Mathematics High School

The radius of a circle is 10 feet. What is the angle measure of an arc 4​ feet long?

Answers

Answer 1
The angle measure is 22.9183 deg

Hope this helps u

Related Questions

Find the side of a square whose diagonal is of the given measure. Given = 12 square root 2ft.

Answers

diagonal^2 = 2 * side^2
diagonal^2 / 2 = side^2
144 * 2 / 2 = side^2
144 = side^2
side = 12





MATH HELP!
Kristen's gross annual income is $47,208. She is paid semimonthly and has 6% deducted from her paychecks for her 403(b). Her employer matches her deduction, up to 5%. How much is deposited into Kirsten's 403(b) each payday?

$98.35
$118.02
$196.70
$216.37

Answers

47,208 / 24 = 1967  

1967 * 0.06 = 118.02

1967 * 0.05 = 98.35

118.02 + 98.35 = 216.37

The amount deposited into Kristen's each payday is is 216.37

Kristen's gross annual income is $47,208.

What is the meaning of semimonthly?

Twice a month

semimonthly per year means

12(2)=24

She paid semimonthly,

47,208 / 24 = 1967  

6% deducted from her paychecks then,

1967 * 0.06 = 118.02

Her employer matches her deduction, up to 5% then,

1967 * 0.05 = 98.35

The amount deposited into Kristen's each payday is

118.02 + 98.35 = 216.37

Therefore,the amount deposited into Kristen's each payday is is 216.37

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helppppppppppppppppppppppppppppppppppppppp

Answers

[2^(1/2)*(2^(3/4)]^2
the answer is  √2^5
Your answer is B if you were to simplify the expression you would get 4√2

miss parks wrote 4 statement to the board and asked the class which one was true. Which statement is true?

A)3 and 2/3 x 4/5 is greater than 3 and 2/3
B)1 and 7/8 x 2 and 1/3 is greater than 2 and 1/3
C)1 and 7/8 x 8/8 is less than 2 and 5/6
D)2 and 3/8 x 4 is less than 4

Answers

(3 2/3)(4/5) = (11/3)(2/5) = 22/5 = 1 7/15 (false}

(1 7/8)(2 1/3) = (15/8)(7/3) = 35/8 = 4 3/8 (true)

(1 7/8) (8/8) = 1 7/8 (true)

(2 3/8)(4) = (19/8)(4) = 19/2 = 9 1/2 (false)

I got two true statements ...

What is the GCF of the terms of 8x3 − 12x2 + 4x?

Answers

i think the GCF is 4x in not sure olz tell me if i'm wrong

Which statement is true about the function f(x)=-√-x
a.The domain of the function is all negative real numbers.
b.The range of the function is all positive real numbers.
c.The domain and range of the function have opposite signs.
d.The domain and range of the function are the same.

Answers

Answer: D.The domain and range of the function are the same.


Step-by-step explanation: Given function f(x)=-√-x.

The given function is a square root function and we have minus sign in front of x inside square root.

A square root always defined for positive values or 0.

In order to get a positive number or 0 inside square root, let us solve the inequality:

[tex]-x\geq 0[/tex]

On dividing both sides by -1, the inequality sign would get flip and we get

Domain: [tex]x \leq 0.[/tex]

We can see that we have a negative sign in front of square root. So, the value of f(x) would be always a negative number or 0.

Therefore, range would also be :[tex]x \leq 0.[/tex].Therefore, correct option is D option.

Answer:

hi thereee, the answer to this question is

d. the domain and range of the function are the same

hope this helps :)

have a good day!

Step-by-step explanation:

i just took the test

a fund drive announces that it has raised 4376 which is 20% of its goal. How much more must be raised?

Answers

Answer:
It must raise an additional 17504

Explanation:
Assume that the amount to be raised is x.
Now, we are given that 20% of x is 4376, therefore:
0.2x = 4376
x = 4376/0.2
x = 21880

It has raised 4376, therefore:
amount left to raise = 21880 - 4376 = 17504

Hope this helps :)
You can solve this problem as follows:
 
 1. Let's call the amount: "y".
 
 2. The exercise says that 4376 which is 20% of its goal, so we have:
 
 y=4376
 20% of its goal=4376
 
 3. Then, we have the equation below:
 
 20y/100=4376
 0.20y=4376
 
 4. When we clear the variable "y", we obtain:
 
 y=4376/0.20
 y=21880
 
 5. Finally, we will have:
 
 21880-4376=17504
 
 6. How much more must be raised?
 
 The anwer is: 17504 

A dentist had some fish in a fish tank. The dentist added 43 more fish to the fish tank. Now there are 66 fish in the fish tank. How many fish were in the fish tank before the dentist added more?

