A swimming pool is in the shape of the following figure. The homeowner wishes to build a fence around the perimeter of the pool. How many feet of fencing are required?
Round your answer to the nearest hundredth, if necessary.

Answer:

Coordinates of A are (-2.5, -1.5)

Coordinates of B are (4.5, -3.5)

According to the imaginary number, the real solution between 30 and 80 is 60

Imaginary number

An imaginary number refers a real number multiplied by the imaginary unit i, which is defined by its property i² = −1.

Given,

Here we have to use the digits -9 to 9 (each only once) to create a real solution between 30 and 80 (a+bi)(c+di).

We know that the digits from -9 to 9 are listed as follows:

(-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9)

Now, we have to choose the digits -9 to 9, as the value of a, b, c and d,

For that we have to choose the value of a = 3, b = -9, c = 2 and d = 6,

Now, we have to apply these value on the given imaginary equation, then we get,

(a + bi) (c + di) = (3 + -9i) (2 + 6i)

When we simplify this one then we get,

=> 6 + 18i + (-18i) – 54i²

We know that value of i² =  -1, then the equation is written as,

=> 6 - 54(-1)

=> 6 + 54

=> 60

Therefore, 60 is a real solution between 30 and 80.

To know more about Imaginary number here.

https://brainly.com/question/23429483

#SPJ1

The correct expression will be;

⇒ 3n - 15 - n = 101

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is;

''A number, n, is added to 15 less than 3 times itself. The result is 101.''

Now,

Since, The algebraic expression is;

''A number, n, is added to 15 less than 3 times itself. The result is 101.''

So, We can formulate;

⇒ 3n - (15 + n) = 101

⇒ 3n - 15 - n = 101

Thus, The correct expression will be;

⇒ 3n - 15 - n = 101

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

Answer: -15 degrees

Step-by-step explanation:

Answer:

-180

Step-by-step explanation:

You would plug in x=3 and y=-6 into the equation

So, the first part would be 36x when x=3, 36(3)=108

The second part would ne -8y^2 when y=-6 (-6 squared is 36), -8(36)=-288

Putting these together, you get 108-288 which is -180

Answer: -180

hops this helps

have a good day

Step-by-step explanation:

The distance between the points, (-8, -2) and (12, 10), is 23.3

From the question, we are to determine the distance between the two given points.

From the given information,

The points are (-8, -2) and (12, 10)

The distance between two points in given by the formula

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where d is the d is the distance between the points

Thus,

d = √[(12 - (-8))² + (10 - (-2))²]

d = √[(12 + 8)² + (10 + 2)²]

d = √[(20)² + (12)²]

d = √[400 + 144]

d = √[544]

d = 23.3

Hence, the distance is 23.3

Learn more on Calculating the distance between two points here: https://brainly.com/question/27520547

#SPJ1

The profit function for the revenue R(x) = 12x and the cost, C(x) = x + 264 is  11x-264 and units must be produced for the business to break even is 24 units.

Profit refers to net income after deducting expenses from earnings, whereas revenue refers to income generated through business operations. Sales, fee-based income, and property-based income are just a few of the different ways that money can come in.

Here,

R(x)=12x

C(x)=x+264

It represents the difference between total revenues and total outlays.

Revenue minus costs equals profit.

Profit = Revenue - Cost

P(x)=R(x)-C(x)

P(x)=12x-x-264

P(x)=11x-264

For  the company to break even,

R(x) = C(x)

12x=x+264

11x=264

x=24

The break-even point for the business is 24 units, and the profit function for the revenue R(x) = 12x and the cost C(x) = x + 264 is 11x-264.

To know more about revenue profit,

https://brainly.com/question/18099281

#SPJ1

Answer: The two lines intersect at (-4,3)

Step-by-step explanation:

So our first step would be to turn both of these into standard slope-intercept form.

1.)

4y + 3x = 0

4y = -3x

y = -3/4x

2.)

4y - x = 16

4y = x + 16

y = 1/4x + 4

Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)

The value of the first term in the sequence is 21.

Let the second term teen be x.

Since the term to term rule is subtract 2 and then multiply by 3. This will be:

(x - 2) × 3 = 165

3(x - 2) = 165

3x - 6 = 165

Collect like terms

3x = 165 + 6

3x = 171

Divide

x = 171 / 3.

x = 57

Second term = 57

We will do same thing again to get first term. Let first term be a.

