Covert the verbal expression into an algebraic expression.
The product of 23 and a number x​

Answers

Answer 1

Answer:

23×x

=23x

Hope it helps

Answer 2

Answer:

23x

Step-by-step explanation:

"The product of" indicates that we will be multiplying the two quantities. 23 multiplied by x can be written as 23 * x which simplifies to 23x.


Related Questions

Consider the following system of equations: y=2x−2 6x+3y=2 The graph of these equations consists of two lines that: 1. intersect at more than one point. 2. intersect in an infinite number of points. 3. intersect at exactly one point. 4. do not intersect.

Answers

Answer:

3.  Intersect at exactly one point.  ( (2/3), (-2/3) )

Step-by-step explanation:

To make the comparison of these lines easier, let's rewrite the 2nd equation into slope-intercept form, as the 1st equation is in slope-intercept form.

[1] y = 2x - 2

---------------------

[2] 6x + 3y = 2 ==> 3y = 2 - 6x ==> y = -2x + (2/3)

[2] y = -2x + (2/3)

So now that we have both equations in slope-intercept form, we can see that the two equations are both linear, have different slopes, and have different y-intercepts.

Since these equations have both different slopes and different y-intercepts, we know that the lines will cross at least one point.  We can confirm that the lines only cross at a single point using the fact that both equations are linear, meaning there will only be one point of crossing.  To find that point, we can simply set the equations equal to each other.

y = 2x - 2

y = -2x + (2/3)

2x - 2 = -2x + (2/3)

4x = (8/3)

x = (8/12) = (2/3)

And plug this x value back into one of the equations:

y = 2x - 2

y = 2(2/3) - 2

y = (4/3) - (6/3)

y = (-2/3)

Thus these lines only cross at the point ( (2/3), (-2/3) ).

Cheers.

Answer:

I don't understand the question

Please help me i don’t know if I’m right

Answers

Answer:

   your choice is correct

Step-by-step explanation:

The magnitude of the difference between the target amount and the actual amount will be no greater than the allowed error.

  |x -34| ≤ 0.25

What is the difference between a coefficient and variable (such as 3x) and a constant (5)?  Why can these two types of terms not be combined?
 

Answers

Answer:

see below (I hope this makes sense!)

Step-by-step explanation:

Constants, as the name suggest, stay constant, meaning that their value never changes. For example, 2 will always be 2 and 9.4 will always be 9.4. On the other hand, the values of variables can change. Take, for example, the variable 2x. When x = 1, 2x = 2 and when x  =2, 2x = 4 so the value of 2x can change depending on what x is. You can't combine constants and variables because they are not like terms, basically, one can change and the other can't and you cannot combine terms that are not like each other.

The angle \theta_1θ 1 ​ theta, start subscript, 1, end subscript is located in Quadrant \text{I}Istart text, I, end text, and \sin(\theta_1)=\dfrac{1}{2}sin(θ 1 ​ )= 2 1 ​ sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 1, divided by, 2, end fraction . What is the value of \cos(\theta_1)cos(θ 1 ​ )cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?

Answers

Answer:

√3/2

Step-by-step explanation:

Given an angle θ₁ located on in the first quadrant and sinθ₁ = 1/2, we are required to calculate the value of cosθ₁.

Firstly, we need to find the value of the angle θ₁ from the expression sinθ₁ = 1/2.

Given sinθ₁ = 1/2

Take the arcsin of both sides

arcsin(sinθ₁) = arcsin(1/2)

The arcsin will cancel out the sin at the left hand side to have only θ₁. Hence;

θ₁  = arcsin(1/2)

Using the calculator, θ₁ = 30°

Since we are to find the value of cosθ₁

cosθ₁ = cos30°

cos30° = √3/2

Hence the value of cosθ₁ is √3/2

Answer:

60/61

Step-by-step explanation:

60/61

khan. #gayrights

how 45 degree angles does it take to make a full turn?
PLSSSSSSSSSSSSSSS HELP

Answers

Answer:

8 turns

Step-by-step explanation:

If we want to take a full turn, we'd turn around 360° since we'd be in the same position.

If we turn in intervals of 45°, we need to find how many times 45 goes into 360. To do this, we can divide.

[tex]360\div45=8[/tex]

Hope this helped!

