If the measure of arc CB is 8/3 units, what is the measure of CAB?

Answers

Answer 1

Question:

If the measure of arc CB is [tex]\frac{8}{3} \pi[/tex] units, what is the measure of ∠CAB?

Answer:

120°

Step-by-step explanation:

The figure has been attached to this response.

The figure shows a circle centered at A and has a radius of 4 units.

Also, the length of the arc CB (as given in the question) is  [tex]\frac{8}{3} \pi[/tex] units.

The length L of an arc is given by;

L = [tex]\frac{\beta }{360} * 2\pi * r[/tex]         -----------------(i)

Where;

β = angle subtended by the arc at the center of the circle and measured in degrees

r = radius of the circle

From the question;

β = ∠CAB

r = 4 units

L =  [tex]\frac{8}{3} \pi[/tex]

Substitute these values into equation (i) as follows;

[tex]\frac{8}{3} \pi[/tex] = [tex]\frac{\beta }{360} * 2\pi * 4[/tex]

=>  [tex]\frac{8}{3} \pi[/tex] = [tex]\frac{\beta }{360} * 8\pi[/tex]

Cancel 8[tex]\pi[/tex] on both sides    

[tex]\frac{1}{3}[/tex] = [tex]\frac{\beta }{360}[/tex]

Cross multiply

3 x β = 360 x 1

3β = 360

Divide both sides by 3

[tex]\frac{3\beta }{3} = \frac{360}{3}[/tex]

β = 120°

Therefore, the measure of ∠CAB is 120°

If The Measure Of Arc CB Is 8/3 Units, What Is The Measure Of CAB?

Related Questions

You are paid $25 per hour.

You work 7 hours a day.

You work 5 days a week.

How much is your total pay each week? $=

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Answer:

The total pay would be $50, But there would also be tax to consider in this situation.

which sequence is a geometric progression
a 2 4 6 8
b 1 1 2 3
c1 2 4 8
d1 3 5 7​

Answers

9514 1404 393

Answer:

  c  1, 2, 4, 8

Step-by-step explanation:

It can work well to look at the first differences.

  a: 4 -2 = 2; 6 -4 = 2 ⇒ differences are 2, 2, 2

  b: differences are 0, 1, 1

  c: differences are 1, 2, 4

  d: differences are 2, 2, 2

__

Sequences 'a' and 'd' have common differences that are constant. These are arithmetic sequences. Sequence 'b' is of no named type.

Sequence 'c' has first differences that have a common ratio, the same as the sequence itself. This is an indication the sequence is geometric. The ratios of values are 2/1 = 2; 4/2 = 2; 8/4 = 2, so the terms have a common ratio.

Sequence c is a geometric progression.

Use the diagram to estimate the perimeter, rounding each number to the nearest hundred.

A parallelogram is shown. Two sides are labeled 5,534 feet. The other two sides are labeled 1,566 feet.


14,200 feet


16,000 feet


14,400 feet


14,000 feet

Answers

Answer:

14,000 feet.

Step-by-step explanation:

A parallelogram has 4 total sides and the opposite sides are characterized as having the same length. Therefore, If we are provided the lengths of two adjacent sides we can easily calculate the perimeter by multiplying these provided lengths by 2 and then adding them together. Since we are asked to round each number to the nearest hundred, it would be the following...

(5,500 * 2) + (1,500 * 2) = x

11,000 + 3000 = x

14,000 = x

Finally, we can estimate that the perimeter of the parallelogram is 14,000 feet.

What percent of 0.2 gram of 32 mg

Answers

Answer:

625

Step-by-step explanation:

First, you have to convert 0.2 grams to mg.  To do this, multiply 0.2 by 1000.  This yield 200.  Now 200 is what percent of 32.  

