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
Answers
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.
Related Questions
emma had originally selected 8 intervals the interval that she put up for swap was not picked up nor did she show up to service it her technical issue had also prevented her from servicinfor 45 minutes emma was also 5 minutes late for two other intervals what was emma resulting ca percentage for the week
Answers
Answer:
83%
Step-by-step explanation:
IM STUCK CAN SOMEBODY HELP ME
Answers
Answer:
-16.15
Step-by-step explanation:
the variable in the equation means that it is ever changing, in this case, ever decreasing.
Given an interest rate of 12% compounded yearly, Find the equivalent rate per year compounded monthly.
Answers
Answer:
Answer below in the picture
I hope my answer helps.
x= 1+ root 2. find (x-1/x)³
I m in grade 9
Answers
Answer:
2√2 / (5√2 + 7)
Step-by-step explanation:
Given :
x = 1 + √2Expanding
(x - 1 / x)³(1 + √2 - 1)³ / (1 + √2)³(√2)³ / (1 + √2)³2√2 / 1 + 2√2 + 3(1)(√2)(1 + √2)2√2 / 1 + 2√2 + 3√2 + 62√2 / (5√2 + 7)Answer:
[tex]-14\sqrt{2}+20[/tex]
Step-by-step explanation:
[tex]\textsf{Substituting}\quad x=1+\sqrt2\quad\textsf{into}\quad\left(\dfrac{x-1}{x}\right)^3[/tex]
[tex]\implies \left(\dfrac{(1+\sqrt2)-1}{(1+\sqrt2)}\right)^3[/tex]
[tex]\implies \left(\dfrac{\sqrt2}{1+\sqrt2}\right)^3[/tex]
[tex]\textsf{Apply exponent rule}:\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}[/tex]
[tex]\implies \dfrac{(\sqrt2)^3}{(1+\sqrt2)^3}[/tex]
Expand numerator:
[tex](\sqrt{2} )^3=\sqrt{2}\sqrt{2}\sqrt{2}=2\sqrt{2}[/tex]
Expand denominator:
[tex]\begin{aligned}(1+\sqrt2)^3 & = (1+\sqrt2)(1+\sqrt2)(1+\sqrt2)\\ & =(1+\sqrt2)(1+2\sqrt{2}+2)\\ & =1+2\sqrt{2}+2+\sqrt{2}+2\sqrt{2}\sqrt{2}+2\sqrt{2}\\ & = 7+5\sqrt{2}\end{aligned}[/tex]
[tex]\implies \dfrac{(\sqrt2)^3}{7+5\sqrt2}[/tex]
Substituting expanded numerator and denominator:
[tex]\implies \dfrac{2\sqrt{2}}{7+5\sqrt2}[/tex]
[tex]\textsf{Mulitply by conjugate :}\quad\dfrac{7-5\sqrt2}{7-5\sqrt2}[/tex]
[tex]\implies \dfrac{2\sqrt{2}(7-5\sqrt2)}{(7+5\sqrt2)(7-5\sqrt2)}[/tex]
[tex]\implies \dfrac{14\sqrt{2}-20}{49-50}[/tex]
[tex]\implies \dfrac{14\sqrt{2}-20}{-1}[/tex]
[tex]\implies -14\sqrt{2}+20[/tex]
A printer can print 14 pages in 28 sec.
The rate in lowest terms is____?
Answers
Answer:
1/2 or 0.5 :)
Step-by-step explanation:
We can divide to see lower forns :)
14/28 = 7/14 = 1/2
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
2 pages every 7 seconds, divide by the common denominator which is 7 to get the answer
Suppose the sales tax in your town is 4%. What are the interpretations of this ratio?
Select all that apply.
DA. You will pay $40 in sales tax for every $1,000 purchase.
B. You will pay $4 in sales tax for every $10 purchase.
c. You will pay 40 cents in sales tax for every $1 purchase.
D. You will pay $4 in sales tax for every $1,000 purchase.
E. You will pay 4 cents in sales tax for every $1 purchase.
F. You will pay $40 in sales tax for every $100 purchase.
G. You will pay 4 cents in sales tax for every $10 purchase.
H. You will pay 40 cents in sales tax for every $10 purchase.
Answers
Answer:
A) {DA???} 0.04x1000=40. Yes
B) 0.4x10 is 4, NOT 0.04. No
C)0.4x1 is 0.4, NOT 0.04. No
D) No
E) Yes
F) No
G) Yes
H) No
find the sum of the first 7 terms of the following series 10,4,8/5
Answers
Answer:
16.6
Step-by-step explanation:
Since the numbers are decreasing as multiples, its a geometric progression.
[tex]S_{n}=\frac{a(1-r^{n} )}{1-r} ; r\neq 1 \ and\ r \ is\ less\ than\ 1\\common\ ratio=\frac{4}{10}=\frac{2}{5}\\ S_{7}=\frac{10(1-(2/5)^{7} )}{1-(2/5)} \\=16.6[/tex]
How many TRIANGLES can be constructed with angles measuring 110°, 50°, and
10°?