Answer:

It will take 8  45 degree angles to make a full turn

Step-by-step explanation:

360 degrees is a full turn

360/45 =8

It will take 8  45 degree angles to make a full turn

Claire and Richard are both artists who use square canvases. Claire

uses the polynomial 50%? + 250 to decide how much to charge for her paintings

and Richard uses the polynomial 40x² + 350 to decide how much to charge for

his paintings. In each polynomial, x is the height of the painting in feet.

a. How much does Claire charge for a 20-foot-tall painting?

b. How much does Richard charge for a 15-foot-tall painting?

c. To the nearest tenth, for what height will both Claire and Richard charge

the same amount for a painting? Explain how to find the answer.

d. When both Claire and Richard charge the same amount for a painting,

how much does each charge?

Answers

Answer:

A.  [tex]Claire = 20250[/tex]

B.   [tex]Richard = 9350[/tex]

C.    Height = 3.2 feet

D. Charges = $760

Step-by-step explanation:

Given

[tex]Claire = 50x^2 + 250[/tex]

[tex]Richard = 40x^2 + 350[/tex]

Solving (a): Claire's 20ft charges

In this case, x = 20

Substitute 20 for x in [tex]Claire = 50x^2 + 250[/tex]

[tex]Claire = 50(20)^2 + 250[/tex]

[tex]Claire = 50(400) + 250[/tex]

[tex]Claire = 20000 + 250[/tex]

[tex]Claire = 20250[/tex]

Solving (b): Richard's 15ft charges

In this case, x = 15

Substitute 20 for x in [tex]Richard = 40x^2 + 350[/tex]

[tex]Richard = 40(15)^2 + 350[/tex]

[tex]Richard = 40(225) + 350[/tex]

[tex]Richard = 9000 + 350[/tex]

[tex]Richard = 9350[/tex]

Solving (c): Height which they both charge the same;

This implies that

[tex]50x^2 + 250 = 40x^2 + 350[/tex]

Solving for x [Collect Like Terms\

[tex]50x^2 - 40x^2 = 350 - 250[/tex]

[tex]10x^2 = 100[/tex]

Divide both sides by 10

[tex]x^2 = 10[/tex]

Take square roots of both sides

[tex]x = \sqrt{10}[/tex]

[tex]x = 3.2ft[/tex]  (Approximated)

Hence; Height = 3.2 feet

Solving (d): How much they charge when the charge the same amount.

Substitute 3.2 for x in any of the given equation

[tex]Claire = 50x^2 + 250[/tex]

[tex]Claire = 50(3.2)^2 + 250[/tex]

[tex]Claire = 50*10.24 + 250[/tex]

[tex]Claire = 512 + 250[/tex]

[tex]Claire = 762[/tex]

[tex]Richard = 40x^2 + 350[/tex]

[tex]Richard = 40(3.2)^2 + 350[/tex]

[tex]Richard = 40 * 10.24 + 350[/tex]

[tex]Richard = 409.6 + 350[/tex]

[tex]Richard = 759.6[/tex]

The reason for the difference is due to approximation

Hence, they both charge approximately 760

Using the conversion 1 mile equals 1.6093 km to convert 4.9 kilometers to miles, round o the nearest tenth of a mile

Answers

Answer:

3.0 miles

Step-by-step explanation:

Using the conversion 1 mile equals 1.6093 km to convert 4.9 kilometers to miles, round to the nearest tenth of a mile.

1 mile = 1.6093 km

Convert 4.9km to mile

We can use cross multiplication :

Let the number of miles = m

1 mile = 1.6093 km

'm' miles = 4.9 km

Cross multiply :

m × 1.6093 = 4.9 × 1

m = 4.9 / 1.6093

m = 3.0448020 miles

Rounding 3.0448020 to the nearest tenth :

3.0 miles

Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-Intercept, and vertex of the function.
f(x)= x^2- 4x-5
+
10-
Line
8
6
4
2-
-10
-8

Answers

Answer:

1) Please find attached the graph sowing the line of symmetry

The symmetry line is a vertical line passing through (2, -9)

2) The x-intercept are (5, 0) and (-1, 0)

The y-intercept is (0, -5)

The vertex is (2, -9)

Step-by-step explanation:

The given function is;

f(x) = x² - 4·x - 5

The data values are generated as follows;

x,          f(x)

