a square swimming pool has a cement sidewalk around it. The sidewalk is the same width all the way around. The outside perimeter of the sidewalk is 80 feet. What is the width of the sidewalk if the area of the pool is 225 square feet?​

the distance is 13 length units

Final answer:

Using the Pythagorean Theorem, we calculate the distance between the points (5, -2) and (-7, 3) to be 13 units.

Explanation:

To find the distance between two points on a coordinate plane, we use the Pythagorean Theorem. Given points (5, -2) and (-7, 3), we calculate the difference in the x-coordinates and y-coordinates separately and then square each result.

d² = (5 - (-7))² + (-2 - 3)²

= (5 + 7)² + (-5)²

= 12² + (-5)²

= 144 + 25

= 169

Now, taking the square root of both sides to calculate the distance:

d = √(169)

= 13

Therefore, the linear distance between the two points, often denoted as 'PQ', is 13 units.

Answer:

A

Step-by-step explanation:

A cube has 6 sides

Only one side of the cube has 2 on it

The probability of getting 2 would be 1/6

Only one side of the cube has 6 on it

The probability of getting 6 would be 1/6

For both events to happen together

1/6 x 1/6 = 1/36

To find the probability of rolling a 2 on the first die and a 6 on the second, multiply the independent probabilities of each event (1/6 for each die) to get 1/36, making the correct answer A) 1/36.

The question asks for the probability of rolling two number cubes and getting a 2 on the first number cube and a 6 on the second number cube. When rolling two dice, the outcome of one die does not affect the other, so the probabilities of each outcome are independent. Since a die has six faces, the probability of rolling any specific number on a single die is 1/6.

Therefore, the probability of rolling a 2 on the first die is 1/6 and the probability of rolling a 6 on the second die is also 1/6. To find the combined probability of both events happening together, you multiply the probabilities of each event by each other, which is (1/6) × (1/6) = 1/36. So, the correct answer is A) 1/36.

The answer is 67.6

You have to find the angle that has cos=8/21=0.381.

Answer:

67.6 degrees

Step-by-step explanation:

You need to use cosine to solve this.

so, cosine is adjacent leg over hypotenuse. which is 8/21. and it is 0.381.

and when you do cos^-1 (0.381), then it is 67.6.

Answer:

168 cubic feet.

Step-by-step explanation:

Equation for volume of cone 1/3*pi*r2*h (abbreviated as 1/3*b*h)

1/3*pi*4^2*10

=1/3*pi*16*10

=1/3*pi*160

=167.551608191

~=168 cubic feet.

~= is approximately, rounded.

The volume of the cube is 168 cubic feet.

radius 4 feet in height 10 feet

Since the volume of a cone is

[tex]= 1\div 3\times \pi\times r^2\times h\\\\= 1\div 3\times \pi\times 4^2\times 10\\\\=1\div 3\times pi\times 16\times 10\\\\=1\div 3\times \pi\times 160[/tex]

=167.55

= 168 cubic feet.

Learn more about the cone here: https://brainly.com/question/864985

Answer:

14 years old

Step-by-step explanation:

Assume Ray's sister's age is x.  

Ray's age is (x/2)+3, i.e (x+6)/2  

If Ray is 10yrs old,then  

(X+6)/2 = 10,  

x+6 = 20  

x = 14  

Therefore,Ray's siSter's /e is 14years

Answer:

1.

Step-by-step explanation:

( 1 - sin^2 O ) / cos^2 O

Now 1 - sin^2 O = cos^2 O

So the function becomes cos^2 O / cos^2 O

= 1.

ANSWER

A. 17.31in²

EXPLANATION

The area of a sector is calculated using the formula:

[tex]Area = \frac{central \: angle}{360 \degree} \times \pi {r}^{2} [/tex]

From the diagram, the central angle is:

145° and the radius is 3.7 in.

We substitute the known values to get;

[tex]Area = \frac{145}{360 \degree} \times 3.14 \times {3 .7}^{2} = 17.3{in}^{2} [/tex]

The approximate area is 17.3 in² to the nearest tenth.

ANSWER

[tex]a_{14} = 5[/tex]

EXPLANATION

The given matrix is a 4 by 4 matrix.

We want to find

[tex]a_{14}[/tex]

This is the entry in Row 1 Column 4.

