Please help me find the domain and range and write them down as an inequality. I need help ASAP. It would be deeply appreciated if you could help and give answers. I’ve been stuck on this problem for HOURS. Thank you.

The width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

Let's represent the width of the pool as x. Then, the length of the pool would be x + 6.

The total area of the pool and walk is given by:

Total area = (length + 2(4)) × (width + 2(4))

Total area = (x + 6 + 8) × (x + 4)

Total area = (x + 14) × (x + 4)

The area of the pool itself is given by:

Pool area = length × width

Pool area = x(x + 6)

Pool area = x² + 6x

We're told that the total area is 272 more than the area of the pool:

Total area = Pool area + 272

(x + 14) × (x + 4) = x² + 6x + 272

Expanding the left side of the equation:

x² + 18x + 56 = x² + 6x + 272

Simplifying the equation:

12x = 216

Solving for x:

x = 18

So the width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

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Full Question: A rectangular pool is surrounded by a walk 4 feet wide. The pool is six feet longer than its wide. If the total area is 272 ft² more than the area of the pool,what are the dimension of the pool?

We are given that one of the endpoints of the line segment is: (x + 2, 14 y)

And that the midpoint of the line segment is: (6,−3)

We can consider using the midpoint formula:

Substituting:

Solving for x₂ and y₂:

ANSWER

the other coordinate expressed in terms of x and y is: (10 - x, - 14y - 6)

Over 400 convicted burglars were surveyed about their habits and motivations. The study found that visible surveillance cameras act as a deterrent, as they make burglars less likely to target a property

Visible surveillance camera systems have the potential to reduce and deter crime.

This conclusion is based on a study conducted by a UNC Charlotte researcher in 2013.

This conclusion is supported by the study's findings, which show that burglars are less likely to target properties with visible surveillance cameras. This information is important for individuals and communities looking to enhance their security measures and reduce the risk of burglary.

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Answer:

Step-by-step explanation:

a+2a+a+10=180

4a=180-10

4a=170

a=42.4°

2a=42.5*2=85°

a+10=42.5+10=52.5°

To find the slope intercept form, solve the equation for y.

Solve the equation for x:

The possible lengths( in whole elevation) for the third side is

9 elevation< x< 45 elevation, i.e in between 9 and 45 elevation.

 For the below question, we've a rule from the properties of triangle, the sum of the length of any two  sides of the triangle must be lesser than the length of the third side.

Hence

She has two sides of length 18 elevation and 27 elevation

Let the third side = x

Hence

a) 18 27> x

45> x

b) 18 x> 27

x> 27- 18

x> 9

thus, the possible lengths( in whole elevation) for the third side is

elevation< x< 45 elevation

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Answer:

a. The graph shows a positive slope.

You have to look at it from left to right. If the line starts going up, it's positive, if it goes down, it's negative.

b. A few other points are (-2, -7), (-1, -4), and (2, 5)

c. The graph has a slope of 3. You have to count up and then to the side It's rise over run. For example looking at the given points (0, -1) and (1, 2). You start at point (0, 1) count up (the rise) until you're level with (1, 2) and then count to the side until you're on point (1, 2)(the run). The rise you get 3 and the run is 1.

3 over 1 is 3.

Let me know if you need any more clarification.

Answer:

I answered this already in your last question, it is 6 1/6

Step-by-step explanation:

hope it helps

Answer:

option C is correct.

hope this answer helps you dear..... take care and may u have a great day ahead!

The formula for the coefficient of xk in the expansion of (x + 1/x)^100 is (100 choose (50+k/2)).

By the binomial theorem, the kth term in the expansion of (x + 1/x)^100 is given by:

C(100,k) * x^k * (1/x)^(100-k) = C(100,k) * x^(2k-100)

Since we are only interested in the coefficient of xk, we need to find the value of k such that 2k - 100 = k, or k = 100/2 = 50.

Thus, the coefficient of x^50 in the expansion of (x + 1/x)^100 is given by:

C(100,50) = (100 choose 50) = (100 choose (50 + k/2))

where we have substituted k = 50 to obtain the final formula.

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The blood platelet count is an illustration of normal distribution Approximately 95% of the data lies within 2 standard deviations of the mean. There are approximately 99.7% of women with platelet count between 65.2 and 431.8

The given parameters are:

μ = 248.5

\(\sigma = 61.1\\\)

(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7

Start by calculating the z-score, when x = 126.3 and x = 370.7

\(Z = \frac{(x-u)}{\sigma}\)

So, we have:

x = -2

Also,

x = 2

The empirical rule states that:

Approximately 95% of the data lies within 2 standard deviations of the mean.

Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.

(b) The percentage with platelet count between 65.2 and 431.8

Start by calculating the z-score, when x = 65.2 and x = 431.8

So, we have:

Z =-3

Also:

Z = 3

The empirical rule states that:

Approximately 99.7% of the data lies within 3 standard deviations of the mean.

Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8

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Answer:

x=20. You can use the app Photomath to help you with math equations.

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

15% of 54=8.1

15% of 240=36

15% of 360=54

15% of 540=81

so the answer is 240

36 is 15 percent of 240.

We have,

To find out what number 36 is 15% of, we can set up the equation:

36 = 0.15x

Here, x represents the unknown number we are trying to find.

To solve for x, we divide both sides of the equation by 0.15:

36 / 0.15 = x

Simplifying the right side gives:

240 = x

Therefore,

36 is 15 percent of 240.

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Answer:

He had - $36.04.

Step-by-step explanation:

If he deposited 26.38 dollars per week, and for three weeks, do 26.38 times 3. You get 79.14. This is the total amount of money he deposited in those three weeks. However, since he was in overdraft, and had 43.1 dollars after three weeks, do 43.1 - 79.14 to get - $36.04 in his balance when he went into overdraft.