___fish

Answers

The answer is 23 fish. :)

Answer:

The dentist had 23 fish before she added 43

Step-by-step explanation:

Help me in this plz plz

Answers

3a. You can tell if a system of linear equations has no solutions if the lines are parallel (do not intersect). They will have infinite solutions if the lines graph as the same line (intersect at every point).

3b. You can tell the system of linear equations has no solution if the equations result in a contradiction, such as 0 = 1. They will have infinite solutions if the result is a tautology, such as x = x or 0 = 0.


Word Problem
(a) There is actually no problem stated. If we assume the problem is to determine the length and width that meet the described conditions, then it would be appropriate to let variables represent the length (L) and width (W). The system of equations restates what the words state:
.. L - W = 2 . . . . . . length and width differ by 2 units
.. 2(L + W) = 40 . . the perimeter is 40 units

(b) You can solve this many ways. One way is to divide the second equation by 2, so you have a "sum and difference" problem
.. L - W = 2
.. L + W = 20
This is easily solved by adding the two equations to get
.. 2L = 22
.. L = 11
.. W = L -2 = 9
The solution is (L, W) = (11, 9). This is interpreted to mean the length of the rectangle is 11 units; the width is 9 units.

A rectangular auditorium seats 1344 people. The number of seats in each rows exceeds the number of rows by 20. Find the number of seats in each row

Answers

Let the number of rows be x

rows = x
seats in each row = x + 20

total seats = 1344
x (x + 20) = 1344
x^2 + 20x - 1344 = 0
(x + 48)(x - 28) = 0
x = -48  (rejected, answer cannot be negative) or x = 28

Therefore,
x = 28 
x + 20 = 48


Check:
Row = 28
Numbers of seat per row = 28 + 20 = 48
28 x 48 = 1344 (Correct)
 
Ans:There are 48 seats per row 

To solve this problem, we must first set up an equation. We are told that the total number of seats in the auditorium is 1344. We are also told that the number of seats in each row exceeds the number of rows by 20.

Let's denote the number of rows as x. Therefore, the number of seats per row is x + 20 (as it exceeds the number of rows by 20). Setting up an equation would be as follows:

x * (x + 20) = 1344

This equation states that the number of rows times the number of seats per row equals the total number of seats.

Solving this equation requires finding the roots of a quadratic equation. We set it up as a quadratic equation ax² + bx + c = 0. Here, a = 1, b = 20, and c = -1344.

Solving a quadratic equation gives us two possible solutions, but in our case, we disregard the negative value, as the number of rows cannot be negative. So, we take the maximum of the two roots.

Solving this equation gives us x = 28.0, which represents the number of rows.

Finally, to find the number of seats in each row, we remember that it exceeds the number of rows by 20. So, we add 20 to the number of rows.

28.0 + 20 = 48.0

So, there are 48 seats in each row.

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What transformations change the graph F(x) to the graph g(x)
f(x) = 3x^2
G(x) = 9x^2-4

A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated DOWN 4 units
B. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated UP 4 units
C. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated up 4 units

Answers

The answer is letter a

Final answer:

The transformation from f(x) = 3x^2 to g(x) = 9x^2 - 4 includes a vertical stretch by a factor of 3 followed by a vertical translation down by 4 units.

Explanation:

The transformations that change the graph f(x) = 3x2 to the graph g(x) = 9x2 - 4 involve two steps:

A vertical stretch by a factor of 3, which is achieved by multiplying the original function f(x) by 3, yielding 9x2. This transformation changes the original coefficient (3) in front of x2 to a new coefficient (9).

A vertical translation down by 4 units, which is represented by subtracting 4 from the result of the stretch transformation.

Therefore, the correct answer to the student's question is:

A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated DOWN 4 units.

Carlo wants to join gym.the total gym offers three options for the membership. Option1:pay as you go.pay only $6 each time You work out. Option2: Regular Deal. Pay $50 a month and $2 each time you workout.