In order to prove mastery please explain how you know
Answers
Answer:
You can't cconstruct any triangle
Step-by-step explanation:
110+50+10=170 A triangle always has 180º
A perimeter of a square field is 160, what is the area of that field?
Answers
Answer: 1,600 sq units.
Step-by-step explanation: The perimeter of a square field is 160. When finding the perimeter of a square, all sides are the same, so you're adding four sides that have the same number to make 160. You can add 40 four times to make 160, so that gives us a hint of what all the square's sides are, which are 40. To find the area of a square, you need to multiply one side by the other. All sides of the square are 40, so we'll multiply 40 two times to make 1,600 sq units. Therefore, 1,600 sq units is your answer.
Have a great day! :)
Find the area of this parallelogram. A) 35 cm B) 75 cm C) 105 cm D) 150 cm
Answers
Answer:
B) 75 cm
Step-by-step explanation:
A = bh
(b =base & h = height)
therefore
area = 5 × 15
= 75 cm
I think this will helpful to you
give me a brainliest
Help picture below problem 9
Answers
Answer:
sometimes...
Step-by-step explanation:
mark me brainliest
A parallelogram is sometimes a rectangle.
A) sometimes
Explanation:because the vertices join the adjacent sides at 90° angles and it has two sets of parallel sides and two pairs of opposite sides that are congruent. (a rectangle has all of the properties of a parallelogram.)
HELP ME OUTT PPL (BRAINIEST)
Answers
Answer:
(0, 6)
Step-by-step explanation:
Point T is at (3, 4), and three units to the left would be (0, 4). They then tell us to go two points up, which would change the ordered pair to (0, 6).
I hope this was helpful! Have a lovely day! :D
I’m not good at these I need help
Answers
Answer:
f(3) = 9
Step-by-step explanation:
From the table, when can see that when x is 3, f(x) is 9.
Therefore, f(3) = 9
Answer:
[tex]f(3)[/tex]=9
Step-by-step explanation:
[tex]f(x)[/tex] is x times a function.
so if you look at the table on the 'x' side and go down the table until you reach '3' and see what number on the 'f(x)' side corresponds with it, you will see '9'
so [tex]f(3) = 9[/tex]
and that means your answer is D
Which equation is a step in solving the equation |5 − 3x| + 2 = 19? A. 5 − 3x = -17 B. |5 + 3x| = 17 C. 5 + 3x = -17 D. |5 − 3x| = -17
Answers
Did the math for you.
[tex]|5 - 3x| + 2 = 19\\|5 - 3x| = 17\\(|5 - 3x|) = 17^2\\25 -15x -15x + 9x^2 = 289\\25 - 30x + 9x^2 -289 = 0\\9x^2 - 30x - 264 = 0\\3(x + 4)(3x - 22)[/tex]
Which fraction is the largest 10/13, 11/14, 14/15 or 17/18
Answers
mrs. vickers is covering her students work table with chalkboard paper. the table is a radius of 3.8 ft. How much paper will she need?
Answers
Answer:
How might the situation lead to bullying?
How might the situation lead to bullying?
How might the situation lead to bullying?
How might the situation lead to bullying?
Step-by-step explanation:
On a given planet the weight of an object varies directly with the mass of an object. Suppose that an object whose mass is 3kg weighs 21N. Find the weight of an object whose mass is 7kg
Answers
Rearrange to get gravity
Gravity = weight/mass
Using 3kg, 21N
Gravity = 21/3 = 7
On this particular planet the gravity is measure at 7 m/s
Therefore:
Weight = 7kg*7= 49N
Mae has 36 orange slices. She will fill each of
7 bags with the same number of orange slices.
How many slices will be in each bag? How many
slices will be left over?
Answers
Answer:
5 orange slices will be in each bag with 1 left over
Step-by-step explanation:
36 ÷ 7 = 5 with a remainder of 1
Right answer = brainliest! :>
The radius of a cylindrical construction pipe is 2.5 ft. If the pipe is 20 ft. long, what is its volume?
Use the value 3.14 for pi, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answers
Answer:
Answer: The volume of the pipe is 412 cubic feet
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Volume of a cylinder = π x radius² x height (Length in this case)
Replacing with the values given:
V = 3.14 (2.5)² 21 = 3.4 (6.25) 21 = 412.12 = 412 cubic feet (rounded)
In conclusion, the volume of the pipe is 412 cubic feet
Feel free to ask for more if needed or if you did not understand something.
Answer:
V = 392.5 cubic feet
Step-by-step explanation:
[tex]v=\pi r^{2} h=\pi (2.5)^{2} (20)=\pi (6.25)(20)=125\pi[/tex]
[tex]\pi =3.14[/tex]
[tex]v=392.5cu.ft[/tex]
Hope this helps
Who was one of the earliest non-king leaders of the Benin people?
A. Sakura
B. Oranyan
C. Ekewa
D. Sundiata
Answers
Answer:
the answer is d , sundiata!
Step-by-step explanation:
the
Please help!!!! I stuck in this
Answers
It is asking for the sum of 1 mechanical pencil and 2 times regular pencil.