200 * 100 / 32

= 625

a fuel mixture consists of 3 parts oil and 11 parts gasoline. the oil costs $0.75 per liter, and the gasoline costs $1.60 per liter. a mechanic makes 392 liters of the mixture. how much should he charge for 15% profit

Answers

Answer:

Total selling price= $663.82

Selling price per liter= $1.69

Step-by-step explanation:

Giving the following information:

Proportion of oil and gasoline:

Oil= 3/14= 0.21

Gasoline= 11/14= 0.79

The oil costs $0.75 per liter.

The gasoline costs $1.60 per liter.

First, we need to calculate the number of liters of oil and gasoline required:

Oil= 0.21*392= 82.32 liters

Gasoline= 0.79*392= 309.68

Now, the total cost to produce 392 liters:

Total cost= 82.32*0.75 + 309.68*1.6

Total cost= $577.23

Finally, the total and unitary selling price:

Total selling price= 577.23*1.15= $663.82

Selling price per liter= 663.82 / 392= $1.69

NEED HELP ON THIS ASAP PLZ!! (Marking BRAINLIST)​

Answers

Answer:

brainllest if right

2

Step-by-step explanation:

Answer:

I don't know sorry

Step-by-step explanation:

what is the value of 9 (n + 2) - 5n when n =1/4​

Answers

9514 1404 393

Answer:

  19

Step-by-step explanation:

The evaluation is easier if we simplify the expression first.

  9(n +2) -5n = 9n +18 -5n = 4n +18

For n = 1/4, this is ...

  = 4(1/4) +18 = 1 +18

  = 19

The value of the expression for n = 1/4 is 19.

A group of coins is shown below. What is the probability of drawing each type of coin?​

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Answer:

likely

Step-by-step explanation:

Which function is graphed on the coordinate plane below?

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Answer:

f(x) = 2x - 6

Step-by-step explanation:

positive slope = 2

y- intercept = -6

Answer:A

Step-by-step explanation:

What is the complementary number of 16
I

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Answer:

2

Step-by-step explanation:

I need help with this problem-

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Answer:

wat

Step-by-step explanation:

33. What does equal in the solution of the system of equations below? 33 – 4y - z= 14 2r + 3y - 32 = 17 x + 2y + x = 20 10 04 -10 O-4​

Answers

9514 1404 393

Answer:

  (a) 10

Step-by-step explanation:

Attached is a graphical solution using "substitution." An expression was written for z using the first equation, and it was substituted into the remaining two equations. This gave two equations in x and y, easily solved graphically.

We found x = 10, y = 3, so ...

  z = 3(10) -4(3) -14 = 30 -12 -14 = 4

The whole solution is (x, y, z) = (10, 3, 4).

the ratio of the measures of the angles in cat is 2:7:9. find the measure of the smallest angle.

Answers

Answer:

20º

Step-by-step explanation:

Total parts

2  + 7 + 9 = 18

Value of each part given 180º in a triangle

180 / 18 = 10º

Smallest angle

2 * 10 = 20º

Answer:

20

Step-by-step explanation:

Multiply each angle by x

2x: 7x: 9x

The sum of the angles in a triangle is 180

2x+7x+9x = 180

Combine like terms

18x = 180

Divide by 18

18x/18 = 180/18

x =10

The smallest angle is 2x

2x = 2(10) =20

Select the equation of a straight line that is parallel to the line 4y = 3x + 5

Answers

Answer:

One equation can be y = 3/4X +2

Step-by-step explanation:

Any equation that has a slope of 3/4 will be parallel to the line 4Y = 3X + 5 because the slope is the same. This can also be shown visually using any graphing calculator.

Which graph shows the point (-2, 3)?
A.
B.
C.
D.

Answers

You didn’t provide the graphs but here is where the point would be on the graph.

X^2-10x = −16 solution??