(a - 2) × 3 = 57

3a - 6 = 57

Collect like terms

3a = 57 + 6

3a = 63

Divide

a = 63/3

a = 21

The first term is 21.

Learn more about sequence on:

brainly.com/question/6561461

#SPJ1

The number of ways to select the banners is given as follows:

a. Matching with the country: 362,880.

b. Not matching with the country: 60,949,324,800

To select the banners matching the country, only the nine countries are chosen, and then the specific banner regarding the country is chosen, thus the arrangements formula is used.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

Hence for item a the total number of outcomes is the factorial of nine, which is the number of countries, is given as follows:

Total = 9! = 362,880.

Then just nine banners are taken at random from a set of 20. The order is important, hence the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 9 banners are selected from a set of 20, hence the number of ways is:

N = 20!/(20 - 9)! = 20!/11! = 60,949,324,800.

More can be learned about the permutation formula at https://brainly.com/question/11732255

#SPJ1

The number of days it would take to collect 2600 cans is; 11 days

We are given the equation that represents the number of cans that Nicholas collected as; y = 235x + 15

where;

x represents the number of days.

y represents the number of cans collected.

Now, we want to make x the subject of the formula;

y = 235x + 15

Subtract 15 from both sides to get;

y - 15 = 235x

divide through by 235 to get;

(y - 15)/235 = x

When y = 2600;

x = (2600 - 15)/235

x = 11 days

Read more about subject of the formula at; https://brainly.com/question/10643782

#SPJ1

Answer:

The Answer is C.

Step-by-step explanation:

It's important to know how the standard form of an equation works.

Remember that y = mx + b, where y is the output value, m is the slope of the equation, and b is the y-intercept (the initial value) of the equation. We know that the pool starts with 25 inches of water in it, so the initial value, or y-intercept is 25, because the pool starts with 25 inches of water after 0 hours. We know that the pool fills up 4 inches per hour, meaning as each hour progresses, the equation will increase by 4. This is the slope. y has been replaced with h in this equation. So, your answer would be h = 4t + 25.

Answer:

1,265

Step-by-step explanation:

10^3=1000*2=2000

105*7=735

2000-735

The relation y = x² represents y as a function of x because every x-value returns a unique y-value.

Using the definition of a function, y=x² is a function because you will only get one unique y-value for each x-value in your domain.

The vertical line test is a quick check you can perform. The function y=x² is a parabola, and if you draw vertical lines anywhere on it, they will only cross the parabola once.

As a result, it is a function. A circle is not an example of a function because a vertical line drawn on a circle crosses at two different points.

Learn more about functions on:

https://brainly.com/question/25638609

#SPJ1

Answer:

∠W = 36.6°

Step-by-step explanation:

Hello!

If angles are complementary, it means that they add up to 90°.

Since the measure of Angle X is 53.4, we can find measure of Angle W by subtracting 53.4 from 90.

The value of W is 36.6°.

Answer:20

Step-by-step explanation:

The equation of line that is perpendicular to the line y = 1/2x + 2 is y = -2x - 7

A perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes. Coordinates and line equation is the prerequisite to finding out the perpendicular line.

The equation of perpendicular line is given as

(y - y₁) = m(x - x₁)

m = slope of the line.

But the slope of a perpendicular line is given as

m₁m₂ = -1

m₁ = 1/2, m₂ = ?

1/2m₂ = -1

m₂ = -2

The new slope is -2.

Substituting the values into the equation above,

(y - y₁) = m(x - x₁)

y - 1 = -2(x - (-4))

y - 1 = -2x - 8

y = -2x - 7

The new equation is y = -2x - 7

Learn more on equation of a perpendicular line here;

https://brainly.com/question/6691986

#SPJ1

If she did some research and learned that the exchange rate is 6 Tala for $2. The number of tala she get if she exchanged $6 is 18 tala.

Given data:

Exchange rate = 6 Tala for $2

Let x represent the tala Ming will get if she exchange $6

$2/6 = $6/X

Cross multiply

2x = 6× $6

2x = 36

Divide both side by 2x

x = 36/2

x = 18 tala

Therefore she would get 18 tala.

Learn more about the exchange rate here:https://brainly.com/question

#SPJ1

The probability of being dealt an ace=4/52

The probability of being dealt another ace = 3/51

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.