Answers

The question is attached in the image.

1- Carlo thinks he will go to the gym 20 times this month. Calculate how much each of these options will cost Carlo for one month.
a- Pay as you go:
Total cost = 6 * 20 = $120
b- Regular deal:
Total cost = 50 + 2(20) = 50 + 40 = $90
c- All-in-one-price:
Total cost = $100
d- The least expensive for Carlo in this case would be the regular deal.

2- How many visits each month would make the cost of the Regular-Deal and the All-in-one the same?
Assume number of visits is x.
Regular deal = All in one
50 + 2x = 100
2x = 100 - 50
2x = 50
x = 25 visits

3a- It costs $300 to join the new Superfit Gym. You then pay $15 each month and $2 each time you work out. Carlo thinks he will use the gym 20 times each month for a year.
Calculate the cost of the Superfit gym for one year.
Total cost = initial payment + 15*number of month + 2*days of workout
initial payment = $300
15*number of months = 15 * 12 = $180
2*days of workout = 2*20*12 = $480
Total cost = 300 + 180 + 480 = $960

3b- How much will Carlo save during the first year if he uses the Superfit gym rather than the regular deal at the other gym?
First we will calculate the total cost of one year using the regular deal at the other gym as follows:
Total cost at other gym = monthly cost + cost of each workout
Total cost at other gym = 50(12) + 2(12)(20) = $1080
Then, we will calculate the difference to know the amount Carlo would save as follows:
Carlo would save = 1080 - 960 = $120

Hope this helps :)

Mr burn's class is taking
a. field trip to the planetarium. The trip will cost $27 for each student. There are 18 students in his class.Use compatible numbers to estimate the total cost of field trip

Answers

the total will be $486

Answer:

600

Step-by-step explanation:

The answer is 600

Why must bowhunters use broadhead points when hunting big game?

Answers

Bowhunters must use broadhead points when hunting big game to ensure that they will be able to kill their game at the least time possible. The broadhead points causes massive blood loss to the prey as it cut through the vital organs and blood vessels of the animal.  

There are states that require a certain measurement of the broadhead point arrows. Theses arrows must be solidly built and must always be razor sharp to ensure quick penetration to the animals thick skin and layers of tissues. 

Bowhunters use broadhead points when hunting big game for their greater cutting surface, penetration, lethality, blood trails, terminal performance, and ethical considerations.

We have,

Bowhunters use broadhead points when hunting big game for several reasons:

- Greater Cutting Surface

Broadhead points have a larger cutting surface area compared to target or field points.

This increased surface area allows for more effective cutting and penetration, which is essential when hunting big game animals that have tough hides, muscles, and bones.

- Penetration and Lethality:

Big game animals often require deep penetration to reach vital organs for an ethical and humane kill.

Broadheads are designed to maximize penetration by creating large wound channels and causing significant tissue damage.

This helps ensure quick and effective kills, minimizing suffering for the animal.

- Blood Trails

- Terminal Performance

- Ethical Considerations

Thus,

Bowhunters use broadhead points when hunting big game for their greater cutting surface, penetration, lethality, blood trails, terminal performance, and ethical considerations.

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If ΔMNO ≅ ΔPQR, which of the following can you conclude as being true? I'LL MARK BRAINLIEST !!!!

Answers

Are there any answer choices?

If the two triangles are congruent, then you can conclude that they have 3 angles in common, or that they are identical or that you could use rigid motions (dilations, translations or reflections) to align them together.

Answer:

NO=QR

Step-by-step explanation:


How would you solve this?

Answers

Hello,

I suppose as we don't see correctely the 2nd image, that it is the first one.

Angles DOY  and  DKY intersept then same arc are equals.

5x+15=3x+21
==>2x=6
==>x=3 and 5x+15=5*3+15=30°, 3x+21=3*3+21=30°
Angle OYK=15x=15*3=45°
Angle ODK=9x+18=9*3+18=45° =Angle OYK which intersept the same arc.

In which way do REITs resemble mutual friends

Answers

Money is invested in a fund that is controlled by a board, and dividends are paid out to the investors.
___________________________________________________________
Final answer:

REITs resemble mutual funds in that they both allow investors to pool their money to invest in a diversified portfolio. REITs consist of a variety of real estate properties, while mutual funds consist of stocks or bonds. Both provide individuals with an opportunity to invest in a professionally managed portfolio.