-1,         0

-0.8,    -1.16

-0.6,    -2.24

-0.4,    -3.24

-0.2,    -4.16

0,         -5

0.2,      -5.76

0.4,      -6.44

0.6,     -7.04

0.8,     -7.56

1,         -8

1.2,      -8.36

1.4,      -8.64

1.6,      -8.84

1.8,      -8.96

2,        -9

2.2,     -8.96

2.4,      -8.84

2.6,     -8.64

2.8,     -8.36

3,        -8

3.2,     -7.56

3.4,     -7.04

3.6,     6.44

3.8,     -5.76

4,        -5

4.2,      -4.16

4.4,     -3.24

4.6,     -2.24

4.8,      -1.16

5,           0

The minimum is found from differentiating the function, f(x), with respect to x and looking for the zeros of the result  as follows;

f'(x) = 2·x -4

f'(x) = 0 = 2·x -4

x = 2

The y-coordinate gives; f(2) = 2² - 4×2 - 5 = -9

Therefore, the symmetry line is a vertical line passing through (2, -9)

The x-intercept is the point at which y = 0, therefore, from f(x) = x² - 4·x - 5, we have;

0 = x² - 4·x - 5 = (x - 5)·(x + 1)  

Therefore, the x-intercept are x = 5 or -1

The x-intercept are (5, 0) and (-1, 0)

The y-intercept occur at the point where the x value = 0, therefore, we have;

The y-intercept occur at y = f(0) = 0² - 4·0 - 5 = -5

The y-intercept is (0, -5)

Re-writing the  equation in vertex form y = a(x - h)² + k gives;

f(x) = x² - 4·x - 5 = 1·(x - 2)² - 9

Therefore, the vertex is (2, -9)

Answer:

see attached graph

The x-intercept are (5, 0) and (-1, 0)

The y-intercept is (0, -5)

The vertex is (2, -9)

Step-by-step explanation:

Point B is on line segment AC. Given BC=9 and AB=11, determine the length AC.

Answers

Answer:

[tex]AC=20[/tex]

Step-by-step explanation:

The line segment AC is the entire length of the line. Within this segment, point  B is found.

Point B, in a way, splits the segment into two, creating the segments AB and BC.

To find the length of AC, add the lengths of the lines AB and BC together:

[tex]AB=11\\BC=9\\AB+BC=AC\\11+9=AC\\20=AC[/tex]

The length of AC is 20.

:Done

Answer:

20 units.

Step-by-step explanation:

Segment AC is broken into two parts by point B. That means that the length of segment AB plus the length of segment BC equals the length of segment AC.

If BC = 9, and AB = 11, AC = 9 + 11 = 20 units.

Hope this helps!

chose the equivelent expresion 5⁶ a.(5⁴)² b.(5⁻²)⁻³ c.(5¹)⁵

Answers

Answer:

[tex]\Large \boxed{(5^{-2})^{-3}}[/tex]

Step-by-step explanation:

Applying the law of exponents : [tex](a^b)^c=a^{bc}[/tex]

[tex](5^4)^2 = 5^{4 \times 2} = 5^{8}[/tex]

[tex](5^{-2})^{-3}=5^{-2 \times -3}=5^6[/tex]

[tex](5^1)^5 =5^{1 \times 5}=5^5[/tex]

Answer:

[tex]\huge\boxed{Option \ B}[/tex]

Step-by-step explanation:

[tex]5^6[/tex] is equivalent to

=>   [tex](5^4)^2 = 5^{4*2} = 5^ 8[/tex]

=> [tex](5^{-2})^{-3} = 5^{-2*-3} = 5^6[/tex]          ← Correct

=> [tex](5^1)^5 = 5^{1*5} = 5^5[/tex]

Theresa swims in a pool that is 75 meters long. Everyday Theresa swims ten lengths of the pool. After 5 days, how many kilometers has Theresa swan?