We trace row 1 Column 4 and identify the entry in their intersection.

This entry is 5

[tex]a_{14} = 5[/tex]

Answer:

Power: (1/5)^3, 2^6

Expanded: 5x5, 6x6x6, 3x3x3/4, 2x2x2x2x2x2

How to say it: 5 raised to the 2nd power, 6 raised to the 3rd power, 3 raised to the 3rd power over 4

Value: 25, 216, 1/125, 9/4, 64

Step-by-step explanation:

Answer:  d) y = -2 sin 2x

Step-by-step explanation:

The general equation of a sin graph is: y = A sin (Bx - C) + D

Compare the given graph with y = sin x

There are 3 differences:

So, the equation of the given graph is: y = -2 sin 2x

Answer: 10 centimeters

Step-by-step explanation:

Answer: 80.0 cm^2

Step-by-step explanation:

We need to assume that the shape of the model is a cone or pyramid, something that tapers linearly to a point. Then its volume is given by the formula ...

V = 1/3Bh

where B is the area of the base, and h is the height. Filling in the given numbers, we have ...

586.7 = (1/3)B(22)

Dividing by the coefficient of B gives ...

B = 3(586.7)/22 = 80.0 . . . cm^2

The area of the base of the model is about 80.0 cm^2.

Answer:

Step-by-step explanation:

Whether you use b or x for the variable does not matter.

5 - 7 is a money problem

If you have 5 dollars and spend 7 where are you? You should think you have a debt of 2. So the answer from your point is - 2

5b - 7b = - 2b

5x - 7x = - 2x

Here is the process I did:

2(6x+4)-6+2x=3(4x+3)+1

Step 1: Distribute the 2 to the numbers in the parentheses (6x +4) on the left side of the equation

6x(2)+4(2)-6+2x=3(4x+3)+1

12x+8-6+2x=3(4x+3)+1

Step 2: On the left side of the equation combine like terms

x's go with x's (12x and 2x):

(12x + 2x)+8-6=3(4x+3)+1

14x+8-6=3(4x+3)+1

normal numbers go with normal numbers ( 8 and -6):

14x+(8+(-6))=3(4x+3)+1

14x+2=3(4x+3)+1

Step 3: Distribute the 3 to the numbers in the parentheses (4x+3) on the right side of the equation

14x+2=4x(3) +3(3) + 1

14x+2=12x + 9 + 1

Step 4: On the right side of the equation combine like terms

normal numbers go with normal numbers ( 9 and 1):

14x+2=12x + (9 + 1)

14x+2=12x + 10

Step 5: Bring 2 from the left side to the right by subtracting it to both sides

14x+(2-2)=12x + (10-2)

14x = 12x + 8

Step 6: Bring 12x from the right side to the left by subtracting it to both sides

(14x - 12x) = (12x - 12x) + 8

2x = 8

Step 7: Isolate x by dividing 2 to both sides

[tex]\frac{2x}{2}  =\frac{8}{2}[/tex]

x = 4

Hope this helped!

Given equation is  one degree equation in x

Also it has only one variable 'x' hence it requires only one equation to solve for x  and the equation is given.

hence solution for x can be given as

2(6x+4)-6+2x =3(4x+3)+1

12x + 8 - 6 +2x = 12x + 9 + 1

12x +2 +2x =12x + 10

14x +2 = 12x +10

14x-12x = 10-2

2x = 8

x = 8/2= 4

for more information please refer to the link given below

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Answer:1, -1,3,-7

Step-by-step explanation:

For this case we must subtract the given matrices and find the values of a, b, c and d:

Subtracting term from term we have:[tex]a = 5-4 = 1\\b = 2-1 = 1[/tex]

We have that different signs are subtracted and the sign of the major is placed.

[tex]c = 3-6 = -3\\d = 0-7 = -7[/tex]

Answer:

[tex]a = 1\\b = 1\\c = -3\\d = -7[/tex]

Answer:

a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths.

Step-by-step explanation:

Answer:a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truth

Step-by-step explanation:

Answer:

Step-by-step explanation:

We know: If a quadrilateral is inscribed in a circle, then the sum of measures of opposite angles is equal to 180°.