Answers

x^2-10x+16= 0
(x-8)(x-2)=0
x = 8 or 2
x^2-10x=-16
x^2-2x-8x+16=0
x(x-2)-8(x-2)=0
(x-2)(x-8)
x=2,8

Please help me, and can you do it by a table math

Answers

Answer:

Yeah

Step-by-step explanation:

There are 3 liters of orange juice at a school party. 10 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get? (enter your answer as a fraction or mixed number)

Answers

Answer:

3 1/3 each

Step-by-step explanation:

10/3=3 1/3

0.3 liters each student

3 liters = 3.000 ml so 3.000(ml) : 10(students) =300 ml which is 0.3 liters

Question is on the screenshot

Answers

Answer: V= 150π

V= πr^2 h
V= π(5)^2 (6)
V= 150π
Approximately y=2.94

Help!!!

Given a room is 12 feet by 10 feet and we have a circular rug with a radius of 3 feet,
calculate the amount of floor left uncovered by the circular area rug in a rectangular
living room.

Answers

Answer:

Step-by-step explanation:

floor = 12*10 = 120 sq ft

rug = π[tex]r^{2}[/tex] = 9π

120-9π = 91.74 sq ft

The amount of floor left uncovered by the circular area rug in a rectangular living room is 91.74 ft²

What is Area?

Area is the space occupied by a 2 dimensional figure.

The room is rectangular and its 12 ft by 10 ft. Therefore,

area of the room = lw

where

l = length

w = width

area of the room = 12 × 10 = 120 ft²

The rug is circular and its use to cover the room. Therefore,

area of rug = πr²

where

r = 3 ft

Therefore,

area of rug = 3.14 × 3² = 28.26 ft²

The amount of floor left uncovered by the circular area rug in a rectangular living room can be calculated as follows:

area uncovered = 120 - 28.6 = 91.74 ft²

learn more on area here; https://brainly.com/question/1389611

I forgot a long time ago, What is the slope of the line?
See the image as the line doesn't go through -2 on the x nor -1 on the y

Answers

Answer:

[tex] - \frac{4}{5}[/tex]

Step-by-step explanation:

Line is passing through the points (-3, 1) & (2, - 3)

Therefore,

Slope of line

[tex] = \frac{ - 3 - 1}{2 - ( - 3)} \\ \\ = \frac{ - 4}{2 + 3} \\ \\ = - \frac{4}{5} [/tex]

The sum of two numbers is 69. One number is 15 less than the other. Find the numbers.

Answers

Answer:

58+-43=15

Step-by-step explanation:

A large auditorium has stadium with stadium seating. There are 8 seats in the first row, 10 seats in the second row, 12 seats in the third row and 300 seats in the last row. How many rows of seats are in the auditorium

Answers

There are 4 rows, and 338 seats total.

Please can somebody help I am not very good at maths

Answers

Answer:

z = 3a + 4

Step-by-step explanation:

Add 4 to both sides

The height of a rocket a given number of seconds after it is released is modeled by h(t)=-16t+32t+10 what does t represent?

Answers

59t cause t is the correct

If it takes 1074 digits to number the pages of a book starting with page 1. how many pages are in the book? The book has a total of pages. ​

Answers

Answer:

394 pages

Step-by-step explanation:

1- digit numbers:

1 to 9, number of digits = 9

2- digit numbers:

10 to 99, number of digits = 2(99 - 9) = 180

3- digit numbers:

100 to 999, number of digits = 3(999 - 99) = 2700

This is more than we have, but we know the number of pages is 3-digit.

Let it be x, then we have:

9 + 180 + 3(x - 99) = 10743(x - 99) = 1074 - 1893(x - 99) = 885x - 99 = 885/3x - 99 = 295x = 295 + 99x = 394

Hello if you're able to answer this question help me and provide work as well, Thank you.

Answers

Answer:

Option A. Only Khaled

Step-by-step explanation:

To know which option is correct, we shall use the formula suggested by both Khaled and Wilma to see which will give the sequence given in the question.

