with expected variability in it. The data collected changes in value. You can quantify them. If the data could not be measured, then you have to think it over again.

What shape is this cross-section?
O A. Circle
OB. Trapezoid
O C. Rectangle
O D. Triangle

Answers

Answer:

C. rectangle is cross section shape

Add. Write your answer as a mixed number in simplest from.

7 3/4 + 4 2/7

Answers

Answer: 12 1/28

Step-by-step explanation:

Add whole numbers. Solve fractions by finding the LCD.



The radius of the circle with a central angle of 2 radians that intercepts an arc with length 99 cm is
cm

Answers

[tex]\textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =2\\ s=99 \end{cases}\implies 99 = r(2)\implies \cfrac{99}{2}=r\implies 49.5=r[/tex]

Bonus question: what is the relationship between the circumference of a tire and the rotations necessary to cover a given distance? (i.e. are they directly proportional or inversely proportional) Explain your answer choice. Hint: think about the rotations necessary for a miniature toy car versus a massive tractor.​

Answers

Answer:

Directly proportional

Step-by-step explanation:

The circumference of the tire is equal to the distance it covers in one rotationThis means the relation is directly proportional

Using the slope​ formula, find the slope of the line through the given points.
12,0 and 2,-5

Answers

Answer:

[tex]\textsf{A.} \quad \textsf{The slope of the line is }\boxed{\dfrac12}[/tex]

Step-by-step explanation:

[tex]\textsf{let}\:(x_1,y_1)=(12,0)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(2,-5)[/tex]

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-5-0}{2-12}=\dfrac12[/tex]

[tex]\textsf{The slope of the line is }\boxed{\dfrac12}[/tex]

Quadrilateral ABCD is cyclic. Identify what the missing angle measures must be.

Answers

Check the picture below.

At a concession stand, three hot dog(s) and two hamburger(s) cost $7.50, two hot dog(s) and three hamburger(s) cost $8.75. Find the cost of one hot dog and the cost of one hamburger

Answers

Step-by-step explanation:

If 3 HD and 2HB cost $7.50

2 HD and 3HB cost $8.75

Let,y be HD

Y be HB

So 3y + 2x = $7.50. Eqn 1

2y + 3x = $8.75. Eqn 2

Solve simultaneously

Make x the subject in Eqn 1

3y + 2x = 7.50

2x = 7.50 - 3y

Devide by the coefficient of x

2x/2 = (7.50 - 3y) / 2

X = (7.50 - 3y) /2 Eqn 3

Put Eqn 3 into 2

2y + 3(7.50 - 3y) / 2 = 8.75

2y (22.5 - 9y) / 2 =8. 75

Multiply by the lcm of the denominators

2y x 2 + ((22.5 - 9) / 2) x 2 = 8.75 x2

4y + 22.5 - 9y = 17.50

Group like terms

22.5 - 17.50 = 9y - 4y

5 = 5y

5/5 = (5y) / 5

1 = y Eqn 4

Therefore 1 HD is $1

Put Eqn 4 into eqn 3

X = (7. 50 - 3y) / 2

X = (7.50 - 3(1)) / 2

X = 4.5 / 2

X = 2.25

Therefore 1 HB is $2.25

Use Descartes’s rule of signs to determine the possible number of positive and negative real zeros of f(x)=8x^4-6x^3-4x^2-7x+3

Answers

let's recall Descartes rule of signs, to get the Real Positive ones we start by checking the sign changes for f(x), and to get the Real Negative ones we check the sign changes for f( -x ).

Check the picture below.

the average of 15 pupils in a room is 11. if a man of 27 years enter the room. what will be the new average age?​

Answers

Answer:

12

Step-by-step explanation:

→ Find the total age of the children

15 × 11 = 165

→ Add the mans age

165 + 27 = 192

→ Divide by 16

192 ÷ 16 = 12

What square should complete the following series of squares?
1
2
3
4

Answers

Red cube will take 1,1 position (first row, first column).

Yellow cube will take 3, 4 position (third row, fourth column).

Green cube will take 4, 1 position (fourth row, first column).

What is pattern?

A pattern is a repeated arrangement of numbers, shapes, colors and so on.

According to the given question.

We have three squares made up of small cubes.

In the three squares, only three cubes of each square are colored by following some pattern.

In the given series of square we can see that, the yellow colored cube moving straight forward. And the green and red cubes are moving diagonally.

Therefore, by following this pattern the  cubes of fourth square of the series will take position:

Red cube will take 1,1 position (first row, first column).

Yellow cube will take 3, 4 position (third row, fourth column).

Green cube will take 4, 1 position (fourth row, first column)

Thus, the third option is correct.

Find out more information about pattern here:

https://brainly.com/question/11606579

#SPJ2

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