Correct Answer will get BRAINLIEST!
Segment $AB$ has midpoint $C$, and segment $BC$ has midpoint $D$. Semi-circles are constructed with diameters $\overline{AB}$ and $\overline{BC}$ to form the entire region shown. Segment $CP$ splits the region into two sections of equal area. What is the degree measure of angle $ACP$? Express your answer as a decimal to the nearest tenth.
Answers
Answer:
The degree measure of ∠ACP is 112.5°
Step-by-step explanation:
The total area of the given diagram is the sum of two semicircles with arc AB and arc CB having radius R and r respectively
Where:
R = AC
r = DB
R = 2 × r
Therefore the area of the semicircles are given as follows;
For the semicircle with arc AB, we have;
Area, A₁ = π × R²/2 = π × (2×r)²/2 = 2×π×r²
For the semicircle with arc CB, we have;
Area, A₂ = π × r²/2 = 1/2×π×r²
The ratio of the two semicircles is presented in the following relation;
\(\dfrac{A_1}{A_2} = \dfrac{2 \cdot \pi \cdot r^2}{\dfrac{1}{2} \cdot \pi \cdot r^2} = \dfrac{2}{\dfrac{1}{2} } = 2 \times \dfrac{2}{1} = 4\)
Therefore, the area of A₁ is four times that of A₂ or A₁ = 4 × A₂
The total area of the given diagram = A₁ + A₂ = 4 × A₂ + A₂ = 5·A₂
∴ Half of the area of the diagram, \(A_H\) = 5·A₂/2 = 2.5·A₂ = 2.5 × 1/2×π×r² = 1.25×π×r²
The ratio of half of the diagram of the figure to the area of the semicircle with arc AB is found as follows;
\(A_H\)/A₁ = (1.25×π×r²)/(2×π×r²) = 5/8
Therefore, the half of the diagram of the figure given by segment PAC is equivalent to 5/8 of the semicircle with arc AB
Given that the arc AB subtends an angle of 180° at the center (angle subtended by a semicircle), the arc AP will subtend 5/8×180 = 112.5°
To verify we have;
Area of a segment of a circle is presented in the following relation;
\(\dfrac{\theta}{360} \times \pi \times r^2\)
As segment PAC is 5/8 of a semicircle, it is therefore 5/(8×2) or 5/16 of the whole circle
Hence;
\(\dfrac{5}{16} \times \pi \times r^2 = \dfrac{\theta}{360} \times \pi \times r^2\)
\(\dfrac{5}{16} = \dfrac{\theta}{360}\)
\(\theta \dfrac{}{} = \dfrac{360 \times 5}{16} = 112.5 ^ {\circ}\)
Therefore the degree measure of ∠ACP is 112.5°.
Related Questions
I need help, please quickly
Answers
Answer: The ratio is 18:3
Step-by-step explanation:
Answer: 6 to 1
Step-by-step explanation:
A ratio refers to a fraction. In this case the question asks how many players to coaches there are.
The word "to" means that is where the fraction bar goes.
Players/Coaches
There are 18 players and 3 coaches.
18/3
18 can be divided by 3, 6 times so the fraction can be simplified to
6/1 meaning there are 6 players for every coach.
how to solve 6r - 1 + 6r =11
Answers
Answer:
r = 1
Step-by-step explanation:
The equation is,
→ 6r - 1 + 6r = 11
Now the value of r will be,
→ 6r - 1 + 6r = 11
→ 12r = 11 + 1
→ r = 12/12
→ [ r = 1 ]
Hence, the value of r is 1.
Answer:
The answer is 1 r is equal to 1
Step-by-step explanation:
Write the equation of the line shown in the graph.
y = ?
Answers
Answer:
y = -1
Step-by-step explanation:
Since there is no slope, our equation looks like this:
y = 0x - 1
Answer:
-1
Step-by-step explanation
Since there is no slope, our equation looks like this:
y = 0x - 1
could someone help with these problems, could you find the positive x and what the angle for each one is. or tell me what steps to take to find each answer. pls
Answers
In this equation its 180 for the total
I need help with this question, I'm not very good at math and all help is appreciated!
Answers
Answer:
A
Step-by-step explanation:
We can solve for H by isolating it on one side of the equation, as follows:
J/H - I/H = G
Taking H as the common denominator:
(J - I)/H = G
Multiplying both sides by H:
J - I = GH
Adding I to both sides:
J = GH + I
Dividing both sides by G:
H = (J - I)/G
So the answer is
(A)
H = (J - I)/G.