The probability of drawing one of the four aces from a typical 52-card deck is 4/52; but, the probability of drawing a second ace is merely 3/51 since, after the first ace was drawn, there were only three more aces remaining in the remaining 51 cards.

To learn more about the probability from the given link

https://brainly.com/question/24756209

#SPJ1

Answer:

The degree of the polynomial is 4.  That is the highest exponent.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

to find degree you look at what the highest exponent when simplified is and that is your answer and inThis case it’s 4

Hopes this helps please mark brainliest

For a year, 1750 students were able to donate to the school.

A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it  by % lacks dimensions and has no associated unit of measurement.

The Latin word per centum, which means "hundred" or "by the hundred," is where the word "percent" originates. The % calculator computes a variety of percentage-based numbers, such as the percentage difference between two provided values.

Given,

The annual salary of a football player is 210000

1 student ----------$120

x  ------------$210000$

x=(210000/120)

x=1750 students

1750 students could send their donation to the school for 1 year.

To know more about percentage, visit:

https://brainly.com/question/16797504

#SPJ1

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

Work Shown:

x = monthly budget

45.50% of x = 0.4550x = 4500

0.4550x = 4500

x = 4500/0.4550

x = 9,890.1098901099 approximately

x = 9,890.11

Answer:

x-3

Step-by-step explanation:

2x²-6x=0

divide both sides by x

2x²/x -6x/x=0

2x-6=0

2x=6

x=6/2

x=3

or (x-3)

Answer:

117

Step-by-step explanation:

20% = 1/5

585 x 1/5 = 117!

The simplified form of the expression  √10•√8 is 4√5.

Expression:

Expression refers the mathematical statements that have two terms at least that contain variables, numbers, or both.

Given,

Here we have the expression √10•√8.

Now we have to find the simplified form of these expression.

Now, we have to multiply the values inside the square root then we get,

=> √10 x √8 = √(10  x 8)

After the multiplication we can get,

=> √80

Now, we have to expand this as the following,

=> √16 x 5

We know that √16 is equivalent for 4²,

So, it can be written as,

=> √4² x 5

Now, we have to simplify this as,

=> 4√5

Therefore, the simplified expression is 4√5

To know more about Expression here.

https://brainly.com/question/14083225

#SPJ1

The bicycle wheel performs 10 revolutions every minute

A revolution in math is a full rotation, or a complete, 360-degree turn. In a 360-degree rotation, the object starts and ends in the same position. A mathematical revolution can be visualized when a top spins.

The bicycle wheel makes 1 complete revolution which is equal to the circumference of the wheel = πD

but D =  diameter = 42 inches, converting inches to feet

12inches is 1 foot, then 42 inches = 42/12 = 7/2 inches

Also circumference = 22/7 x 7/2 = 11 feet/rev

Also if the rider travelled 110 feet per minute.

Then the wheel's revolution per minute = 110/11
                                                                   = 10 rev/minute

In conclusion the bicycle wheel revolves 10 times every minute

Learn more about circumference of a circle: https://brainly.com/question/20489969

#SPJ1

The value of x is 5 when the line is JL and the midpoint of the JL is K.

Given that,

The line is JL and the midpoint of the JL is K.

JL= 13x-9 and JK= 28.

We have to find the value of x.

The midpoint is the point on a line that connects two points that is exactly in the middle of the line.

We know that,

JL= JK+ JK

JL=2JK

13x-9 = 2×28

13x-9= 56

13x= 56+9

13x= 65

x=65/13

x=5

Therefore, The value of x is 5 when the line is JL and the midpoint of the JL is K.

To learn more about line visit: https://brainly.com/question/2696693

#SPJ1

The percentage reduction of the jacket is 20 percent.

Percentage decrease or reduction means subtracting a given percentage of a value from the original value.

Therefore, the jacket cost 80 dollars and it is reduced to 64 dollars.

The percentage reduction of the jacket can be calculated as follows:

% reduction = (Decreased Value / Original Value) × 100

Decreased value = 80 - 64 = 16

Original Value = 80

% reduction = 16 / 80 × 100

% reduction = 1600 / 80

% reduction = 20%

Therefore, the percentage reduction is 20%.

learn more on percentage reduction here: https://brainly.com/question/25779145

#SPJ1

Monthly payment would be $956.24
Loan APR is 4.892%