Mathematics College

A pool measuring 8 meters by 24 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 720 square meters, what is the width of the path? 8 + 2x 8 24 - 2x

The Width of the path is ____ meters

Answers

Answer 1

The real answer is 6

Step-by-step explanation:

Answer 2

the width of the path is 6 meters.

Let's assume the width of the path is represented by 'x' meters.

The overall dimensions of the combined pool and path would be:

Width = 8 + 2x

Length = 24 + 2x

To calculate the area of the combined pool and path, we multiply the width and length:

Area = (8 + 2x) * (24 + 2x)

Given that the area is 720 square meters, we can set up the equation:

(8 + 2x) * (24 + 2x) = 720

Expanding the equation:

192 + 16x + 48x + 4x² = 720

4x² + 64x + 192 = 720

Rearranging the equation:

4x² + 64x - 528 = 0

Now we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. After solving the equation, we find that x = 6.

Therefore, the width of the path is 6 meters.

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Related Questions

Evaluate...............

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Answer:

Step-by-step explanation:

11..............????

I need help pleasseee ....

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Answer:

-4.3

Step-by-step explanation:

thats the slope im 90 percent sure

tolong bantu jawab please, makasih sebelumnya!

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Answer:

2x² - 3x - 2

Explain:

Use the FOIL method: (a +b)(c +d) = ac + ad +bc +bd.

2x² + x - 4x - 2

Collect like terms.

2x² + (x - 4x) - 2

Simplify.

2x² - 3x - 2

Simplify: 2y + x + 3x - y

Answers

Answer:

y + 4x

Step-by-step explanation:

For this problem, we will simply combine like terms using the distributive property and the commutative property.

First, let's use the commutative property:

2y + x + 3x - y

= 2y - y + x + 3x

Second, let's use the distributive property:

2y - y + x + 3x

= y ( 2 - 1 ) + x ( 1 + 3 )

= y ( 1 ) + x ( 4 )

= y + 4x

Hence, the simplification of 2y + x + 3x - y is y + 4x.

Cheers.

When a number changes position, but the answers are still the same this is called?
associative property
B identity property
C commutative property of addition or multiplication
D

Answers

Answer:

Step-by-step explanation:

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Question 6
>
Consider the parabola given by the equation: f(x) = – 4x2 + 6x – 2
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two 2-Intercepts of the parabola and write them as a list, separated
by commas:
It is OK to round your value(s) to to two decimal places
> Next Question

Answers

Answer:

Step-by-step explanation:

trust me ON this one OK

find the average of 72,95,100,85,and 88

Answers

Answer:

Step-by-step explanation:

72 + 95 + 100 + 85 + 88=440

440/5=88

Look at the figure. How can you prove the triangles are congruent?

A. ∆ABD ≅ ∆CDB by the SAS Postulate.

B, It is not possible to determine if the triangles are congruent.

C. ∆ABD ≅ ∆CDB by the SSS Postulate.

Answers

Answer:

A. ∆ABD ≅ ∆CDB by the SAS Postulate.

Step-by-step explanation:

You know lines AB and DC are congruent because of the lines on each. Additionally, angles B and D are congruent for the alternative interior angles rule and they also are marked as congruent in the image. Finally, DB is congruent to DB because of the reflexive property. So you have two sides and the included angle, this makes the SAS postulate true.

Answer:

the answer is A

Step-by-step explanation:

Which graph is inverted

y = 1+x^2
y = 1 - x^2
y = x^2 -1
-y = 1 - x^2

Answers

Answer:

Please help me and my question, it would mean alot, I think that the graph inverted is D

Step-by-step explanation:

2051
20
SINO-V3 COSO - 2
2

Answers

Answer:WHAT DOES THAT EVEN MEAN!?!?

Step-by-step explanation:

!!!!!!!!

Marie and fe work in a flower shop 6 hours on weekend to add their daily allowance in school. They spends 2 1/3 hours for making bouquet, 1 1/2 hours for cutting leaves, and the rest for flower arrangements. How many hours on weekend they spend in flower arrangements?