Explanation:

REITs (Real Estate Investment Trusts) resemble mutual funds in that they both allow investors to pool their money together to invest in a diversified portfolio. Just as mutual funds consist of a variety of stocks or bonds from different companies, REITs consist of a variety of real estate properties such as office buildings, apartments, and shopping centers. Investors buy shares of a REIT and receive a return based on the performance of the real estate portfolio as a whole. Both REITs and mutual funds provide individuals with an opportunity to invest in a professionally managed portfolio without having to directly invest in individual stocks or properties.

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Choose the option that correctly completes the statement.

The sum of the measures of the interior angles of a quadrilateral is _____ degrees.
270
180
90
360

Answers

The sum of the measures of the interior angles of a quadrilateral is 360 degrees.

Answer:

D. 360 degrees.

Step-by-step explanation:

We have been given an incomplete statement. We are asked to complete the given statement using provided options.

Statement:

The sum of the measures of the interior angles of a quadrilateral is _____ degrees.

We know that a quadrilateral is a polygon with 4 vertices.

We can divide a quadrilateral into two triangles by drawing a diagonal. We know that sum of three angles of a triangle is equal to 180 degrees, so sum of angles of two triangles would be 360 degrees.

Therefore, the sum of the measures of the interior angles of a quadrilateral is 360 degrees and option D is the correct choice.

an angle with measure between 90 and 180 is called

Answers

obtuse is what it is called            

An angle with measure between 90° and 180° is called obtuse angle.

The definition of an obtuse angle in geometry states that an angle whose measure is greater than 90° and less than 180° is called an obtuse angle.

So, if the angle measure between 90 degree and 180 degree is obtuse angle.

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30 POINTS + BRAINLIEST!

Answers

The secant tangent theorem states that the distance from (y to the tangent point x) squared = the external segment * length of the secant.
Put in plane English
YX^2 = YV * YZ
YV = 9
YZ = 9 + 19 = 28
YX^2 = 28 * 9
yX^2 = 252
YX = sqrt(252)
YX = 15.87

The answer is 15.87.

I need help please with these two questions.

1. What is the volume of this sphere? (First Picture)




8π cm³

16π cm³

27π cm³

36π cm³

2. What is the volume of this sphere? (Second Picture)

Use 3.14 for pi and round to the nearest hundredth when necessary.




615.44 cm³

2461.76 cm³

11,488.21 cm³

91,905.71 cm³

Answers

Answer:

(1) Volume of a sphere is [tex]36 \pi\ cm^{3}[/tex] .

(2)volume of the sphere is 11488.21 cm³ .

Step-by-step explanation:

Formula

[tex]Volume\ of\ a\ sphere = \frac{4}{3} \pi r^{3}[/tex]

Where r is the radius of the sphere .

Part First

As given the radius of the circle is 3cm .

Putting values in the formula

[tex]Volume\ of\ a\ sphere = \frac{4\times 3\times 3\times 3}{3} \pi[/tex]

[tex]Volume\ of\ a\ sphere = \frac{108}{3} \pi[/tex]

[tex]Volume\ of\ a\ sphere = 36 \pi\ cm^{3}[/tex]

Therefore the volume of a sphere is [tex]36 \pi\ cm^{3}[/tex] .

Second Part

As given

Diameter of the sphere is 28 cm .

[tex]Radius (r) = \frac{Diameter}{2}[/tex]

[tex]Radius (r) = \frac{28}{2}[/tex]

[tex]Radius (r) = 14\ cm[/tex]

[tex]\pi = 3.14[/tex]

Putting all the values in the formula

[tex]Volume\ of\ a\ sphere = \frac{4}{3}\times 3.14\times 14\times 14\times 14[/tex]

[tex]Volume\ of\ a\ sphere = \frac{4\times 3.14\times 14\times 14\times 14}{3}[/tex]

[tex]Volume\ of\ a\ sphere = \frac{34464.64}{3}[/tex]

[tex]Volume\ of\ a\ sphere =11488.21\ cm^{3}[/tex]

Therefore the volume of the sphere is 11488.21 cm³ .

1. The volume of the sphere is 16π cubic centimeters, which matches option B.

2. The correct answer for the volume of the second sphere is:

C. 11,488.21 [tex]cm^3[/tex]

1. For the sphere shown in the image with a diameter of 3 cm, the correct choice for its volume is:

B. 16π cm³

To calculate the volume of a sphere, we use the formula:

V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] r^3

Where r is the radius of the sphere.

