A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a 2 feet wide and has an area of 448 square feet including the pool.Find the dimensions of the pool

Answers

Answer 1

Answer:

The width and the length of the pool are 12 ft and 24 ft respectively.

Step-by-step explanation:

The length (L) of the rectangular swimming pool is twice its wide (W):

[tex] L_{1} = 2W_{1} [/tex]

Also, the area of the walkway of 2 feet wide is 448:

[tex] W_{2} = 2 ft [/tex]

[tex] A_{T} = W_{2}*L_{2} = 448 ft^{2} [/tex]

Where 1 is for the swimming pool (lower rectangle) and 2 is for the walkway more the pool (bigger rectangle).

The total area is related to the pool area and the walkway area as follows:

[tex] A_{T} = A_{1} + A_{w} [/tex]    (1)          

The area of the pool is given by:

[tex] A_{1} = L_{1}*W_{1} [/tex]        

[tex] A_{1} = (2W_{1})*W_{1} = 2W_{1}^{2} [/tex]  (2)          

And the area of the walkway is:

[tex] A_{w} = 2(L_{2}*2 + W_{1}*2) = 4L_{2} + 4W_{1} [/tex]    (3)          

Where the length of the bigger rectangle is related to the lower rectangle as follows:                  

[tex] L_{2} = 4 + L_{1} = 4 + 2W_{1} [/tex]   (4)        

By entering equations (4), (3), and (2) into equation (1) we have:

[tex] A_{T} = A_{1} + A_{w} [/tex]

[tex]A_{T} = 2W_{1}^{2} + 4L_{2} + 4W_{1}[/tex]                

[tex]448 = 2W_{1}^{2} + 4(4 + 2W_{1}) + 4W_{1}[/tex]            

[tex] 224 = W_{1}^{2} + 8 + 4W_{1} + 2W_{1} [/tex]

[tex] 224 = W_{1}^{2} + 8 + 6W_{1} [/tex]

By solving the above quadratic equation we have:

W₁ = 12 ft

Hence, the width of the pool is 12 feet, and the length is:

[tex] L_{1} = 2W_{1} = 2*12 ft = 24 ft [/tex]

Therefore, the width and the length of the pool are 12 ft and 24 ft respectively.

I hope it helps you!                                                                                          


Related Questions

Salma is going to build a large wooden box. The box will be in the shape of a rectangular prism.... check photos,
40 points.

Answers

Answer:

162

Step-by-step explanation:

7x3 is 21 21x6 is 126

that’s the area

we don’t need it lol

7x3 is 21

7x6 is 42

3x 6 is 18

all of these together plus 2 make 162

how could you represent the following scenarios of the graph ? Silvia has $5.50 in her piggy bank and earns $2
per chore she does at her house.

Answers

Answer:

We know that Silvia has $5.50 in her piggy bank, and she earns $2 per chore she does at her house.

So if she does x chores at her house, she will have:

y = f(x) = $2*x + $5.50

where y = her savings.

This is a linear relationship, to graph this, we need to evaluate the function in two different values of x so we can get two ordered pairs.

Then we graph the ordered pairs in the coordinate axis, and then we draw a line that passes through both points.

We can use the points given by x = 0.

y = f(0) = $2*0 + $5.50 = $5.50

Then we have the point (0, $5.50)

and if we use x = 1 we get:

y = f(1) = $2*1 + $5.50 = $7.50

Then we have the point (1, $7.50)

Now we just need to graph the points (0, $5.50) and (1, $7.50), and draw a line that passes through them.

The graph is shown below.

At a recent breakfast, four friends paid for their own drinks and shared the cost of a bag of donuts. Joe's drink was $1.75. He paid a total of $3.20 for breakfast. How much did the bag of donuts cost?