Answers

Answer:

She swam 2 kilometers

Step-by-step explanation:

MATHEMATICS
SECTION A (VERY SHORT ANSWERS)
1. Which of the following is irrational?
a V25
V12
b. Vs
c.
V3
2. V768 in its simplest form is:
dve
16
a.
16 V3
b. 64 V3 c.4 V3
d. 8 V3
3. The simplest rationalisation factor of 27 is:
a. b. 73
c. 27
d. 3
4. If x=2 and y = 3, then the value of xy + yt is:
a. 15
b. 17
c. 19
d. 21
a
2
5. The value of [ 8-43 + 22/12 is:
b. 2 ch d. 4
6. If p(x) = x2 – 3x + 2, then what is the value of p(0) + p(2).
7. Find the value of k, if (2x - 1) is a factor of the polynomial 6x2 + kx - 2.
8. Expand (x - y)
9. If x11 + 101 is divided by (x + 1), then what remainder do we get?
10. Find the value of x2 + 3, if(x - 5) = 13
SECTION B (SHORT ANSWERS
11. Express 0.123 in the form where p and q are integers and qf0
9
√7-√6
12. Rationalise the denominator of
√ + √6
13. Find the value of x if
&2x
14. If x2 + = 7 then find x3 +
15. If x + y + z = 10 and x2 + y2 + z = 40 find xy + y2 + zx and x3 + y + z3 - 3xyz
16. Factorize 8x3 - (2x - y)3
81
16

Answers

1 is c
2 is d
3 is b
4 is c
5 is a

PLEASE help me solve this question! This is really URGENT! No nonsense answers please.

Answers

Answer:

[tex]\boxed{\sf 6.4 \ seconds}[/tex]

Step-by-step explanation:

t = time (s) ⇒ ?

d = distance falling (m) ⇒ 200 (m)

a = acceleration due to gravity ⇒ 9.8 (m/s²)

The time in seconds is not given. Solve for time using the formula.

[tex]t=\sqrt{\frac{2(200)}{9.8} }[/tex]

[tex]t=\sqrt{\frac{400}{9.8} }[/tex]

[tex]t= 6.388766...[/tex]

Round answer to nearest tenth of a second.

[tex]t \approx 6.4[/tex]

Solve the equation for x.
[tex] \frac{1}{8} x + 8 = 12[/tex]

Answers

Answer: x=32

Step-by-step explanation:

[tex]\frac{1}{8}x+8=12[/tex]

subtract 8 on both sides

[tex]\frac{1}{8}x+8-8=12-8[/tex]

[tex]\frac{1}{8}x=4[/tex]

multiply 8 on both sides

[tex]8\cdot \frac{1}{8}x=4\cdot \:8[/tex]

[tex]4\cdot8=32[/tex]

[tex]x=32[/tex]

A point is randomly chosen on a map of North America. Describe the probability of the point being in each location: North America: New York City: Europe:

Answers

Answer:

We know that the map is of North America:

The probabilities are:

1) North America:

As the map is a map of North America, you can point at any part of the map and you will be pointing at North America, so the probability is p = 1

or 100% in percentage form.

2) New York City.

Here we can think this as:

The map of North America is an extension of area, and New Yorck City has a given area.

As larger is the area of the city, more probable to being randomly choosen, so to find the exact probability we need to find the quotient between the area of New York City and the total area of North America:

New York City = 730km^2

North America = 24,709,000 km^2

So the probability of randomly pointing at New York City is:

P = ( 730km^2)/(24,709,000 km^2) = 3x10^-5 or 0.003%

3) Europe:

As this is a map of Noth America, you can not randomly point at Europe in it (Europe is other continent).

So the probaility is 0 or 0%.

Answer:

North America: certain

New York City: unlikely

Europe: impossible

Step-by-step explanation:

simply

Tom finished reading 3/7 of a book in the first week, and he read 3/4 of the remainder in the second week. what fraction is left?​

Answers

Answer:

1/7 is left

Step-by-step explanation:

What is left to read after the first week

1 - 3/7

7/7 - 3/7

4/7

He read 3/4 of this the second week

4/7 * 3/4

3/7 was read

4/7 - 3/7 is what is left

1/7 is left

Answer:

The correct answer is

Step-by-step explanation:

1/7 of the book is left to read.

Hope this helps....

Have a nice day!!!!