For Khaled:

F(n) = 1 • 3ⁿ¯¹

n = 1

F(n) = 1 • 3ⁿ¯¹

F(1) = 1 • 3¹¯¹

F(1) = 1 • 3⁰

F(1) = 1 × 1

F(1) = 1

n = 2

F(n) = 1 • 3ⁿ¯¹

F(2) = 1 • 3²¯¹

F(2) = 1 • 3¹

F(2) = 1 × 3

F(2) = 3

n = 3

F(n) = 1 • 3ⁿ¯¹

F(3) = 1 • 3³¯¹

F(3) = 1 • 3²

F(3) = 1 × 9

F(3) = 9

For Wilma

F(n) = 1 • 3ⁿ

n = 1

F(n) = 1 • 3ⁿ

F(n) = 1 • 3¹

F(1) = 1 × 3

F(1) = 3

n = 2

F(n) = 1 • 3ⁿ

F(2) = 1 • 3²

F(2) = 1 × 9

F(2) = 9

n = 3

F(n) = 1 • 3ⁿ

F(3) = 1 • 3³

F(3) = 1 × 27

F(3) = 27

SUMMARY

Using Khaled's formula i.e F(n) = 1 • 3ⁿ¯¹ we obtained 1, 3, 9,..

Using Wilma's formula i.e F(n) = 1 • 3ⁿ

We obtained 3, 9, 27,..

Now, comparing the sequence obtained using the formula of both Khaled and Wilma, we can see that only the sequence of Khaled is the same with the one given in the question. Therefore, only Khaled's formula is correct.

What is the solution to the system of equations below?
y=-3x+9 and y-ſx-12
(21, 2)
(21, -10)
(-21, 16)
(-21, -26)


Answers

I tried every combination. there seems to be something wrong with the informations you gave.

the second equation contains errors, and none of these 4 points can be solutions to the first equation alone

Write the equation of the line that has the indicated slope and contains the indicated point. Express the final equation in standard form.
m = 1/2, (6, 9)

Answers

Answer:

[tex]x-2y=-12[/tex]

Step-by-step explanation:

Hi there!

1) Determine the equation of the line in slope-intercept form

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)

Plug in the slope [tex]\frac{1}{2}[/tex]

[tex]y=\frac{1}{2}x+b[/tex]

Plug in the given point (6,9) and solve for b

[tex]9=\frac{1}{2}(6)+b\\9=3+b[/tex]

Subtract 3 from both sides

[tex]9-3=3+b-3\\6=b[/tex]

Plug 6 back into [tex]y=\frac{1}{2}x+b[/tex]

[tex]y=\frac{1}{2}x+6[/tex]

2) Rearrange the equation into standard form

Standard form: [tex]Ax+By=C[/tex] where A, B and C are integers and A is typically positive

[tex]y=\frac{1}{2}x+6[/tex]

Multiply both sides by 2 to remove the fraction

[tex]2y=1x+12\\2y=x+12[/tex]

Subtract x from both sides to isolate 12 as C

[tex]2y-x=x+12-x\\2y-x=12\\-x+2y=12[/tex]

Multiply both sides by -1 to make A positive

[tex]x-2y=-12[/tex]

I hope this helps!

A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30 cm, and the bicycle wheel
makes 3 full rotations before stopping.
How long is the trace of water left on the floor?
Round your answer to the nearest cm.

Answers

Answer:

The trace of the water left on the floor is 566 cm.

Step-by-step explanation:

The bicycle wheel has a circular shape, therefore;

1 revolution is the same as the circumference of the wheel. So that 3 revolutions is the same as multiplying the circumference of the wheel by 3.

circumference = 2[tex]\pi[/tex]r

where r is the radius of the wheel (r = 30 cm).

Thus,

circumference = 2 x [tex]\frac{22}{7}[/tex] x 30

                        = [tex]\frac{1320}{7}[/tex]

circumference = 188.57 cm

3 revolutions = 3 x 188.57

                      = 565.71 cm

Therefore, the trace of the water left on the floor is 566 cm.

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