Given:

- Diameter of the sphere = 3 cm

- Therefore, radius (r) = 3/2 = 1.5 cm

Substituting in the formula:

V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] (1.5)^3

V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] 3.375

V = 4 [tex]\times[/tex] π [tex]\times[/tex] 3.375/3

V = 16π cm³

So the volume of the sphere is 16π cubic centimeters, which matches option B.

2.For the second sphere shown with a diameter of 28 cm, to calculate its volume using π = 3.14 and rounding to the nearest hundredth, we follow these steps:

1) Find the radius by dividing the diameter by 2:

  Radius = 28 cm / 2 = 14 cm

2) Use the formula for sphere volume: V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] r^3

  Substituting the values:

  V = (4/3) [tex]\times[/tex] 3.14 [tex]\times[/tex] (14 cm)^3

  V = (4/3) [tex]\times[/tex] 3.14 [tex]\times[/tex] 2744

  V = 11,488.53 cm^3

3) Rounding to the nearest hundredth as instructed:

  V = 11,488.53 cm^3 rounds to 11,488.21 cm^3

Therefore, the correct answer for the volume of the second sphere is:

C. 11,488.21 [tex]cm^3[/tex]

The correct question is:

1. What is the volume of this sphere? (First Picture)

A. 8π cm³

B. 16π cm³

C. 27π cm³

D. 36π cm³

2. What is the volume of this sphere? (Second Picture)

Use 3.14 for pi and round to the nearest hundredth when necessary.

A. 615.44 cm³

B. 2461.76 cm³

C. 11,488.21 cm³

D. 91,905.71 cm³

Item 20The width of a rectangular room is 60% of its length. The length of the room is 10 feet. What is the area of the room?

Answers

60% of 10 is 6, so 10x6 is the area which is 60ft^2

Four sides of a octagon each measure 12 cm. The perimeter of the octagon is 70 cm. What is the length of each remaining side, if each remaining side has the same length?

Answers

an octagon has 8 sides

4 * 12 = 48

70-48 = 22
 so the remaining 4 sides need to = 22 cm

22 / 4 = 5.5
 each remaining side = 5.5 cm

Answer:

It would be 5.5 cm

Step-by-step explanation:


Rhett decides to build a square room for his movie and music collection. If the area of the room is 9x^2 − 6x + 1 square feet, what is the length of one side of the room?

(3x + 1) feet
(9x − 1) feet
(3x − 1) feet
(9x + 1) feet

Answers

The answer is (3x-1) feet.

The combined average weight of an okapi and a llama is 450450450 kilograms. The average weight of 333 llamas is 190190190 kilograms more than the average weight of one okapi. On average, how much does an okapi weigh, and how much does a llama weigh?

Answers

I'm going to assume that you meant 450kg for the combined weight, 190kg more and 3 Llamas. I'm pretty sure Llamas and Okapis don't weigh 450450450kg (that's 993,073,252 pounds). :)

x= Okapi weight
y= Llama weight

EQUATIONS:
There are 2 equations to be written:

1) 450kg is equal to the weight of one Okapi and one Llama

450kg= x + y

2) The weight of 3 llamas is equal to the weight of one Okapi plus 190kg.

3y=190kg + x


STEP 1:
Solve for one variable in one equation and substitute the answer in the other equation.

450kg= x + y
Subtract y from both sides
450-y =x


STEP 2:
Substitute (450-y) in second equation in place of x to solve for y.

3y=190kg + x
3y=190 + (450-y)
3y=640 -y
add y to both sides

4y=640
divide both sides by 4

y=160kg Llama weight


STEP 3:
Substitute 160kg in either equation to solve for x.

3y=190kg + x
3(160)=190 + x
480=190 + x
Subtract both sides by 190

290= x
x= 290kg Okapi weight


CHECK:
3y=190kg + x
3(160)=190 + 290
480=480

Hope this helps! :)

Llama's weight will be 160kg and Okami's weight will be 290kg.

What is an average?

An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.

The weight for both will be calculated as below:-

x= Okapi weight

y= Llama weight

There are 2 equations to be written:

1) 450kg is equal to the weight of one Okapi and one Llama.