Answer:

£2121.8

Step-by-step explanation:

2000 X 1.03 X 1.03 = 2121.8

Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

The original price of the suit without sale is 2929.16 rupees.  

According to the question,

The price of the suit on sale, P = 703

Discount provided on sale, d = 76%

The first step to find the original price of the suit includes converting discount percentage into decimal by dividing it by 100.

Percentage into decimal number = 76/100 = 0.76

Now, to find the original price of the suit, set up an equation:

P = (1 - d) x, where P is the sale price, d is the discount in decimal numbers, and x is the original price of the suit.

putting the values in the above equation, we get:

703 = (1 - 0.76) x

703 = (0.24) x

x = 703/0.24

x = 2929.16

Therefore, the original price of the suit without the discount is 2929.16 rupees.

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Complete question is:

Susan bought a suit on sale for 703. This price was 76% of the original price. What is the original price of the suit?

The integral \(\int \frac{\mathrm{d}x}{(x^2-100)\sqrt{x^2-100}}\) is equal to ln|sec(θ) + tan(θ)| + C, or \(\ln\left|\frac{x}{10} + \frac{\sqrt{x^2-100}}{10}\right| + C\).

Using trigonometric substitution, we can rewrite the integral \(\int\frac{dx}{(x^2-100)\sqrt{x^2-100}}\) as follows:

Let x = 10 * sec(θ), so dx = 10 * sec(θ) * tan(θ) dθ.

Then, x² - 100 = 100 * (sec²(θ) - 1) = 100 * tan²(θ). Taking the square root gives:

\(\sqrt{x^2 - 100}\) = 10 * tan(θ)

Substituting these values, we get:

\(\int \frac{10 \sec \theta \tan \theta}{100 \tan^2 \theta \cdot 10 \tan \theta} d\theta\)

= ∫sec(θ) dθ

The integral of sec(θ) is ln|sec(θ) + tan(θ)| + C. To convert back to x, recall that x = 10 * sec(θ) and x² - 100 = 100 * tan²(θ).

Therefore, the integral\(\int \frac{dx}{(x^2-100)\sqrt{x^2-100}}\) is equal to ln|sec(θ) + tan(θ)| + C, or \(\ln\left|\frac{x}{10} + \frac{\sqrt{x^2-100}}{10}\right| + C\).

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Answer:

x=4

y=3

Step-by-step explanation:

substitute into one of the equations

9x+17=x+49

x=4

y=4+49

y=53

In a sample of 26 days from the desert, the average of the high daily temperature is 114 degrees F, and the sample standard deviation is 5 degrees F.

To determine the 90% confidence interval for the average temperature, we can use the t-distribution as follows:To find the critical value of t, we can use the t-table. Since our sample has n = 26, the degrees of freedom (df) are n - 1 = 25. At a confidence level of 90%, with 25 degrees of freedom, the critical t-value is 1.708.The standard error of the mean is calculated as s / sqrt(n), where s is the sample standard deviation and n is the sample size. Therefore, the 90% confidence interval for the average temperature is (114 - 1.67, 114 + 1.67), or (112.33, 115.67) degrees F.

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She cannot draw an array of 17 counters with three rows.

The given parameters are:

Counter = 17

Rows = 3

An array is represented as:

Array = Rows * Columns

Where Rows and Columns are integers greater than 0

So, we have

3 * Column = 17

Divide by 3

Column = 5.667

Recall that Rows and Columns are integers greater than 0

This means that she cannot draw an array of 17 counters with three rows.

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The required properties for the algebraic expression are Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root.

The algebraic expression consists of constants and variables. eg x, y, z, etc.

Here,

Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution and square root qualities are the main nine properties of equality.

Algebraic equations involving real numbers can be resolved with the aid of the addition, subtraction, multiplication, and division characteristics of equality.

Thus, the required properties for the algebraic expression are Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root.

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The average rate of change over the interval \([0,2]\) is -6. The average rate of change of a function \( y = f(x) \) over an interval is a measure of how the function's values change on average within that interval.

To find the average rate of change, we calculate the ratio of the change in the function's values to the change in the input variable (x) over the given interval.

First, let's consider the average rate of change over the interval \([0,3]\), which is given as -1. This means that, on average, the function's values decrease by 1 unit for every 1 unit increase in the input variable within the interval \([0,3]\).

Next, let's consider the average rate of change over the interval \([2,3]\), which is given as 5. This means that, on average, the function's values increase by 5 units for every 1 unit increase in the input variable within the interval \([2,3]\).

Now, let's determine the average rate of change over the interval \([0,2]\) by subtracting the average rate of change over \([2,3]\) from the average rate of change over \([0,3]\).

Average rate of change over \([0,2]\) = Average rate of change over \([0,3]\) - Average rate of change over \([2,3]\)

= (-1) - 5

= -6

Therefore, the average rate of change over the interval \([0,2]\) is -6.

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Answer:

7.2m

Step-by-step explanation:

24 x 6 = 14.4

14.4/2=7.2m

Answer:

The exponential function represents growth, the percentage rate of increase is 7.8 %

Step-by-step explanation:

Please see the attachment.

The exponential function represents growth, the percentage rate of increase is 7.8 %

Answer: y²-2y-48=(y-8)(y+6)

Step-by-step explanation:

\(y^2-2y-48=\\\\y^2-8y+6y-48=\\\\y(y-8)+6(y-8)=\\\\(y-8)(y+6)\)

Answer:

y²-2y-48=(y-8)(y+6)

Step-by-step explanation:by factorization

y2-2y-48= y2-8y+6y48= y(y-8)+6(y-8)= (y-8)(y+6)