Colleen can paint a room in 12 hours.Rebecca can paint the same room in 20 hours.How long does it take for both Colleen and Rebecca to paint the room if they are working together? Write an equation that using the variable t to represent the time it takes to paint the room together that can be used to solve the problem.

Answers

Answer 1
Hello!

The answer is:

It will take 7.5 hours to paint the room together.

Why?

Using the given information we need to write an equation considering both Colleen and Rebecca rates.

For Colleen we know that she can paint a room in 12 hours, so, her equation will be:

[tex]\frac{1Room}{12hours}*t=\frac{t}{12}[/tex]

Being "t" the time used to paint.

For Rebecca, we know that she can paint a room in 20 hours, so, her equation will be:

[tex]\frac{1Room}{20hours}*t=\frac{t}{20}[/tex]

Now, if we want to calculate the time needed to paint 1 room, we have:

[tex]\frac{t}{12}+\frac{t}{20}=1\\\\\frac{12*t+20*t}{12*20}=1\\\\\frac{12t+20t}{240}=1\\\\\frac{32t}{240}=1\\\\32t=240*1\\\\t=\frac{240}{32}=7.5[/tex]

Hence, we have that it will take 7.5 hours to paint the room together.

Have a nice day!


Related Questions

which of the following isnot a valid FICO credit store​

Answers

Answer:

Where are the followings

Step-by-step explanation:

A valid FICO credit score ranges from 300 to 850. A score outside this range is not valid. Key components of a FICO score include credit mix and the impact of new credit, both accounting for 10% of the score respectively.

When it comes to determining what is not a valid FICO credit score, it's important to understand that FICO scores range from 300 to 850. Any score that is not within this range would be considered invalid. Components that make up a FICO score include payment history, amounts owed, length of credit history, new credit, and credit mix. Credit mix refers to the variety of credit types you have, such as credit cards, retail accounts, installment loans, finance company accounts, and mortgage loans, and makes up 10% of your FICO score. Regarding new credit, opening a new account can temporarily lower your score because it reduces the average age of your accounts, which also accounts for 10% of your FICO score.

Two common myths are that opening a new retail credit card is always good for your credit score and that it hurts your score to comparison shop for loans. In reality, opening a retail credit card can lower your score initially, though responsibly managing your new credit can eventually have a positive effect. When it comes to loan comparison shopping, FICO provides a grace period for hard inquiries that are related, bundling them into a single inquiry if they occur within a 14 to 45-day span, depending on the type of credit. This is designed to not penalize consumers who are responsibly shopping for the best rates.

56 students signed up for the school play. About 34% of these students were boys. At the auditions only 31 girls attended. What percent of girls who signed up for the play attended the auditions?
EXPLAIN HOW TO SOLVE

Answers

56 students represents 100 % and

X boys represent 34%,

so x= 56•34/100= 19.04 so approximately 19 boys

56-19= 37 girls signed up.

Now 37 girls represent 100% and 31 girls represent x % ,

So x= 31•100/37= 83.78% about 84% of the girls attended

To find the percentage of girls who attended the auditions, calculate the number of boys and girls who signed up, and then determine the percentage of girls who attended. About 83.78% of the girls who signed up for the school play attended the auditions.

The question: 56 students signed up for the school play. About 34% were boys. At the auditions, only 31 girls attended.

Calculate the number of boys who signed up: 56 x 0.34 = 19 boys.

Find the number of girls who signed up: 56 - 19 = 37 girls.

Calculate the percentage of girls who attended auditions: (31 girls / 37 girls) x 100% = 83.78%.

What is the answer to
4x-x

Answers

4x - x

If there is a single variable with no number in front you can assume that there is a 1. How I think of it is that all singular variables have an invisible one in front

so...

4x - 1x

Since these are like terms you may subtract them like normal numbers. The only difference is that you'll have to add an x at the end of your answer

4 - 1

3

(REMEMBER to add the x back to the three)

so...

4x - x = 3x

Hope this helped!

~Just a girl in love with Shawn Mendes

greatest common factor of 117 and 19,110?​

Answers

Answer:

1

Step-by-step explanation:

These numbers have no common factors. The only comon factor they have is one. Therefore, the GCF of 117, 19, and 110 is one.