Answer: A
Step-by-step explanation:
\(\frac{J}{H} = G + \frac{I}{H}\) >Since you are solving for H bring I/H to the other side
by subtracting I/H from both sides
\(\frac{J}{H}- \frac{I}{H} = G\) >There is a common denominator so you can
combine the fractions
\(\frac{J-I}{H} = G\) >Multiply both sides by H or cross multiply whichever
way your mind things about how to get H on top
\(J-I = G(H)\) >Divide both sides by G
\(\frac{J-I}{G} = H\) >Answer is A
A project will take a total of 720 person-days to complete. If the project must be completed in 30 days, how many people must be employed? PLEASE HURRY
Answers
Answer:
192 hours per day / 8 hours per person per day = 24 people
Step-by-step explanation:
Assuming each person works for 8 hours a day, the total number of hours needed to complete the project is:
720 person-days x 8 hours = 5,760 hours
To complete the project in 30 days, the total number of hours needed per day is:
5,760 hours / 30 days = 192 hours per day
Exploring Square Roots and Rational Numbers ( PLEASE HELP )
Answers
Answer:
(To simplify the answers, I will refer to the first sentence of the question as part A and the second sentence as part B.)
Question 17
Part A: the square root is between 6 and 7
Part B: the square root is 6.5
Question 18
Part A: the square root is between 9 and 10
Part B: the square root is 9.4
(Extra: the answer in simplified radical form is 2√22)
Question 19
Part A: the square root is between 7 and 8
Part B: the square root is 7.9
(Extra: the answer in simplified radical form is 3√7)
Question 20
Part A: the square root is between 8 and 9
Part B: the square root is 8.7
(Extra: the answer in simplified radical form is 5√3)
Question 21
Part A: the square root is between 5 and 6
Part B: the square root is 5.5
Question 22
Part A: the square root is between 9 and 10.
Part B: the square root is 9.8
Step-by-step explanation:
First of all, it says you can use a calculator! If you do not know how to, let me know in the comments and I can try to help you out! Read the explanation to understand how to do this.
Question 17
Using a calculator, you get 6.48074069… for your decimal.
Rounding it to the nearest tenth, your answer would be 6.5
Now, to find the two consecutive whole numbers the square root is between…
However, there is another way to do this. Remember that 7x7=49. We know that 49 is greater than 42, so let’s see try out a number smaller than 7! 6x6=36. 42 is between 36 and 49, so the square root is between 6 and 7.
Another way to do this is… we know that the decimal is about 6.5, which is between 6 and 7, since those are the two whole numbers before and after that decimal!
Question 18
Using a calculator, you get 9.380833151… for your decimal.
This rounds to 9.4
The whole numbers surrounding this decimal are 9 and 10.
You can also do this by knowing that 9x9, or 9^2, is 81 and 10x10, or 10^2, is 100, and those are the numbers surround 88.
In non-decimal form (simplified radical), your answer can be 2√22.
Question 19
Using a calculator, you get 7.93725393… for your decimal.
This rounds to 7.9
The whole numbers surrounding this decimal are 7 and 8.
You can also do this by knowing that 7x7, or 7^2, is 49 and 8x8, or 8^2, is 64, and those are the numbers surround 63.
In non-decimal form (simplified radical), your answer can be 3√7.
Question 20
Using a calculator, you get 8.66025403… for your decimal.
This rounds to 8.7
The whole numbers surrounding this decimal are 8 and 9.
You can also do this by knowing that 8x8, or 8^2, is 64 and 9x9, or 9^2, is 81, and those are the numbers surround 75.
In non-decimal form (simplified radical), your answer can be 5√3.
Question 21
Using a calculator, you get 5.47722557… for your decimal.
This rounds to 5.5
The whole numbers surrounding this decimal are 5 and 6.
You can also do this by knowing that 5x5, or 5^2, is 25 and 6x6, or 6^2, is 36, and those are the numbers surround 30.
Question 22
Using a calculator, you get 9.84885780… for your decimal.
This rounds to 9.8
The whole numbers surrounding this decimal are 9 and 10.
You can also do this by knowing that 9x9, or 9^2, is 81 and 10x10, or 10^2, is 100, and those are the numbers surround 97.
Note: the symbol "^" means that the number following that symbol is an exponent. So 2^2 is 2 squared, \(2^2\), or 2 to the power of 2.
Hope that helps! <3
Disclaimer: I am not responsible for anything you get incorrect, as I only have the context and information you provide, and I give my response based on my knowledge supported with credible information from experts and online professional articles.
it’s a pretty easy topic… i’m sure u will get the hang of it :)
HELP PLEASE!!!!! PLEASE EXPLAIN WHEN GIVING THE ANSWER!!!! GIVING BRAINLIEST TO THE BEST EXPLANATION!!!!
Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.
Sarah can use the expression 5(2j + 3 + j) to represent the amount of money she can earn.
Write a few sentences to end Sarah’s story. How many shark teeth did she find? How many shark teeth did John find? How much money did Sarah earn?