Answers

Answer:

$5.80

Step-by-step explanation:

To answer, we must first subtract the toal cost Joe paid by the amount he paid for his drink, because ha paid for his drink separately. so:

3.20 - 1.75 = 1.45

And because there were a total of 4 friends, we mulitply the answer by 4:

1.45 * 4 = 5.8

So, the bag of donuts costed $5.80

Hope this helps :)

Anyone can help ? I have no clue what the answer maybe

Answers

Since both the triangles are similar,

(y-2)/(y+4) = 4/8

8(y-2) = 4(y+4)

8y - 16 = 4y + 16

8y - 4y = 16 + 16

4y = 32

y = 32/4

y = 8


The perimeter of triangle PQR:
4 + 6 + (8-2)

= 10 + 6

= 16 ft.

help I will give brainiest it will mean alot. find the scale factor​

Answers

The scale factor is 4 . I assume both pictures are the same

Answer:

Step-by-step explanation:

16:1

Write an inequality to represent a number is at most two".​

Answers

Answer:

Step-by-step explanation:

X<= 2

Which is x is less than or equal to 2.

Answer:

[tex]n\leq 2[/tex]

Step-by-step explanation:

find the distance round to the nearest tenth (-8, -6) (-3,-2)​

Answers

Answer:

[tex]\displaystyle d \approx 6.4[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Step-by-step explanation:

Step 1: Define

Point (-8, -6)

Point (-3, -2)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formula]:                                                   [tex]\displaystyle d = \sqrt{(-3+8)^2+(-2+6)^2}[/tex][√Radical] (Parenthesis) Add:                                                                        [tex]\displaystyle d = \sqrt{(5)^2+(4)^2}[/tex][√Radical] Evaluate exponents:                                                                    [tex]\displaystyle d = \sqrt{25+16}[/tex][√Radical] Add:                                                                                              [tex]\displaystyle d = \sqrt{41}[/tex][√Radical] Evaluate:                                                                                        [tex]\displaystyle d = 6.40312[/tex]Round:                                                                                                            [tex]\displaystyle d \approx 6.4[/tex]

Answer:

6.4

Step-by-step explanation:

d=√((−3−(−8))^2+(−2−(−6))^2)

d=√((5)^2+(4)^2)

d=√(25+16)

d=√(41)

d=6.403124

d=6.4

On a scale drawing 1cm represents 4 m.What length on the drawing would be used to represent 6.5 m

Answers

Answer:

1.6cm

Step-by-step explanation:

1cm=4m

      =6.5m

6.5÷4=1.625 round it off to the nearest tenths=1.6

A pyramid has a surface area of 539 ft.² what is the surface area of a similar pyramid that is smaller by a scale Factor of 1/7

Answers

Answer:

77 ft²

Step-by-step explanation:

Given that:

Surface Area of larger pyramid = 539 ft²

Scale factor of the smaller pyramid = 1/7

Tbe surface area of the smaller pyramid will be :

Scale factor * surface area

1/7 * 539ft²

= 539 ft² / 7

= 77 ft²

Help Plz!!
What system is Y = 2x + 1 and Y = -2x + 5?
A. Consistent system
B. Dependent system

Answers

Answer:

consistent

Step-by-step explanation:

Plz tell me the answer

Answers

2. A
3. A
4. B
5. D
Hoped that helped sorry if wrong

Hi, could someone help me with these two questions please? Thank you!

Answers

7 is option C
8 is option A

Which one is the correct answer please please.

Answers

Answer:

option 1

plz mark as brainiest

Step-by-step explanation:

Answer:

1/2 (option 1)

Step-by-step explanation:

the equation is in y=mx+b form (slope-intercept form)

y: y-axis

m: slope

x: variable

b: y-intercept

If triangle LMN is similar to triangle XYZ, then side LN corresponds to side

Answers

Answer:

The side it corresponds to is XZ

I will give you branilest! This is due and if I fail this I will have an F.
While in New York City, is it a better deal for a group of friends to take a taxi or the subway to get from the Empire State Building to the Metropolitan Museum of Art? Explain your reasoning.
Here is some information about New York City and its transportation system.
Information about NYC taxi cabs:

As of 2020, taxi cabs charge an initial fee of $2.50. Then there is an additional charge of $0.50 per 1/5 mile if the car is traveling about 12 miles per hour. In slower or stopped traffic, the additional fee is $0.50 per minute.