What is the equation of the line that is perpendicular to y= 1/5 x + 4 and that passes through (5, -4 )

Answers

Answer:

y = -5x + 21

Step-by-step explanation:

The perpendicular slope is opposite of the inverse.  The inverse of 1/5 is 5/1, and the opposite of that is -5/1.

So m = -5.

Then use point-slope form:

y + 4 = -5 (x - 5)

If you wish, convert to slope-intercept form:

y + 4 = -5x + 25

y = -5x + 21

There are 52 people in a conference room.
The ratio of females to males in the room is 15 to 11.
How many females need to leave the room so that the ratio of females to males
in the room is 1 to 1?

Answers

8 Females have to leave the room which then it would be 22 males and 22 females which is a 1-1 ratio

A ratio shows us the number of times a number contains another number. The number of females who should leave the conference room is 8.

What is a Ratio?

A ratio shows us the number of times a number contains another number.

The ratio of females to males in the room is 15 to 11, therefore, the numbers of female to male ratio can be represented by 15x to 11x.

The sum of the total number of people in the room is 52, and can be represented as,

15x + 11x = 52

26x = 52

x = 2

Thus, the number of females in the conference room is 30(15x=15×2), while the number of males in the conference room is 22(11x=11×2).

Now, for the ratio to be 1:1, the number of males should be the same and the number of females should be equal to the number of males. Therefore, the number of females who should leave the conference room is,

Number of females who should leave conference room = Number of females before - Number of females after

Number of females who should leave conference room = 30 - 22 = 8

Hence, the number of females who should leave the conference room is 8.

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simplify 10.26 - 1.9 x 3.7 + 0.1 2

Answers

Final answer:

The simplification of the expression 10.26 - 1.9 x 3.7 + 0.1, using proper order of operations, gives the result of 3.33.

Explanation:

The student's question asks to simplify a mathematical expression. To accomplish this, we use the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

The given equation to simplify is 10.26 - 1.9 x 3.7 + 0.1. First, perform the multiplication: 1.9 x 3.7 = 7.03. Substitute this value into the expression to get 10.26 - 7.03 + 0.1. Then, perform subtraction and addition from left to right. This will result in 3.23 + 0.1 = 3.33. Therefore, the simplified result of the expression 10.26 - 1.9 x 3.7 + 0.1 is 3.33.

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Find the exact circumference of a circle with the given radius 5” c=?

Answers

Answer: 10pi

Step-by-step explanation:

C=2*pi*r

C=2*pi*5

C=10*pi (exact)

This is exact if u want numbers, you’ll have to round-off and you can just put 10xpi into a calculator If u want to see.

Answer:

C = 31.42

Step-by-step explanation:

radius = 5

C = 2 π r

C = 2 · π · 5

C = 31.41593

then you round so it equals 31.42 instead

I need help please???

Answers

False.

For a point to lie on the X-axis, the second number needs to be 0, not the first one.

When the first number is 0, the point is on the Y-Axis.

The graph below represents which system of inequalities?


graph of two infinite lines that intersect at a point. One line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line. The other line is solid, and goes through the points 1, 1, 2, negative 1 and is shaded in below the line.

Answers

Answer:

The system of inequalities is

[tex]y\leq x+3[/tex] and [tex]y\leq -2x+3[/tex]

The solution is the shaded green area

Step-by-step explanation:

step 1

Find the equation of the inequality A

The line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line

Find the slope

(-3,0),(-4,-1)

m=(-1-0)/(-4+3)=1

The equation of the line is y=mx+b

we have

m=1

b=3 ----> the y-intercept (see the graph)

substitute

y=x+3 -----> equation of the solid line A

The equation of the inequality is

[tex]y\leq x+3[/tex] -----> inequality A

step 2

Find the equation of the inequality B

The line is solid and goes through the points 1, 1, 2, negative 1 and is shaded in below the line

Find the slope

(1,1),(2,-1)

m=(-1-1)/(2-1)=-2

The equation of the line is y=mx+b

we have

m=-2

b=3 ----> the y-intercept (see the graph)

substitute

y=-2x+3 -----> equation of the solid line B

The equation of the inequality is

[tex]y\leq -2x+3[/tex] -----> inequality B

therefore

The system of inequalities is

[tex]y\leq x+3[/tex] -----> inequality A

[tex]y\leq -2x+3[/tex] -----> inequality B

The solution is the shaded green area

Final answer:

The graph represents the system of inequalities y >= -x - 3 and y >= -3x + 4. This is concluded by observing the slopes, intercept points, and shading regions.