Answers
Answer:Simplificando
5 (2j + 3 + j) = 0
Reordene os termos:
5 (3 + 2j + j) = 0
Combine termos semelhantes: 2j + j = 3j
5 (3 + 3j) = 0
(3 * 5 + 3j * 5) = 0
(15 + 15j) = 0
Resolvendo
15 + 15j = 0
a verdadeira questão é por que o vizinho de Sarah quer dentes de tubarão
Step-by-step explanation:
Mova todos os termos contendo j para a esquerda, todos os outros termos para a direita.
Adicione '-15' a cada lado da equação.
15 + -15 + 15j = 0 + -15
Combine termos semelhantes: 15 + -15 = 0
0 + 15j = 0 + -15
15j = 0 + -15
Combine termos semelhantes: 0 + -15 = -15
15j = -15
Divida cada lado por '15'.
j = -1
Simplificando
j = -1
Tubarão ou cação é um tipo de peixe de esqueleto cartilaginoso e um corpo hidrodinâmico (com exceção dos Squatiniformes, Hexanchiformes e Orectolobiformes)
In a jar of marbles, the ratio of green marbles to black marbles is 3:5. If the jar contains 21 green marbles, how many black marbles are in the jar?
green 3 21
black 5 ?
Your answer:
10
12
30
35
Answers
Answer:
there are 35 black marbles in the jar
Step-by-step explanation:
3*7=21
so..
5*7=35
When we use the formula for the area of a triangle, why do we use the height and not the hypotenuse?
Answers
Answer:
area is a half x l x h
Step-by-step explanation:
we cannot use the hypotenuse because it wouldn't bring the area
Jack wanted to measure the perimeter of the triangular sandbox. One side was 4.5 feet. The second side was 6.4 feet. The third side was 4.6 feet. What was the perimeter of the sandbox?
Group of answer choices
Answers
Answer:15.5
Step-by-step explanation:
Answer:
15.5 feet
Step-by-step explanation:
To work out the perimeter of any shape, you need to add the lengths of all the sides together for the total perimeter.
4.5 + 6.4 + 4.6 = 15.5 ft
PLEASE HURRYYYYYYYYYYYYYYYYYYYYYY!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
A) 63\(\frac{351}{441}\)
Step-by-step explanation:
the answer is A) 63\(\frac{351}{441}\)
Answer:
63 Remainder 351
Step-by-step explanation:
For small division problems, the quotient and remainder can easily be thought of. But for larger division problems, long division is one technique that will work for any division problem, no matter how small or large it is.
Let's take a look at how long division works with the simple division problem of 7 / 3 first.
Setting up the problem, it looks like this with the 7 inside the division bracket and the 3 outside.
pasty needs 3 1/3 cups of flour for a recipe. write the numbers of cups as an inproper fraction
11/3
9/3
10/3
7/3
Answers
It’s 9/3 bc all you have yo do it 3x3 then you add the 1 and that equals 9 and then you keep your denominator.
If you roll a fair number cube 30 times, what is the experimental probability of rolling a 2
Answers
Answer:
1/6 chance or 16.667% chance
Step-by-step explanation:
a fair number cube has six sides so if you roll that 30 times that's 180 sides and the probability of rolling a 2 out of a single dice is 1/6 and since 180 * 1/6 is equal to 30 that is 30 out of 180 which is 1/6
Predict how many students received a flu vaccine if a school had 65 cases of the flu.
Answers
y is flu cases
x is flu shots
solve for x when y = 65
\(65 = \frac{-1}{4}x + 85\\-20 = \frac{-1}{4}x\\-80 = -x\\x = 80\)
Which scenario can be modeled by the linear function
y = -15x + 500?
A. The temperature on Jupiter is
15℉ and increases by 500℉ every day.
B. There is a population of 500 giraffes in Western Africa that decreases by 15 giraffes each year.
C. A carpet cleaning service charges $500 plus an additional $15 for every hour.
D. A membership fee for a movie streaming service is free, but each rental costs $15.
Answers
Find the area of the trapezoid by decomposing it into other shapes
.A)56 cm*2
B)60 cm*2
C)64 cm*2
D)72 cm*2
Answers
A
56 cm*2
Area
The table shows the results of randomly selecting a colored cube from a bag 80 times. The cube was returned to the bag after each selection.
Based on these results, what is the expected probability of randomly selecting a red cube from the bag in one attempt?
A) 0.20
B) 0.04
C) 0.24
D) 0.30
Answers
Two parallel lines are cut by a transversal as shown below
Answers
Answer:
<2 and <4 = 74 degrees
Step-by-step explanation:
<7=<1, alt exterior angles
<1=<3, opposite angles
<1+<2= 180
since angle one is 106 just subtract 106 from 180 and you get 74= <2
<2 and <4 are opposite angles so they are congruent
therefore, <2 and <4 = 74 degrees.
