Go step by step to reduce the radical

The required equation for the width of the rectangular playpen is w² + 4w -32 = 0.

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

here,
let the length be l and width be w,
According to the question,
l = w + 4
Now,
Area of the pen = length × width
Area of the pen = (w + 4) × w
32 = w² + 4w
w² + 4w -32 = 0

Thus, w² + 4w -32 = 0 is the required equation that represents the rectangular playpen.

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Answer:

The 2 numbers are 27 and 30

Step-by-step explanation:

Let call them x and y where x is the larger number and y is the smaller number :

x + y = 57 (obtained from the first line of the question)

x - y = 3 (obtained from the second line of the question)

Now we are going to use the rules of simultaneous equations to find x and y :

I will use elimination method :

Add the 2 equations to eliminate the y :

2x = 60

x = 30

Substitute x into equation 1 :

(30) + y  = 57

Subtract 30 from both sides :

y = 57 - 30

y = 27

So

x = 30 and y = 27

As you can see the difference is also 3

The 2 numbers are 27 and 30

Hope this helped and have a good day

Answer:

c = 14

Step-by-step explanation:

The true statements about the circle are

From the question, we have the following parameters that can be used in our computation:

x² + y² - 2x - 8 = 0

Generally, To convert this equation to standard form, we need to complete the square.

First, we can rearrange the terms on the left-hand side of the equation so that all the x terms are together and all the y terms are together:

x² - 2x + y² - 8 = 0

Then, we need to add and subtract a value that allows us to rewrite x² - 2x term as a perfect square.

To do this, we take half of the coefficient of the x term (which is -2), square it, and add it to both sides of the equation:

So, we have

x² - 2x + (1²) + y² - 8 = 0 + (1²)

Evaluate

(x - 1)² + y² - 8 = 1

Finally, we can rearrange the terms

So, we have

(x - 1)² + y² = 9

Express 9 as the square of 3

(x - 1)² + y² = 3²

So, the standard form of the equation is (x - 1)² + y² = 3²

The standard equation of a circle is represented as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

When these equations are compared, we have

Center = (a, b) = (-1, 0)

Radius = r = 3

The point (-1, 0) lies on the x-axis

This means that the center is on the x-axis.

Also, it means that the radius of the circle is 3 units

This radius is the same for a circle that has the form x² + y² = 9

This is so because 9 can be expresses as the square or 3, and r = 3

Hence, the correct statements are (a), (b) and (e)

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Complete Question

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true?

Select three options.

Answer:

y= -9

Step-by-step explanation:

Subtract 3 from both sides

-2y + 3-3= 21-3

-2y=18

Divide both sides by the same factor

-2y/-2 = 18/-2

y= -9

Answer: y = -9

Step-by-step explanation:

-2y+3=21

-2y=21-3

-2y=18

Divide that by -2:

y=-9

V = 20,000 * 0.81^2 and V = 20,000 * (1 - 0.19)^2 are the equation(s) that represent the exponential relationship.

The value of the car two years later is represented by the variable V. The initial value of the car is represented by the constant 20,000. The relationship between the value of the car two years later and the initial value of the car is exponential, because the value of the car decreases by a fixed percentage each year.

One equation that represents this relationship is:

V = 20,000 * 0.81^2

This equation says that the value of the car two years later is equal to the initial value of the car multiplied by the decay factor of 0.81 raised to the power of 2. The decay factor represents the percentage by which the value of the car decreases each year.

Another equation that represents this relationship is:

V = 20,000 * (1 - 0.19)^2

This equation says that the value of the car two years later is equal to the initial value of the car multiplied by (1 - 0.19) raised to the power of 2. The term (1 - 0.19) represents the percentage by which the value of the car remains after it has depreciated.

Both of these equations represent the exponential relationship between the value of the car two years later and the initial value of the car.

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Answer:

Step-by-step explanation:7.48521878104

The scale factor, if The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards, is 1.8.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).