Explanation:

The system of inequalities represented by the graph you provided can be deduced by the slopes, intercept points, and the regions of shading. Given the information, the solid line that goes through the points (-3, 0) and (-4, -1) can be represented by the equation y >= -x -3. Since the line is solid and the area below the line is shaded, the inequality symbol includes an equal sign which means the line itself is part of the solution.

For the second solid line that goes through the points (1, 1) and (2, -1), it can be represented by the equation y >= -3x + 4. Similarly, because the line is solid and the region below this line is shaded, the inequality symbol includes an equal sign.

Therefore, the system of inequalities that the graph represents is y >= -x - 3 and y >= -3x + 4.

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25 points
Please explain your answer, thank you!

Which expression is not a polynomial?
A. -5x+6y
B. -3/x
C. 2p^3q^2-pq^3
D. 7-z

Answers

Answer:  The correct answer is:  [B]:

_________________________________________

                " [tex]\frac{-3}{ x}[/tex] " .

_________________________________________

Step-by-step explanation:

_________________________________________

Note:  A number; "divided by a variable" ; is Not a "polynomial" .

Answer choice:  [B]:  " [tex]\frac{-3}{ x}[/tex] " ;  

         is a "number;  divided by a "variable" ;  and as such, is Not a "polynomial".

_________________________________________

2sqrt3 +2i to polar representation

Answers

Recall that

[tex]\cos\dfrac\pi6=\dfrac{\sqrt3}2[/tex]

[tex]\sin\dfrac\pi6=\dfrac12[/tex]

Then

[tex]2\sqrt3+2i=4\left(\dfrac{\sqrt3}2+\dfrac12i\right)=4\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)=4e^{i\pi/6}[/tex]

If f(×)= x^1/2-× and g(×) = 2x^3-×^1/2-×, find f(×)-g(×). Pleade ASAP

Answers

Answer:  

-2x^3 + 2x^(1/2)

Step-by-step explanation:

step one- plug in the values of each in f(x) - g(x)

x^(1/2)-x - (2x^3-×^(1/2)-x) ; g(x) is in parentheses bc we need to distribute the negative

x^(1/2)-x-2x^3 + x^(1/2) + x ; combine like terms (letters with the same exponents) ; the x's cancel, and the x^(1/2) + x^(1/2) combine to form 2x^(1/2); the -2x^3 remains

you should get

-2x^3 + 2x^(1/2)

Answer:

[tex]f(x) - g(x) = 2(\sqrt{x}-x^3)[/tex]

Step-by-step explanation:

We have the functions

[tex]f(x)= x^{\frac{1}{2}}-x[/tex]  and   [tex]g(x) = 2x^3-x^\frac{1}{2}-x[/tex]

The operation [tex]f (x) -g (x)[/tex] is the subtraction of the function f(x) minus the function g(x). Thus

[tex]f(x) - g(x) = x^{\frac{1}{2}}-x -(2x^3-x^\frac{1}{2}-x)[/tex]

Simplifying the expression we have left that:

[tex]f(x) - g(x) = x^{\frac{1}{2}}-x -2x^3+x^\frac{1}{2}+x[/tex]

[tex]f(x) - g(x) = 2x^{\frac{1}{2}}-2x^3[/tex]

[tex]f(x) - g(x) = 2(\sqrt{x}-x^3)[/tex]  Because [tex]x^{\frac{a}{n}} = \sqrt[n]{x^a}[/tex]

Suppose that ym has length 12 in. and its distance from point L is 5 in. Find the radius of ⊙L to the nearest tenth.