The trams operate using an overhead cable which supplies a high-voltage electric current to the tram. Explain how the electric energy is transformed in this example. Include at least three different transformations in your explanation.
Answers
hey can you help, please
Answers
Answer:
C is the answer I did this and got it right.
Step-by-step explanation:
(plsss give brainliest T-T)
Answer: I got C as an answer
A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form f(x) = abx to represent the number of birds after x years. Which values should she use for a and b? a = b =
Answers
Answer:
a=240
b= 1.16
Step-by-step explanation:
The general form of exponential function for growth is given by:
y = a(1+r)ˣ
We can rewrite it by letting 1+r = b
y= abˣ
a from the given equation represents the initial number of birds, which is given by 240. Hence, a = 240
In (1+r), r is given as the rate of increase, which is given as 16% or 16/100=0.16.
For r = 0.15
b = 1+r
b = 1+ 0.16
b = 1.16
Substituting it in the initial equation:
y = abˣ
y = 240 (1.16)ˣ
where a = 240 and b = 1.16
Answer:
Look at Attachment
Step-by-step explanation:
Solve for y.
−2y+7=−5
Responses
y = 6
y = 1
y = -1
y = -6
Answers
Answer: y = 6
Step-by-step explanation:
1. Subtract 7 from both sides to isolate -2y.
-2y = -12
2. Divide both sides by -2 to isolate the y.
y = 6
Help
During a 20% off sale, the sale price of a microwave was $60. The sale has expired but Kristen has a coupon good for 15% off the regular price of any one item. How much will Kristen pay for the microwave before tax? Round to the nearest cent.
Answers
Answer:
it would take 9 dollar OFF!! so subtracted by 60 your welcome!!
(its 51 just saying.)
Step-by-step explanation:
x - 0.2x = 60
Simplifying the left side, we get:
0.8x = 60
Dividing both sides by 0.8, we get:
x = 75
So the regular price of the microwave is $75. Now, we can use Kristen's coupon to find the price she will pay:
Regular price = $75
Discount from coupon = 15%
Amount of discount = 0.15 x $75 = $11.25
Subtracting the discount from the regular price, we get:
Price after coupon = $75 - $11.25 = $63.75
Therefore, Kristen will pay $63.75 for the microwave before tax.
Please helpp!! Ty ty!♡♡
Answers
Answer:
25
Step-by-step explanation:
4a +12 -2c + c
4( ) + 12 - 2( ) + ( )
4(4) + 12 - 2(3) + 3
16 + 12 - 6 + 3
28 - 6 + 3
22 + 3
25
Helping in the name of Jesus.
Therefore, 4a + 12 - 2c + c = 25
Step-by-step explanation:a = 4
c = 3
Swap letters for numbers:4a + 12 - 2c + c
(4)(4) + 12 - (2)(3) + 3
16 + 12 - (2)(3) + 3
28 - (2)(3) + 3
28 - 6 + 3
22 + 3 = 25
Draw a conclusion:
Hence your answer is:4a + 12 - 2c + c = 25
I hope this helps!
I NEED HELP ASAP: Round 3,942,588 to the nearest thousand. WILL BE MARKED AS BRAINLIEST IF THE ANSWER IS CORRECT
Answers
only answer if you know the answer and if you understand it.
7. The same restaurant offers a coupon for $5.00 off a purchase of $10.00 or more or 15% off a purchase of any amount. Which row in the table below (A, B, or shows a correct expression that can be used to determine the cost of purchasing 8 hamburgers and 6 orders of fries using each coupon option?
Answers
I don't know this answer
Which expression is equivalent to 3m÷4n⋅5p?
3m÷5p⋅4n, 3m÷5p⋅4n, 3m⋅5p÷4n, or 4n÷3m⋅5p?
Answers
Answer:
Its (C)
Step-by-step explanation:
\(\frac{3}{4}\) * 5 = \(\frac{15}{4}\)
Only answer that is equivalent is C
Help meh emergency. No links please give a right answer, need helppppp
Answers
Answer:
70.91 x 10 = 709.1
70.91 x 100 = 7,091
70.91 x 1000 = 70,910
Answer:
It is the bottom right one.
Step-by-step explanation:
70.91 to the right 3 times is 70910, or you couldve just used a calculator.
A quarter circle is attached to the side of a square as shown.
What is the best approximation for the area of this figure?
Use 3.14 to approximate pi.
A.)28.6 m²
B.)41.1 m²
C.)66.24 m²
D.)116.5 m²
Note: I helping my brother math work so i hope you can answer this question
Answers
Answer: A
Step-by-step explanation: You have to find the area first, after you use pie and you get 28.6
Answer:
D
Step-by-step explanation:
Just did this good luck