Given:

The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards,

Calculate the scale factor as shown below,

Scale factor = Original dimension / new dimension

Scale factor = (4 × 6) / (3 × 4.5)

Scale factor = 1.8

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If 87. 5 percent of a sample of pure 131 I decays in 24 days, then the half-life of 131 i is 8 days.

In this question we have been given 87.5 percent of a sample of pure 131i decays in 24 days

We need to find the the half-life of 131i

We know that the rate constant expression is given as :

k = (2.303/t)*(log (a / a-x))

where, t = 24 days

a = 100

a -x = 100 - 87.5

      = 12.5 g

From the rate constant expression,

k = (2.303 / 24) * (log(100/12.5))

k = 0.0866

Now, the half life is given as :

k = 0.693 / t(1/2)

t1/2 = 0.693 / 0.0866

t1/2 = 8 days.

Therefore, the half-life of 131 i is 8 days.

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The solution of the system of equation is as follows;

when x = -2 , y = -4

when x = 4, y = 8

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Let solve the system of equation by substitution method.

Therefore,

y = 2x

y = x² - 8

Using substitution,

2x = x² - 8

x² - 2x - 8 = 0

x² + 2x - 4x - 8 = 0

x(x + 2) - 4(x + 2) = 0

(x - 4)(x + 2) = 0

x = -2 or 4

Hence,

when x = -2

y = 2(-2) = -4

when x = 4

y = 2(4) = 8

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Answer:

D

Step-by-step explanation:

base area = (6 · 4)/2 = 24/2 = 12 cm²

half base length = 6 : 2 = 3 cm

leg = [tex]\sqrt{3^2+4^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex] cm

perimeter = (5·2) + 6 = 10 + 6 = 16 cm

lateral area = 16 · 20 = 320 cm²

surface area = (2 · 12) + 320 = 24 + 320 = 344 cm²

The area of the circle would be 36π.

What is the area of a circle?

If the circle has a radius then the area of the circle can be computed by using the formula

area = π * radius²

The perimeter of the square = 24

4 * side = 24

Side of a square = 24/4 = 6

Side of a square = radius of the circle

Substituting the radius of 6 into this formula gives:

area = π * 6²

Which simplifies to:

area = π * 36

Hence, the area of the circle would be 36π.

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Answer:

1,368

Step-by-step explanation:

4.56x36=164.16

164.16/0.12=1368

Answer:

1368

Step-by-step explanation:

1368

The function that  is used to find the total amount of money Giovanni will earn each day is; A = 14 + 45d

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, we are told that;

Giovanni works as a tour guide during the summer.

Amount he earns daily = $45

Amount earned for each tour = $14

Now, if the number of days he spends as a tour guide is d, then we can say that the total amount of money Giovanni will earn each day is expressed as;

A = 14 + 45d

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In case A:

The amount to be paid = $41.75

In case B :

The amount to be paid = $41.76

So, the Case A is better option.

Finding the right answer using the round off to nearest hundredth.

How to change any value to it's nearest hundredth ?

Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.

Steps to find nearest hundredth of any value:

Step 1:

Since we need to round the given decimal number to the nearest hundredth, we mark the digit at the hundredths place.

Step 2:

Then, we observe the 'thousandths' place digit, which lies to the right of the hundredths column.

Step 3:

If the digit at the thousandths place is less than 5, we write the hundredths place digit as it is and remove all the digits to its right.

Step 4:

If the digit at the thousandths place is 5 or more than 5, we add 1 to the digit at the hundredths place, that is, we increase the hundredths place by 1 and remove all the digits to its right.

Case A :

The price for each gallon = $3.479

So, the total price for 12 gallon = $41.748

In case A total amount is rounded off

So, the price = $41.75

Case B :

The price for each gallon = $3.479

Rounding off the price for each gallon = $3.48

So, the total amount for 12 gallon = $41.76.