Answers

Answer:

The radius of circle L is [tex]7.8\ in[/tex]

Step-by-step explanation:

Remember that a line that passes through the center divide the circle into two equal parts

YV=VM=6 in

VL is perpendicular to YM

so

The triangle VLM is a right triangle

The radius is equal to LM ----> hypotenuse of the triangle VLM

Applying the Pythagoras Theorem

[tex]LM^{2}=VM^{2}+VL^{2}[/tex]

substitute the given values

[tex]LM^{2}=6^{2}+5^{2}[/tex]

[tex]LM^{2}=61[/tex]

[tex]LM=7.8\ in[/tex]

Sara and Triston want to collect data to find out what games should be played at the elementary school’s field day. Describe a group that they could survey to collect quality data.

Answers

i would think teachers

what is the positive difference between-8 and -14​

Answers

Answer:

22

Step-by-step explanation:

8 - (-14)

keep, change, change

8 + 14 = 22

Answer:

6

Step-by-step explanation:

-14 is smaller than -8.  We subtract -14 from -8, obtaining +14 - 8, or +6.

The positive difference between -8 and -14 is 6.

Determine the best unit of measurement to represent each description

Answers

Answer:

see the attached figure

Step-by-step explanation:

The best unit of measurement that represent each description in the attached figure

Answer:

Step-by-step explanation:

Miles

1. Distance traveled on a bike ride

2. Length of the border between Texas and Oklahoma

3. Distance around a lake.

Feet

1. Distance traveled by a base ball.

2. Height of a mature tree

Inches

1. Diagonal of a computer screen

2. Diameter of a basket ball

3. Width of a sheet of a paper.

PLEASE ANSWER RIGHT AWAY!!!

Answers

Answer:

$150

Step-by-step explanation:

Given

The graph with speed over speed limit on x-axis and amount of ticket on y-axis. In order to find the answer a person must know how to translate or read graphs.

As it is given in the question that the person is charged based on the extra miles over the speed limit. If the speed limit was 50 mph and the driver was driving at 61 mph, then the number of miles over the speed limit

=> 61-50

=> 11 miles

So, we have to look for 11 on x-axis and then we look for the y-axis's intercept that intersects with 11.

So, in the given graph, the value 11 of x-axis intercepts with the $150 on y-axis.

So the fine will be $150 ..

1) Select the equations that are equivalent to the equation y-4=5(x+2). Select all that apply.
A) y=2x+5
B) y=5x+14
C) 5x-y=-14
D) 2x+y=14
2) Which of the following represents an equation of a line with a slope of 5 and a y-intercept of 1?
A) y=5x+1
B) y=5x-5
C) x-5y=-5
D) y= -1/5x+1

Answers

Answer:

see explanation

Step-by-step explanation:

1

Given

y - 4 = 5(x + 2) ← distribute parenthesis

y - 4 = 5x + 10 ( add 4 to both sides )

y = 5x + 14 → B

Subtract y from both sides

0 = 5x - y + 14 ( subtract 14 from both sides )

- 14 = 5x - y → C

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

2

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 5 and c = 1, thus

y = 5x + 1 → A

One serving of pancakes takes one and two thirds cups of milk how many cups of milk will 36 servings of pancakes require?

Answers

Final answer:

To determine the amount of milk needed for 36 servings of pancakes, multiply one and two-thirds cups of milk by the number of servings. This results in a total of 60 cups of milk required.

Explanation:

To find out how many cups of milk are needed for 36 servings of pancakes, when one serving requires one and two-thirds cups of milk, we use multiplication. We can make a conversion factor using our original recipe, likening it to a mathematical relationship or a stoichiometric relationship in chemistry. Here is the step-by-step calculation:

First, we convert one and two-thirds cups to an improper fraction: 1 2/3 = 5/3 cups.Next, we multiply the amount needed for one serving by the total number of servings: (5/3 cups) × 36 servings = 180/3 cups.Finally, we simplify the fraction 180/3 cups to get the total number of cups required: 180/3 = 60 cups.

So, for 36 servings of pancakes, you would need 60 cups of milk.