Information about the NYC subways:

As of 2020, a single subway ride is 2.75. However, multiple day passes can be purchased at a discount rate.

Information about the NYC tourist attractions:

The distance between the Empire State Building and the Metropolitan Museum of Art varies between 2.5 miles to 3.2 miles depending on your route.

Answers

Answer:

It would definitely be cheaper by Subway..

Step-by-step explanation:

Subway is 2.75 per person and taxi (given all variables) could be close to $20...however, the Subway takes much longer but is still the best bet. Especially if traffic is an issue

Line 6 subway•24m

US$3

Taxi•5m

US$16-US$20

Tell whether the equation has one, zero, or infinitely many solutions.9(x − 3) + 15 = 9x − 11.

Answers

Answer:

Zero solutions; there are no variables and thus there are no solutions

Step-by-step explanation:

We start out with the equation 9 (x - 3) + 15 = 9x - 11

Which simplifies to 9x - 27 + 15 = 9x - 11

The 9x terms cancel each other out, and we're left with 15 - 27 = -11

And we end up with -12 = -11, which is not true.

This tells us that the equation has zero solutions, because no matter what value we substitute for x, the equation will not be true.

Answer:

No solution

Step-by-step explanation:

9(x-3)+15= 9x-11

9x-27+15=9x-11

-15 on both sides

9x-27=9x-26

add 26 on both sides

9x -1=9x

add 1 on both sides

9x=9x+1

divide 9 on both sides

x=x+1/9

No solution

2/5 + 1/3 = ??​
It's fractions btw

Answers

Answer: 11/15

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

Answer:

sorry sweetie no

Step-by-step explanation:

What is 193 + y ≥ 201.

Answers

Answer:

y≥ 8

Step-by-step explanation:

[tex]\frac{2y+1}{3}[/tex]=[tex]\frac{y-2}{4}[/tex]

Answers

The answer is y=-2 ! Hope this helps

Which of the following functions represents an arithmetic sequence?
Of(n) 3"-4"
Of(n) 3-4
O fm) 374
O fin) - 34

Answers

Answer:

Step-by-step explanation:

The O is not part of the function.

f(n) = 3n-4 is an arithmetic sequence. The first term is -1 and the common difference is 3.

The width of a rectangular video game cartridge is 2 in. more than the length. The area is 16 in?.
Find the dimensions of the cartridge.
Equation:
Solution:

Answers

Equation: The cartridge has a 8 inch length and a 2 inch width.

Solution: l(w) 8(2)= 16 meaning 16 is the area. Meaning we found the length which is 8.

PLEASE HELP ASAP!!

When a ball is dropped, the function () = 4(0.6)x models the ball’s height in feet after each bounce, where x is the bounce number. To the nearest hundredth, what is the height after the third bounce?

Answers

Answer:

7.2 feet

Step-by-step explanation:

plug in x = 3 since we are looking for the height after the 3rd bounce

4(0.6)(3)

4(1.8)

7.2

The height after the third bounce is 0.86 feet.

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 4 x [tex]0.6^x[/tex] models the ball’s height in feet after each bounce.

Where x is the bounce number.

Now,

Substituting x = 3,

f(x) = 4 x [tex]0.6^x[/tex]

f(x) = 4 x [tex]0.6^3[/tex]

f(x) = 4 x 0.6 x 0.6 x 0.6

f(x) = 0.864

f(x) = 0.86

The height after the third bounce is 0.86 feet.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ6

is -11/8 greater or less than -1.37? HELP

Answers

Answer:  less than plz mark as brainliest

Step-by-step explanation:

Amanda bought tickets for a concert for $218. Jamie bought tickets to the same concert but paid 14% less than Amanda. What were the price of Jamie's tickets?