The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70​

Answers

Answer:

         d = 245

Step-by-step explanation:

d is directly proportional to the square of a speed v

d = av²

5 = a•10²

5 = 100a

a = 0.05

d = 0.05v²

d = 0.05•70²

d = 0.05•4900

d = 245

Solve the triangle. A = 51°, b = 14, c = 6, I'll give 20 points

Answers

Answer:

Step-by-step explanation:

We have that

A = 51°, b = 14, c = 6

step 1

find the value of a

Applying the law of cosines

a²=c²+b²-2*c*b*cos A

a²=6²+14²-2*6*14*cos 51-------> 126.27

a=11.2

we know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

we have

a=11.2

b=14

c=6

so

(a+b) > c-------------> (11.2+14)=25.2

25.2 > 6-----> is not correct

therefore

the answer is the option

a. No triangles possible

I don't know if i am right sorry if this is wrong

G(x)= -\dfrac{x^2}{4} + 7g(x)=− 4 x 2 ​ +7g, left parenthesis, x, right parenthesis, equals, minus, start fraction, x, squared, divided by, 4, end fraction, plus, 7 What is the average rate of change of ggg over the interval [-2,4][−2,4]open bracket, minus, 2, comma, 4, close bracket?

Answers

Answer:

-1/2

Step-by-step explanation:

Given the function [tex]G(x)= -\dfrac{x^2}{4} + 7[/tex], the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;

Rate of change of the function is expressed as g(b)-g(a)/b-a

where a - -2 and b = 4

[tex]G(4)= -\dfrac{4^2}{4} + 7\\G(4)= -\dfrac{16}{4} + 7\\G(4)= -4 + 7\\G(4) = 3\\[/tex]

[tex]G(-2) = -\dfrac{(-2)^2}{4} + 7\\G(-2)= -\dfrac{4}{4} + 7\\G(-2)= -1 + 7\\G(-2)= 6[/tex]

average rate of change of g(x) over the interval [-2,4] will be;

[tex]g'(x) = \frac{g(4)-g(-2)}{4-(-2)}\\ g'(x) = \frac{3-6}{6}\\\\g'(x) = -3/6\\g'(x) = -1/2[/tex]

In a recent Super Bowl, a TV network predicted that 53 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 79 people who saw the commercials and found that 41 of them said they would watch one of the television shows.Suppose you have the following null and alternative hypotheses for a test you are running:H0:p=0.53H0:p=0.53Ha:p≠0.53Ha:p≠0.53Calculate the test statistic, rounded to 3 decimal places

Answers

Answer: -0.196

======================================================

Explanation:

We're conducting a one proportion Z test.

The hypothesized population proportion is p = 0.53, which is not to be confused with the p-value (unfortunately statistics textbooks seem to overuse the letter 'p'). Luckily this problem is not asking for the p-value.

The sample population proportion is

phat = x/n = 41/79 = 0.518987 approximately

The standard error (SE) is

SE = sqrt(p*(1-p)/n)

SE = sqrt(0.53*(1-0.53)/79)

SE = 0.056153 approximately

Making the test statistic to be

z = (phat - p)/(SE)

z = (0.518987 - 0.53)/0.056153

z = -0.19612487311452

z = -0.196

Which is approximate and rounded to 3 decimal places.

Which data set has the greatest spread for the middle 50% of its data?
OA
{18, 13, 22, 17, 21, 24}
B.
{17, 19, 22, 26, 17, 14}
OC. {13, 17, 12, 21, 18, 20)
OD.
{18, 21, 16, 22, 24, 15)

Answers

Answer:

b

Step-by-step explanation:

the answer is b because b have the greatest spread for the middle 50%

I hope this was helpful

The answer is (17, 19, 22, 26, 17, 14) which is b

Find the measure of each angle indicated. Round to the nearest tenth.

A) 65.20
C) 55.1°
B) 51°
D) 55.70​

Answers

Answer:

51

Step-by-step explanation:

Answer: D) 55.7 degrees approximately

=====================================================

The reference angle has AC = 12.3 as the opposite side and BC = 8.4 as the adjacent side. The tangent ratio ties the opposite and adjacent sides together.