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I need to know the correct trigonometric ratios that could be sued to determine the length of LN

Answers

Answer:

A, E

Step-by-step explanation:

Remember SOH-CAH-TOA:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Therefore, we can say:

sin 20° = LN / 8

cos 70° = LN / 8

tan 70° = MN / LN

Only the first and last options are correct.

(X-1)^2 + (y-3)^2=10 convert equation from rectangular form to polar form

Answers

Answer:

[tex]r= 2(cos(\theta) + 3sin(\theta))[/tex]

Step-by-step explanation:

To convert an equation of rectangular shape to polar form use the following equivalences

[tex]x=rcos(\theta)[/tex]

[tex]y=rsin(\theta)[/tex]

[tex]x^2 + y^2=r^2[/tex]

In this case we have the following equation.

[tex](x-1)^2 + (y-3)^2=10[/tex]

First we expanded the expression

[tex](x-1)^2 + (y-3)^2=10\\\\(x^2 -2x +1) +(y^2 -6y + 9) = 10\\\\\\x^2 +y^2 -2x -6y = 10-9-1\\\\x^2 +y^2 -2x -6y = 0[/tex]

Now we know that [tex]x^2 + y^2=r^2[/tex], [tex]x=rcos(\theta)[/tex] and [tex]y=rsin(\theta)[/tex]

So

[tex]r^2 -2rcos(\theta) -6rsin(\theta) = 0\\\\r^2 - 2r(cos(\theta) + 3sin(\theta))=0\\\\r^2 = 2r(cos(\theta) + 3sin(\theta))\\\\r= 2(cos(\theta) + 3sin(\theta))[/tex]

Convert the expression to simplified radical form.
32^(1/2)x^(5/2)y^(3/2)

Answers

Answer:

[tex] {32}^{ \frac{1}{2} } {x}^{ \frac{5}{2} } {y}^{ \frac{3}{2} } = \sqrt{32 {x}^{5} {y}^{3} } = (4 \sqrt{2} )( {x}^{2} \sqrt{x} )(y \sqrt{y} ) = 4 {x}^{2} y \sqrt{2xy} [/tex]

What degree of rotation will cause the triangle below to map onto itself ?

Answers

Answer:

The triangle is rotated 360° ⇒ answer D

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or  

anti-clockwise around the origin

- If point (x , y) rotated about the origin by angle 360°

∴ Its image is (x , y)  the point itself

* There is no difference between rotating 360° clockwise or  

anti-clockwise around the origin

* Now lets solve the problem

∵ The vertices of the triangle ABC are:

  A is (-6 , 3) , B is (-5 , 7) , C is (-4 , 3)

∵ The triangle map onto itself

∴ A = A'

∴ B = B'

∴ C = C'

∴ The triangle is rotated 360° about the origin

D= 360

When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.

PLEASE HELP!!!! 25 POINTS!!!!! I NEED THIS ASAP!!!!!!

Answers

Answer:

[tex]\large\boxed{\left\{\begin{array}{ccc}y-17z=-15&(a)\\-2y+17z=13&(b)\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x-3y+5z=5&(1)\\4x-5y-7z=-5&(2)\\-6x+7y+2z=-2&(3)\end{array}\right\\\\\\\text{From (1) and (2)}\\\left\{\begin{array}{ccc}2x-3y+5z=5&(1)&\text{multiply both sides by (-2)}\\4x-5y-7z=-5&(2)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-4x+6y-10z=-10\\4x-5y-7z=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad y-17z=-15\qquad(a)[/tex]

[tex]\text{From (1) and (3)}\\\left\{\begin{array}{ccc}2x-3y+5z=5&(1)&\text{multiply both sides by 3}\\-6x+7y+2z=-2&(3)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}6x-9y+15z=15\\-6x+7y+2z=-2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-2y+17z=13\qquad(b)[/tex]

Alison's car travels at 65 miles per hour. How far does she travel in 4.5 hours?

Answers

Answer:

292.5 miles

Step-by-step explanation:

Ok so what you want to do is multiply 4.5 and 65 together.