Answers

Answer:

Jamie's tickets = $187.48

Step-by-step explanation:

The amount for which Amanda bought tickets = $218

Jamie bought tickets to the same concert but paid 14% less than Amanda.

Jamie's tickets = [tex]218-14\%\ of\ 218[/tex]

We can solve it as follows :

[tex]218-14\%\ of\ 218=218-\dfrac{14}{100}\times 218\\\\=218-30.52\\\\=\$187.48[/tex]

So, the price of Jamie's tickets is $187.48.

26 sit ups in 2 minutes . find the unit rate and how many in 5 minutes

Answers

Answer:

Unit rate: 13 sit ups per minute

65 sit ups can be done in 5 minutes

Step-by-step explanation:

Find the unit rate by dividing 26 by 2

26/2

= 13

This means 13 sit ups can be done in 1 minute.

To find how many can be done in 5 minutes, multiply 13 by 5.

13(5)

= 65

So, the unit rate is 13 sit ups per minute, and 65 sit ups can be done in 5 minutes.

26/2 = 13 sit ups per minute

So 13 x 5= 65 sit ups

Please help, Thank you.​

Answers

Answer:

It's all about the ratios of corresponding sides.

I'll do #6 for you.

x=13.33

Step-by-step explanation:

4/x=(4+3)/(x+=10)  this is the ratio

4(x+10)=(3+4)(x)

4x+40=7x

4x-4x+40=7x-4x

3x=40

x=13.33

Freddy’s savings account went from $520 to $321 after he purchased a new bike. What was the percent decrease?

Answers

Step-by-step explanation:

The bike cost $199 to get $199 you do a number line then label 520 then at the end label 321 so then you do -20 then -100 then -50 then -20 then -9. so now you add them up 20+100+50+20+9 which equals =199

so bike cost $199

then 520%×199= 1034.8

or 520%×321=1669.2

so the  percentage is 1669.2 or 1034.8 probably 1669.2 but they bot count.

In 2011, a professional climber scaled the outside of the Burj Khalifa, making it all the way to 828 meters (the highest point on which a person can stand) in 6 hours.

Answers

Answer:

276 meters in the first 2 hours

Step-by-step explanation:

Given that,

Professional climbers climb 828 meters in 6 hours.

Let us assume we need to find how far did they climb in the first 2 hours.

6 hours = 828 m

⇒ 1 hour = 138 m

So, in 2 hours,

2 hours = 138 × 2 m

= 276 m

So, the climber climb 276 meters in the first 2 hours

*HELP ASAP*
The total length of two ships is 2341 feet. The difference in their lengths is 13 feet.
a. Find the length of each ship.
b. If a football field has a length of 100 yards, determine the length of the longer ship in terms of football fields.

Answers

3 feet in a yard

2341/3= 780.333

100 yards per field

780.333/100

Answer: 7 football fields and 80 yards
7 8/10 football fields (improper fraction)

Answer:

The smaller ship is 1,164 ft

The larger ship is 1,177 ft

The larger ship is 3.923 football fields

Step-by-step explanation:

A. Find the length of each ship

x + x + 13 = 2,341 ft

2x + 13 = 2,341 ft

2x = 2,328 ft

x = 2,328/2

x = 1,164 ft ( This is the length of the smaller ship)

1,164 + 13 = 1,177 ft (length of the larger ship)

B)If a football field has a length of 100 yards, determine the length of the longer ship in terms of football fields.

1,177/3ft= 392.3 yards

392.3 yards /100 yards = 3.923 football fields

What is the equation of a circle with a radius of 7 and centered at point (3, -4)? please help fast!

Answers

Answer:

Vertex (3, –4) r = 7

Step-by-step explanation:

[tex](x -3)^{2} + (y+4)^{2} = 49[/tex]

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