So, the case A is better option.

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The total time taken is 24 hours.

What is total time?

Total refers to a whole or full amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A automobile that has been totalled in an accident is irreparably damaged. Total Time is the result of multiplying the number of minutes in a day by the number of days in a given calendar month.

An inlet pipe takes 8 hours to fill a tank. An outlet pipe takes 12 hours to empty.

[tex]$\Rightarrow$[/tex] Time is taken to fill in 1 hour =1 / 8

[tex]$\Rightarrow$[/tex] Time taken to empty in 1 hour =-1 / 12

[tex]$\Rightarrow$[/tex] If both pipes are opened simultaneously tank be filled in 1 hour =1 / 8-1 / 12 =1 / 24 hours

[tex]$\therefore$[/tex] The total time taken is 24 hours.

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P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.

The possibility or likelihood of an event occurring is expressed numerically as probability. Probabilities are expressed as ratios (0 to 1) and percentages (0 to 100). It is founded on the likelihood that something will occur. The theoretical probability is built on the fundamental principle of probability justification. For instance, there is a 12 percent chance of receiving heads while flipping a coin.

P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.

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-3(7f + 3f + 9) - 4f

Distribute.

(−3)(7f) + (−3)(3f) + (−3)(9) + −4f

−21f + −9f + −27 + −4f

Combine like terms.

−21f + −9f + −27 + −4f

(−21f + −9f + −4f) + (−27)

−34f + −27

-34f + -27

Answer: 157.14

Step-by-step explanation: SDHU IK

Answer:

the correct answer to this question would be D

The inequality is [tex]115\leq x\leq 495[/tex]

What is inequality?

A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">", "<", "≥". Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

Given [tex]60\leq 0.5x+2.5\leq 250[/tex]

splitting the equation:

[tex]60\leq 0.5x +2.5[/tex] and [tex]0.5x +2.5\leq 250[/tex]

[tex]60-2.5\leq 0.5x\\57.5\leq 0.5x\\115\leq x\\x\geq 115[/tex]

also

[tex]0.5x +2.5\leq 250\\0.5x\leq 247.5\\x\leq 495[/tex]

therefore the equation is

[tex]115\leq x\leq 495[/tex]

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Answer:4

Step-by-step explanation:i did the quiz

The earnings-to-stock-price ratio in simplest terms is 20.

Here given,

Stock price = $55.00

Earnings per share = $2.75

We have to find ratio od earnings,

The formula is,

Ratio is : P/E

By substituting the values,

Ratio = $55.00 / $2.75

         = 20

this is the explanation above with some examples

Bob lifts a 15N rock through a distance of 1.7m, 25.5 J work does Bob do

An item should be converted to energy before being moved. The use of force is one way to transfer energy. The amount of energy used by a force to move an item is referred to as the work done.

The amount of the displacement and the component of the applied force of the object in the displacement direction is the work done by a force. Pushing a block with force "F" causes the body to move more quickly, meaning that work has been completed.

Work done (W) = F × s

Where, F = force

s = displacement

Now putting the values, we get-

or, W = 15 N × 1.7 m

or, W = 25.5 N-m or Joule

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The retail price of the car is  $ 9802.9.

A car dealership pays $8350 for a car.

They mark up the price by 17.4%

8350 * 17.4%  = 1452.9

retail price = 8350 + 1452.9 = $ 9802.9

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A characteristic of quality data which pertains to the expectation for the time between when data are expected and when they are available for use is timeliness of information.

Information's timeliness is a crucial aspect of data quality since incomplete or outdated information can influence people's actions. That consequently costs businesses time, money, and reputational harm.

The term "completeness" describes how thorough the information is. Consider if all the information you require is there when evaluating data completeness; for example, you might just require a customer's first and last name, but their middle initial might be optional.

Reliability in the context of data quality traits refers to the absence of contradiction between one piece of information and another piece of information from a different source or system.

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