Answers

Answer:

2 1/6 hours

Step-by-step explanation:

2 1/3 + 1 1/2 + x = 6

convert all mixed numbers to improper fractions

7/3 + 3/2 + x = 6/1

change all numbers to have a common denominator

14/6 + 9/6 + x = 36/6

combine like terms

23/6 + x = 36/6

subtract 23/6 from both sides

x = 13/6

convert improper fraction to mixed number

2 1/6

What two integers does the square root of 38 come between

Answers

Answer:

38 is not a perfect square.

square root of 38 is 6.164

it is between 6 and 7

Can anyone answer these questions?

Answers

Answer:

7.) r = 6. 8.) v = 3.3

Step-by-step explanation:

........

cube root both sides

area exercises 1 5\8 hours per day if he exersises five days a week how many total hours does he exersise in a week

Answers

He exercised 8 1/8 hours a week

Assuming equal rates, 120 miles in 6 hours implies 150 miles in how many hours?

Answers

Answer:

9 hours

Step-by-step explanation:

Which number line represents he number 0.7?

Answers

I would say A!! Hope that this is correct have a great day!!

1. The value of 25 x (8.5) is:
a.
More than 250
b. Less than 250

Answers

25x(8.5)=212.5 therefore being b. Less than 250

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The value of 25×8.5 is less than 250. The correct option is B.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The value of 25×8.5 is needed to be calculated in order to know if the product is more than 250 or not. Therefore, the value of the 25×8.5 can be calculated as,

25×8.5

= 25 × (85/10)

= 2125/10

= 212.5

Since the value of the product of 25 and 8.5 is 212.5 which is less than 250. It can be calculated that the number is smaller than 250.

Hence, the value of 25×8.5 is less than 250.

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|4x|+6=22?????????????????????

Answers

Answer: x=4, x=-4

Step-by-step explanation: because it is absolute value, negative or positive does not matter.

Which is greater, 25% of $200 or 80% of 100?

Answers

Answer:

80% of 100

Step-by-step explanation:

25% of something is basically dividing it by 4, meaning 25% of 200 is 50,

While 80% of 100 is 80

A good way to memorize this is if youre taking anything as a percent of 100, get rid of a 0 on the 100, and put a decimal place in the number.

(e.g. 90% of 10 is 9. whereas 90% of 100 is 90)

Just remember which you're dealing with!

Hope this helps!

Answer:

80% of 100 is greater

Step-by-step explanation:

25% of 200 is

0.25*200 = 50

80% of 100 is

0.8*100 =80

As 80 > 50,

the second number is greater

. Which of the following could be the graph of the equation y=-2x?
A.
B.
C.

Answers

Answer:

Step-by-step explanation:

The linear equation y = -2x is passing through the origin. Then the correct option is B.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y = -2x

The y-intercept in the above equation is zero. Then the linear equation is passing through the origin.

The linear equation y = -2x is passing through the origin. Then the correct option is B.

More about the linear equation link is given below.

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Which of the following is the point and slope of the equation y - 2 = 3/2(x - 7)?

(7, 2), 3/2

(7, 2), 3

(-7, -2), 3/2

(7, -2), 3

Answers

Point-slope form of the linear functions is like this :

[tex]y - y(point) = (slope) \times ( \: x - x(point) \: ) \\ [/tex]

[tex]y - 2 = \frac{3}{2}(x - 7) \\ [/tex]

So :

[tex]slope = \frac{3}{2} \\ [/tex]

And

Point = ( 7 , 2 )

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Which line is perpendicular to a line that has a slope of -1/3?

Answers

Answer:

Any line with slope -1/(-1/3)=3.

Step-by-step explanation:

If a line l has slope m, any line perpendicular to l will have slope equal to -1/m.

Answer: line EF

Step-by-step explanation:

Did it in edg

write an equation to solve for x your only writing the equation. 7x+9 5×+3 there's three answers the bottom one is if none of the other two are right I thought the answer was number two but the person that answered it gave me a different number so somebody can help me I would mark this brainest did you see the third option is blank I came up with the answer number two is that correct or is it the 7x + 9 + 5x + 3 equals 180 brainest awared

Answers

Answer:

7x + 9 + 5x + 3 = 180

Step-by-step explanation:

its a supplementary angles:

so the equation is add the two equation equals to 180

7x + 9 + 5x + 3 = 180

Please help im stuck. Integrated 2 Math.

Answers

Need more information~

What is the quotient of 3÷1/6 multiply 3 by

Answers

Answer:

Step-by-step explanation:

Change 3 into a fraction.