She travels at 65 miles per hour and she travels for 4.5 hours

Identify the slope and y-intercept of the following linear equation: y=-5/3 x-2/3 The slope is , and the y-intercept is . The slope is -, and the y-intercept is . The slope is , and the y-intercept is -. The slope is -, and the y-intercept is -.

Answers

Answer:

Slope: 5/3

Y - intercept: -2/3

Step-by-step explanation:

The slope is the coefficient of the x term, so that is 5/3. The y - intercept is the number being added to the x term, which is -2/3.

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut point with the "y" axis

We have the following equation:

[tex]y = - \frac {5} {3} x- \frac {2} {3}[/tex]

So we have to:

[tex]m = - \frac {5} {3}\\b = - \frac {2} {3}[/tex]

Answer:

The slope is[tex]- \frac {5} {3}[/tex]and the intersection with "y" is [tex]- \frac {2} {3}[/tex]

3x-8y=-16 -5x-10y=7 give y intercept

Answers

Answer:

3x-8y=-16

The y intercept is;

(0, 2)

-5x-10y=7

The y intercept is;

(0, -0.7)

Step-by-step explanation:

The y-intercept refers to the point where the graph of an equation intersects or crosses the y-axis. At this point, the corresponding value of x is 0.

From the first equation given;

3x-8y=-16

Substitute x with 0 in the equation and solve for y;

3(0) -8y = -16

-8y = -16

y = 2

The y intercept is thus;

(0, 2)

From the second equation;

-5x-10y=7

Substitute x with 0 in the equation and solve for y;

-5(0) - 10y = 7

-10y = 7

y = -0.7

The y intercept is thus;

(0, -0.7)

Josh made his school basketball team this year. He played 10 minutes in his first game, but he played twice that amount in each of the other games. Let y represent the total number of minutes Josh played in x games.

Which type of sequence does the situation represent?

A.
The situation represents an arithmetic sequence because the successive values have a common difference of 10.
B.
The situation represents an arithmetic sequence because the successive values have a common difference of 20.
C.
The situation represents a geometric sequence because the successive values have a common ratio of 2.
D.
The situation represents a geometric sequence because the successive values have a common ratio of 5.

Answers

Answer:

  B.  The situation represents an arithmetic sequence because the successive values have a common difference of 20.

Step-by-step explanation:

(x, y) values appear to be ...

  (1, 10) . . . . 10 minutes played in the first game

  (2, 30) . . . 20 minutes played in the second game, adding 20 to the total

  (3, 50) . . . 20 minutes played in the third game, adding 20 to the total

From here, we can see that each additional game adds 20 minutes to the total (y), so the sequence is ...

  an arithmetic sequence because the successive values have a common difference of 20

Two poles are located 3.2m apart. A wire links the tops of the two poles. Find the length of the wire if the poles are 3.8m and 6m in height. (one decimal place)

Answers

considering the diagram,the top part is a triangle with the base of 3.2m and height of 2.2m. since the triangle 8s is a right angle triangle. we use Pythagoras theorem to solve for the hypotenus

Final answer:

The length of the wire connecting the tops of two poles of heights 3.8m and 6m, and spaced 3.2m apart is approximately 3.9 meters when calculated using the Pythagorean theorem.

Explanation:

To calculate the length of the wire connecting the tops of two poles of different heights, we can use the Pythagorean theorem.

This theorem states that in a right angle triangle, the square of the length of the hypotenuse (the wire) is equal to the sum of the squares of the lengths of the other two sides (the distances between the tops of the poles and the ground).

Let's denote:

Pole A as the shorter pole with a height of 3.8m

Pole B as the taller pole with a height of 6m

The distance between the two poles as 3.2m

The difference in height between the two poles is 6m - 3.8m, which is 2.2m. Thus, we have a right triangle where one leg is 3.2m (distance between poles) and the other leg is 2.2m (height difference between poles).

Applying Pythagorean theorem:

c² = a² + b²

c² = 3.2² + 2.2²

c² = 10.24 + 4.84

c² = 15.08

c = √15.08

c ≈ 3.9m

Therefore, the length of the wire is approximately 3.9 meters.

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