450kg= x + y

2) The weight of 3 llamas is equal to the weight of one Okapi plus 190kg.

3y=190kg + x

Solve for one variable in one equation and substitute the answer in the other equation.

450kg= x + y

Subtract y from both sides.

450-y =x

Substitute (450-y) in the second equation in place of x to solve for y.

3y=190kg + x

3y=190 + (450-y)

3y=640 -y

Add y to both sides.

4y=640

Divide both sides by 4.

y=160kg Llama weight

Substitute 160kg in either equation to solve for x.

3y=190kg + x

3(160)=190 + x

480=190 + x

Subtract both sides by 190.

290= x

x= 290kg Okapi weight

Therefore, Llama's weight will be 160kg and Okami's weight will be 290kg.

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Choose the correct simplification of (7x3y3)2.

14x6y6
49x5y5
49x6y6
14x5y5

Answers

The correct answer is 49x6y6 because the exponent 2 gives you (7x3x3)*(7x3x3) and the coefficient 7 is multiplied to 49 and the exponent 2 multiplies the exponents of 3 which gives you x6y6

The correct simplification of (7x3y3)2 = 49x6y6

What is simplification?

Simplification is defined as the removal of parentheses in an algebraic expressions in such a way that it would be understood.

From the expression given,

(7x3y3)2 = 2 × 7x × 3y × 3

= 49x6y6

Therefore, the correct simplification of (7x3y3)2 = 49x6y6

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helpppppppppppppppppppppppppppp

Answers

Nr B:
x = -7 +/- √(-64)
x = -7 +/- 8*√-1
x = -7 +/- 8i
in this case it is to find the roots of the polynomial.
 We have then:
 x ^ 2 + 14x + 17 = -96
 Rewriting:
 x ^ 2 + 14x + 113 = 0
 Applying resolver we have
 x = (- b +/- root (b ^ 2 - 4ac)) / (2a)
 Substituting values:
 x = (- (14) +/- root ((14) ^ 2 - 4 (1) (113))) / (2 (1))
 x = (- (14) +/- root ((196 - 452)) / (2 (1))
 x = (- 14 +/- root (-256))) / (2)
 x = (- 14 +/- i * 16)) / (2)
 x = (- 7 +/- i * 8)
 Answer:
 x = (- 7 +/- i * 8)
 (option 2)

If point P is at the center of the circle, and the length of equals 12 inches, which is the length of AP?

a)4.5 inches

b)6 inches

c)9 inches

d)12 inches

Answers

B)6 inches
you divide by 2

Help please.....!!!!!

Answers

The correct answer is:  [A]:  "Graph A" {the red graph}.
______________________________________________________
Note: 
_______________________________
When x = 0 ; 

y = f(x) = 5(2)⁻ˣ = 5* (2)⁻⁰ = 5 * 1 = 5 .
_______________________________
By inspection of the graph, the only given answer choices with graphs that fall on the point "(0, 5)" are:  

  [A]:  "Graph A" (the red graph) ; and:

  [B]:  "Graph B" (the green graph) .
________________________________________________________
Now, let us look at other points and see if the selected points are true values for the given function/ equation; 

Start with "Graph B" (the green graph):  Upon inspection, it is clear that                  "(0.5 , 7)" is a point on the graph;  that is, for "Graph B" , 
                                                                                      when "x = 0.5" ,  y = 7" .

Let us plug these values into the equation: y = 5(2)⁻ˣ  ; to see if the equation holds true;  that is, when "x = 0.5" , does "y = 7" ?

5* 2^(-0.5) = 5 * 0.7071067811865475 ;
 
 →  5 * (√2/2) =

3.5355339059327375;

→  3.5355339059327375 [tex] \neq [/tex] 7 .
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So; we are left with:  Choice:  [A]:  "Graph A" {the red graph}.
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Find the length of both arc AB and arc APB, where

Answers

The length of the arc cannot be found without knowing some linear measure of the circle. None are given.

The measure of arc AB is twice that of angle APB, so is
   2*108° = 216°.
The measure of arc APB is the difference between that and 360°, so is
   360° -216° = 144°.
check the picture below.

as you can see, the angle at P is the inscribed angle, and the intercepted arc is AB, thus 2P = arcAB.

and since a circle has a total of 360°, the other arc is just 360 - arcAB.
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