Which gives you 3/1

multiply 3/1 by the inverse of 1/6

3/1x1/6

Then you get 1 :)

A new savings account is opened with $400 and gains 3% every year. What is the
exponential function?

Answers

It’s the first one F(x)=400(1+3)

Determine whether the following statement is true or false. The y-coordinate of the vertex of f(x) = - X + 4x + 3 is f(2). Select the correct choice below and fill in the answer box to complete your choice. A. The statement is true because the x-intercept of the parabola is B. The statement is false because the y-coordinate of the vertex is f(()). C. The statement is true because the x-coordinate of the vertex is 4 D. The statement is false because the y-coordinate of the vertex is

Answers

Answer:

Listen don't use this site

Step-by-step explanation:

They are using people to make money

Justify each step of this inequality by stating the property that was used to get to each step. Given: -5(r+3)<12-10r+3r Property used: Step 1: -5(r+3)<12-7r Step 1: Step 2: -5r-15<12-7r Step 2: Step 3: 2r-15<12 Step 3: Step 4: 2r<27 Step 4: Step 5: r<13.5 Step 5:

Answers

Answer:

See below.

Step-by-step explanation:

We have:

Given:

[tex]-5(r+3)<12-10r+3r[/tex]

Step 1: Combining Like Terms (on the right):

[tex]-5(r+3)<12-7r[/tex]

Step 2: Distributive Property (distribute the -5 on the left):

[tex]-5r-15<12-7r[/tex]

Step 3: Addition Property of Equality (add 7r to both sides):

[tex]2r-15<12[/tex]

Step 4: Addition Property of Equality (add 15 to both sides):

[tex]2r<27[/tex]

Step 5: Division Property of Equality (divide both sides by 2):

[tex]r<13.5[/tex]

And we're done!

Answer:

Step 1: Combining Like Terms

Step 2: Distributive Property

Step 3: Addition Property of Equality

Step 4: Addition Property of Equality

Step 5: Division Property of Equality

Point N Is on line segment MO. Given NO= 14 and MO = 18 determine the length MN

Answers

Answer:

Step-by-step explanation:

12.) Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer. Pleaseee helppp

Answers

Answer:

Step-by-step explanation:

Given Parallel lines Converse

a. ∠13 ≅ ∠17 a║c Corresponding angles

b. ∠4 ≅ ∠9 d║e Exterior alternate angles

c. m∠20 + m∠21 = 180° a║b Consecutive interior angles

d. ∠8 ≅ ∠19 Vertical angles

e. ∠10 ≅ ∠23 b║c Interior alternate angles

f. m∠14 + m∠17 = 180° a║c Consecutive interior angles

From the given diagram and information, it can be concluded that lines a, b, and c are parallel, and lines d and e are parallel.

The given lines in the diagram are a, b, c, d, and e.

a. It is given that the measure of angle 13 is equal to that of angle 17.

Now, these two angles are made by lines a, c, and d. Now, the angles are corresponding and equal, and hence, lines a and c will be parallel.

b. It is given that the measure of angle 4 is equal to that of angle 9.

These two angles are made by lines d, e, and b. Now, the angles are alternate exterior and equal, and hence, lines d and e will be parallel.

c. It is given that the sum of the measure of angles 20 and 21 is equal to 180 degrees.

These two angles are made by lines a, b, and e. Now, the angles are supplementary and their sum is 180 degrees, and hence, lines a and b will be parallel.

d. It is given that the measure of angle 8 is equal to that of angle 19.

These two angles are vertically opposite angles between lines a and e.

e. It is given that the measure of angle 10 is equal to that of angle 23.

These two angles are made by lines b, c, and e. Now, the angles are alternate interior and equal, and hence, lines b and c will be parallel.

f. It is given that the sum of the measure of angles 14 and 17 is equal to 180 degrees.

These two angles are made by lines a, c, and d. Now, the angles are supplementary and their sum is 180 degrees, and hence, lines a and c will be parallel.

Therefore, it can be concluded that lines a, b, and c are parallel, and the lines d and e are parallel.

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Other Questions

A pool measuring 8 meters by 24 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 720 square meters, what is the width of the path? 8 + 2x 8 24 - 2xThe Width of the path is ____ meters​

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A pool measuring 8 meters by 24 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 720 square meters, what is the width of the path? 8 + 2x 8 24 - 2x

The Width of the path is ____ meters