Therefore we have the equations:

[tex](1)\qquad2x+(2x+4)=180\\\\(2)\qquad y+(3y+8)=180[/tex]

Solve:

[tex](1)\\2x+2x+4=180\qquad\text{subtract 4 from both sides}\\\\4x=176\qquad\text{divide both sides by 4}\\\\x=44\\\\(2)\\y+3y+8=180\qquad\text{subtract 8 from both sides}\\\\4y=172\qquad\text{divide both sides by 4}\\\\y=43[/tex]

Answer:

A. x=44 y=43

Step-by-step explanation:

i just did the test yrdlf

I believe the answer will be (9,9)

Answer:

option c is correct.

Step-by-step explanation:

[tex]7\left(\sqrt[3]{2x}\right)-3\left(\sqrt[3]{16x}\right)-3\left(\sqrt[3]{8x}\right)[/tex]

WE need to simplify this equation.

Solve the parenthesis of each term.

[tex]=7\left\sqrt[3]{2x}\right-3\left\sqrt[3]{16x}\right-3\left\sqrt[3]{8x}\right[/tex]

Now, We will find factors of the terms inside the square root

factors of 2: 2

factors of 16 : 2x2x2x2

factors of 8: 2x2x2

Putting these values in our equation:[tex]=7\left(\sqrt[3]{2x}\right)-3\left(\sqrt[3]{2X2X2X2 x}\right)-3\left(\sqrt[3]{2X2X2 x}\right)\\=7\left(\sqrt[3]{2x}\right)-3\left(\sqrt[3]{2X2X2} \sqrt[3] {2 x}\right)-3\left(\sqrt[3]{2X2X2} \sqrt[3]{x}\right)\\=7\left(\sqrt[3]{2x}\right)-3\left(\sqrt[3]{2^3} \sqrt[3] {2 x}\right)-3\left(\sqrt[3]{2^3} \sqrt[3]{x}\right)\\=7\left(\sqrt[3]{2x}\right)-3*2\left(\sqrt[3] {2 x}\right)-3*2\left(\sqrt[3]{x}\right)\\=7\left(\sqrt[3]{2}\sqrt[3]{x}\right)-6\left(\sqrt[3] {2}\sqrt[3]{x})-6\left(\sqrt[3]{x}\right)[/tex]

Adding like terms we get:

[tex]=7\left(\sqrt[3]{2}\sqrt[3]{x}\right)-6\left(\sqrt[3] {2}\sqrt[3]{x})-6\left(\sqrt[3]{x}\right\\=(\sqrt[3] {2}\sqrt[3]{x})-6\left(\sqrt[3]{x}\right)\\[/tex]

[tex](\sqrt[3] {2}\sqrt[3]{x})-6\left(\sqrt[3]{x}\right)\\can\,\,be \,\, written\,\, as\,\,\\(\sqrt[3] {2x})-6\left(\sqrt[3]{x}\right)[/tex]

So, option c is correct

What that person said so basically C

Answer:

x= 3/4

Step-by-step explanation:

x^3 = 27/64

x= (3 is the exponent of the squared root √ (27/64)

x=3/4

The measure of the major arc is found by calculating the circumference of the entire circle 2πr and then using the proportion that the angle of the major arc represents out of 360 degrees.

The measure of the major arc in a circle depends on the angle subtended by the arc at the center of the circle. If we define the angle Θ (theta) in degrees, that subtend the arc, the length of the major arc can be found by using the circumference of the entire circle, which is 2πr (where r is the radius), and the proportion of the circle that the major arc represents. Since the entire circle is 360 degrees, if the major arc corresponds to an angle Α, which is the complement of Θ (since Α + Θ = 360 degrees for the minor and major arcs together), the major arc length will be 2πr (Α/360). To summarize, if you're given the central angle of the minor arc or can otherwise determine the central angle for the major arc, you can use this proportion to calculate the arc length.

Answer:

AC = 5

Step-by-step explanation:

AC is the diagonal of the rectangle ABCD and splits the rectangle into 2 right triangles.

Using right triangle ABC with hypotenuse AC

Applying Pythagoras' theorem gives

AC² = AB² + BC² ← substitute given values

AC² = 4² + 3² = 16 + 9 = 25

Take the square root of both sides

AC = [tex]\sqrt{25}[/tex] = 5

Answer:

C) {4, 9, 8, 11, 10, 12, 14}

Step-by-step explanation:

Answer:

{9, 8, 9, 6, 12, 10, 13}

Step-by-step explanation:

Write the data in numerical order. Find the first quartile, the median, the third quartile, the minimum (smallest value) and the maximum (largest value).