--------

tan(angle) = opposite/adjacent

tan(theta) = AC/BC

tan(theta) = 12.3/8.4

theta = arctan(12.3/8.4)

theta = 55.6697828044967

theta = 55.7 degrees approximately

--------

arctan is the same as inverse tangent which is written as [tex]\tan^{-1}[/tex]

make sure your calculator is in degree mode

Write the phrase as an expression. Then evaluate the expression when x = 5.
the sum of a number x and 4, all divided by 3
Expression:
When r= 5, the value of the expression is

Answers

Answer:

Step-by-step explanation:

expression = (x + 4) / 3

x = 5

(5 + 4) / 3

= 9/3

= 3

Hope this helps

plz mark as brainliest!!!!!!

what is the coefficient of x in the equation of 32+2x=10
solve after finding the coefficient

Answers

Answer:

x= -11

Step-by-step explanation:

the coefficient is variable that appears before a number . bearing this in mind, the coefficient of x is therefore 2 .

the value of x is:

>32+2x=10

>2x=10-32

>2x= -22

>x= -11

Answer:

Step-by-step explanation:

Coefficient of x = 2

32 + 2x  = 10

Subtract 32 from both side

32 + 2x -32 = 10 - 32

              2x =  - 22

Divide both sides by 2

            2x/2 = -22/2

x = -11

HELP!!!
The solutions to (x + 3)^2- 4=0 are x = -1 and x = -5

True or false

Answers

Answer:

False

Step-by-step explanation:

We can simplify this equation and then solve for x.

[tex](x+3)^3-4=0\\\\x^2+6x+9-4=0\\\\x^2+6x+5=0\\\\(x+2)(x+3)=0\\\\x=-3\\x=-2[/tex]

As you can see, the solutions are not x=-1 and x=-5.

Therefore, the answer is false.

Answer:

True

Step-by-step explanation:

Given

(x + 3)² - 4 = 0 ( add 4 to both sides )

(x + 3)² = 4 ( take the square root of both sides )

x + 3 = ± [tex]\sqrt{4}[/tex] = ± 2 ( subtract 3 from both sides )

x = - 3 ± 2

Thus

x = - 3 - 2 = - 5

x = - 3 + 2 = - 1

ASAP!!! PLEASE help me solve this question! No nonsense answers, and solve with full solutions.

Answers

Answer:

Option (4)

Step-by-step explanation:

By the theorem of inscribed angles and the intercepted arc,

"In a circle, angles subtended by the same arc always measure the same and the arc measures the double of the inscribed angle."

If an inscribed angle in a circle measures 75° then all inscribed angles by the same arc will measure 75°.

In addition to this, measure of arc subtended by these inscribed angle will measure double of the inscribed angle (150°)

Therefore, Option (4) will be the answer.


Consider 6x2 + 6x + 1. Which term immediately tells you that this expression is NOT a perfect square trinomial? Justify your answer.

Answers

Answer:

Step-by-step explanation:

The 6x^2 because 6  is not a perfect square.

Answer:

6x^2

Step-by-step explanation:

6 isn't a perfect square

The area of a square of side 2.4 cm is​

Answers

Answer:

area of cube = a^2  ( a is side)

2.4^2 = 5.76 cm^2

Answer:

5.76 cm^2

Step-by-step explanation:

Hey there!

Well if the side length is 2.4 cm then the area would be,

A = l•l

A = 2.4 • 2.4

A = 5.76cm^2

Hope this helps :)

31. Solve for w:

[tex] \frac{3w + 6}{28} = \frac{3}{4} [/tex]

HELP! answer if you can​

Answers

Answer:

w = 5

Step-by-step explanation:

Hey there!

Cross multiply,

84 = 12w + 24

-24 to both sides

60 = 12w

Divide both sides by 12

w = 5

Hope this helps :)

Find the length of AB

Answers

Answer:

AB = 3π

Step-by-step explanation:

The formula for the circumference of a circle is:

C = 2πr

By substituting 27 for r:

C = 2π(27)

C = 54π

The whole circumference is 54π. A circle is 360º around. We can set up a proportion to find the length of the 20º arc:

[tex]\frac{360}{54p}[/tex] = [tex]\frac{20}{x}[/tex]

Cross-multiply:

360x = 1080π

Divide both sides by 360:

x = 3π

AB = 3π

Answer:

AB = 3π

Step-by-step explanation:

The arc AB can be calculated as

AB = circumference of circle × fraction of circle

The central angle is equal to the measure of arc AB = 20° , thus

AB = 2πr × [tex]\frac{20}{360}[/tex]

     = 2π × 27 × [tex]\frac{1}{18}[/tex] ( cancel 18 and 27 by 9 )

     = 2π × 3 × [tex]\frac{1}{2}[/tex] = 6π × [tex]\frac{1}{2}[/tex] = 3π

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