Samantha collected 352 books to give to her students. If she gives 4 books to her students each day, how many days will it take her to give all of her books away?
Answers
Answer: 88
Step-by-step explanation:since we know 4 books are given each day and the total is 352 . 352 divided by 4 is 88
Answer:
the answer is 88
Step-by-step explanation:
352÷4=88
A tree of 14m height is broken by the wind so that its top touches the ground and makes an angle of 60° with the ground. Find the length of the broken part of the tree.
Please help me,
I'll will mark as BRAINLIEST...
Answers
Answer:
7.50 m
Step-by-step explanation:
The side lengths of the "special triangle" with angles 30°-60°-90° have the ratios 1 : √3 : 2. These ratios can be used to solve the problem.
__
The parts of the tree of interest correspond to the long side and the hypotenuse of a 30-60-90 triangle.
In terms of the above ratio units, the fraction of tree height that is broken off is ...
[tex]\dfrac{\text{hypotenuse}}{\text{hypotenuse $+$ long side}}=\dfrac{2}{2+\sqrt{3}}\approx0.535898[/tex]
So, the length of the broken part of the tree is ...
0.535898 × 14 m ≈ 7.50 m
What is the length of AB? I
Answers
Answer:
9 units
Step-by-step explanation:
Line O bissects AC at its midpoint, creating a right angle. So, we know that AB is exactly 1/2 of AC.
Algebraically:
AB = AC/2
AB = 18/2
AB = 9 units
Hope this helps!
Answer:
AB = 9
Step-by-step explanation:
Perpendicular line from the center of the cirlcle to the chord bisects the chord.
AB = 18/2
AB = 9
Sandy wants to carpet the game room in her house. How many square feet of carpet will she need to complete her project if the diameter of the semicircle portion of her room is 10 ft and the base of the triangle is 5 ft? Carpet is only sold in whole number quantities.
Answers
Answer:
52ft²
Step-by-step explanation:
Explanation is in photo
Find AE. Round the answer to the nearest tenth.
A 9.7
B. 13.5
C. 16.1
D. 17.3
Answers
AE= 17.4 to nearest tenth
Step-by-step explanation:
Opposite + hypotenuse = SOH / sin
Sin 31 = 6/h
xh, then ÷ sin31
H= 6/sin31
H= 11.649....(a or b & 6 being a or b)
a^2 + b^2 = c^2
c = 13.1
Actually it's not a right-angle triangle
180 - 13+31 (or 44) = 136 degrees
Cosine rule: a^2=b^2+c^2 - 2bc cosA
AE = root 11.649...^2 + 7^2 - 2x11.649...x7xcos136
= 17.3791......
AE= 17.4 to nearest tenth
Hope this helps!
Using proportions to solve for missing sides.
BCD~GEF, find BD.
Answers
Answer:
BD = 19
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so we have ...
BD/GF = BC/GE
(2x -7)/57 = (x +4)/51 . . . . use the values marked on the diagram
17(2x -7) = 19(x +4) . . . . . . . . multiply by 969
34x -119 = 19x +76 . . . . . eliminate parentheses
15x = 195 . . . . . . . . . add 119-19x
x = 13 . . . . . . . . . . divide by 15
BD = 2(13) -7 . . . . use the found value of x in the expression for BD
BD = 19
If the standard quota for how many new schools will open in the 5 boroughs are:
Bronx: 20.73
Brooklyn: 10.12
Queens: 35.46
Manhattan 25.16
Staten Island 5.44
Use Jefferson's plan to apportion the Bronx quota.
Answers
The apportion of Bronx quota is the alloted profit to Bronx
The apportion for Bronx quota is 20
How to apportion the Bronx quota?The dataset is given as:
Bronx: 20.73Brooklyn: 10.12Queens: 35.46Manhattan 25.16Staten Island 5.44From the dataset, we have:
Bronx: 20.73
Remove the numbers after the decimal point
Bronx = 20
Hence, the apportion for Bronx quota is 20
Read more about quota at:
https://brainly.com/question/1499498
Find the area of the plane figure :
Answers
Answer:
99.9 [tex]cm^{2}[/tex]
Step-by-step explanation:
Given, AB=13 cm, BC=4 cm
AC is the diagonal of parallelogram ABCD.
Also AC=16 cm
We know, △ABC≅△ACD [S−S−S Congruence]
Also, area of parallelogram ABCD = Area of △ABC + Area of △ACD
= 2 × Area of △ABC
= [tex]2\sqrt{s(s-13)(s-4)(s-15)}[/tex]
[tex]s= \frac{13+15+4}{2}[/tex] = [tex]2\sqrt{16(16-13)(16-4)(16-15)}[/tex]
= 16 = 99.9
inequality? 6(x - 2) + 21 <39
A x < 5
C X> 3
B x >5
D x <3
Answers
Answer:
A. X < 5
Step-by-step explanation:
6(x -2) + 21 < 39
6x - 12 + 21 < 39
Group like terms
6x < 39 + 12 - 21
6x < 30
Divide through by 6
X < 30/6
X < 5