{6, 8, 9, 9, 10, 12, 13}

Thus,

low -- 6

1st quartile -- 8

median -- 9

3rd quartile -- 12

high -- 13

Therefore, this data does not match the graph.

Answer:

∑5n=(−1)^n(2+5n)

Hope this helps you out!

Vehicle A travels 750 feet and Vehicle B travels 600 feet in 15 seconds. Adding these distances together, we find they are 1350 feet apart after 15 seconds.

The subject of your question falls under the realm of Mathematics, specifically in the area of vector addition or relative velocity. Let's imagine the two vehicles are moving away from each other in a straight line at an angle. We mainly need to consider the relative velocity of vehicle B to vehicle A.

After 15 seconds, vehicle A will have traveled (50 feet/second * 15 seconds) = 750 feet. Similarly, vehicle B will have traveled (40 feet/second * 15 seconds) = 600 feet. In this situation, the total distance separating vehicle A and vehicle B is the sum of their individual distances traveled, which equals 750 feet + 600 feet = 1350 feet.

Therefore, the two vehicles are 1350 feet apart after 15 seconds.

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Answer:

He drove 244 miles

Step-by-step explanation:

First multiply 4/7*427/1 and you get 1,708/7

Then convert 1,708/7 to 244/1

And so your answer is 244

Ben drove 244 miles before he stopped for lunch.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole.

As per the given data:

Ben has already driven 4/7 of the way to his friend's house before he stopped to eat lunch.

The total distance from Ben's house to his friend's house is 427 miles.

We have to find the Ben has already driven before he stopped to eat lunch.

Distance Ben's driven = 4/7 of the total distance

Distance Ben's driven = 4/7 × 427

Distance Ben's driven = 4 × 61 = 244 miles

Ben's already drove 244 miles before he stopped for lunch.

Hence, Ben drove 244 miles before he stopped for lunch.

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Answer:

12lbs

Step-by-step explanation:

let x be the amount of apples you need, then:

x-0.14x= 10 8/25

0.86x = 10 8/25

(10 8/25) : 86 * 100 = x

x=12

Answer:

Total fresh apple needed = 12

Step-by-step explanation:

It is given that, While drying apple loses 14% of its weight

To find the fresh apple needed

Let x be the total fresh apple needed.

Apple loses 14% of its weight. Final we need 10 8/25 lbs of dried apple

x - 14x/100 = 10 8/25

0.86x = 10 8/25

0.86x = 258/25 = 10.32

x = 12

Answer:

7:50

Step-by-step explanation:

We need both measures in the same units. Let's convert meters to cm.

1 m = 100 cm, so 3 m = 300 cm

Now we write the ratio and reduce it.

42 cm to 3 m =

= 42 cm to 300 cm

= 42:300

= 14:100

= 7:50

Answer:

A. π

Step-by-step explanation:

this is a graph of  a cosine function and and the interval during which it completes one cycle starting from the origin, according to the graph is  π

Answer:

First we need to calculate the are of each wall, since we alredy knew the length (l) and the width (w) which is the height of the wall in this case:

A = wl = 9 . 12 = 108 (ft²)

We also know that he painted 3 walls, we need to multiply our first result by 3, in other words, the area of wall that Brett painted is the sum of the area of three walls: 108 . 3 = 324 (ft²)

Answer:

324 ft^2

Step-by-step explanation:

ok so to calculate the area its A = wl (width x length)

9 x 12 = 108 ft^2

buuuuuut since we have 3 walls were going to have to multiply it by three as cuz 108 ft^2 is the outcome of one wall

108 ft x 3 = 324 ft^2

~batmans wife dun dun dun....

Answer:

The answer is x=40

Step-by-step explanation:

Answer:

It's x = 40 that's correct.

In this case, we're looking for a number that is higher than 10. We can't say 29, 37 or 47 but 40

Step by step explanation:

x / 4 > 10

Carry over the 4 and you'll get 4 × 10 -> x = 4 × 10 = 40

Therefore x = 40

A (2, -3/2) baisicly it is is a line and it is vertical so this one is more easy.

Answer:

I believe its A.

Step-by-step explanation: