What restriction should be applied to y = tanx for y = arctanx to be defined?

Answer:

(0,3)

Step-by-step explanation:

x - y = -3

y = -1/4x + 3

x - (-1/4x + 3) = -3

x = 0

y = -1/4 x 0 + 3

y = 3

(0,3)

Answer: 24

Step-by-step explanation:

−3−6=−

4

1

​

(x+12)

Subtract 6 from −3 to get −9.

−9=−

4

1

​

(x+12)

Use the distributive property to multiply −

4

1

​

 by x+12.

−9=−

4

1

​

x−

4

1

​

×12

Express −

4

1

​

×12 as a single fraction.

−9=−

4

1

​

x+

4

−12

​

Divide −12 by 4 to get −3.

−9=−

4

1

​

x−3

Swap sides so that all variable terms are on the left hand side.

−

4

1

​

x−3=−9

Add 3 to both sides.

−

4

1

​

x=−9+3

Add −9 and 3 to get −6.

−

4

1

​

x=−6

Multiply both sides by −4, the reciprocal of −

4

1

​

.

x=−6(−4)

Multiply −6 and −4 to get 24.

x=24

Given : Force applied is given as : 200 N

Area : 50m²

We know that the pressure is the force applied perpendicular to the surface of an object per unit area. or

=> P = 200N / 50m²

Each person will get 1.2 of the Blueberry muffins

The number blueberry muffins in 5

6 people wants to share the 5 blueberry muffins

Therefore the number of blueberry muffins each person will get can be calculated by dividing 6 by 5

= 6/5

= 1.2

Hence each person will get 1.2 blueberry muffins if the muffins are shared equally.

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The missing values in the ratio are 2.5 and 17.5.

What is mean by Ratio?

A Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

Now, The missing values are find as;

Ratio of Pounds to the weeks are;

In first column,

Pounds : Weeks = 10 : 4

In second column,

Pounds : Weeks = x : 1

In third column,

Pounds : Weeks = y : 7

Since, All ratio are equal.

Hence,

10 : 4 = x : 1

It can be written as,

10/4 = x / 1

After cross multiplication we get;

x = 10/4

x = 2.5

And,

10 : 4 = y : 7

It can be written as,

10/4 = y/7

After cross multiplication we get,

10 * 7 = y * 4

y = 70/ 4

y = 17.5

Hence, The missing values in the ratio are 2.5 and 17.5.

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Answer:

192 [in²]

Step-by-step explanation:

Area=(4*4)*2+(4*10)*4=192.

Answer: 0.681818

Hope this helps!

Answer: 227=4x+127

x=$25

Step-by-step explanation:

227=4x+127  ==> equation

227-127=4x+127-127

4x=227-127

4x=100

4x/4=100/4

x=100/4

x=$25

Using proportions, it is found that 240 doughnuts were there in all at the beginning of the day on Tuesday.

The percentages are missing and are given in the graph at the end of the answer.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures using the unit rates and operations such as multiplication and division.

One example of application of proportions is for percentage problems, as the decimal equivalent of the percentages are used to find either the equivalent amount or the total amount, by multiplication operations.

The percentages of doughnuts displayed are given as follows:

Hence 45% of the total amount is equivalent to 108 doughnuts, hence:

0.45n = 108.

n = 108/0.45

n = 240.

Which is the number of doughnuts that were there in all at the beginning of the day on Tuesday.

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This is just a linear equation, then the domain is the set of all real numbers and the range is the set of all real numbers.

Here we have the function:

f(x) = (x^2 + 5x + 4)/(x + 4)

The numerator can be rewritten if we find the zeros:

x = (-5 ± √( 5^2 - 4*1*4))/(2*1)

x = (-5 ± 3)/2

Then the zeros are:

x = (-5 - 3)/2 = - 4

x = (-5 + 3)/2 = -1

So the numerator can be rewritten to (x + 4)*(x + 1)

And the function is rewritten to:

f(x) = (x^2 + 5x + 4)/(x + 4) = (x + 4)*(x + 1)/(x + 4) = (x + 1)

This is just a linear equation, then the domain is the set of all real numbers and the range is the set of all real numbers.

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Answer:

The information that I do not need is how much the customer gave the parking attendant.

The garage charged $5.00

Step-by-step explanation:

2 + .75h       h stands for the number of hours the car was parked.

2 + .75 (4)

2 + 3 = 5

C=5

Explain explain Explain

Answer:

(x) = 2x

Step-by-step explanation:

Answer:

Here's a screenshot of the work i've done

Step-by-step explanation:

Your welcome

Answer: 121.176

Step-by-step explanation:

First, multiply out the decimal points. To get 408 from 4.08, multiply by a hundred. Likewise, with 29.7, multiply it by 10.

Then, do long multiplication with 408 and 297 (you get 121176 from that).

Finally, use your answer from the long multiplication and divide it by how many times you multiplied your original numbers. So, you have to divide by 100, and then also divide by 10.

From that, you get 121.176

Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad A(\stackrel{x_2}{0}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BA=\sqrt{(~~0 - (-3)~~)^2 + (~~0 - 6~~)^2} \implies BA=\sqrt{(0 +3)^2 + (0 -6)^2} \\\\\\ BA=\sqrt{( 3 )^2 + ( -6 )^2} \implies BA=\sqrt{ 9 + 36 } \implies BA=\sqrt{ 45 }\implies BA\approx 6.7[/tex]

Answer:

28.4707 is rounded up to 28.5

Explanation: you have to round up any number higher than 5 to the number on the left

The solution to the equation and the explanation for each step is given below.

Given the equation, -3/4(x + 4) - 6 = 54, the steps to find the value of x is given below:

-3/4(x + 4) - 6 = 54 [given]

-3/4(x) -3/4(4) - 6 = 54 [Distributive property]

-3/4x + (-3) - 6 = 54 [Use multiplication to simplify]

-3/4x - 9 = 54 [Simplify using addition]

-3/4x = 63 [Add 9 to each side and simplify]

x = -84 [Multiply each side by -4/3 and simplify]

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The total cost  is  $616.98.

The amount he has left to spend is  $43.02.

The total cost to Douglas is the sum of the total cost of the thirteen doors and the sum of the six bags of fertilizers

The total cost of the thirteen doors = (cost of one door x total number of doors that would be bought)

$43.44 x 13 = $564.72

The total cost of six bags of fertilizers = (cost of one bag x total number of bags)

$8.71 X 6 = $52.26

Total cost = $564.72 +  $52.26 = $616.98

Amount he has left to spend = $660 - $616.98 = $43.02

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The set of points on this graph is a relation but not a function

We know that every function can be a relation but every relation cannot be a function.

A relation means the connection between the input and the output.

A function means that for every input there should only be one output.

Here, we have the data as:

(2,5), (1,2), (3,4), (3, 1), (6,5) and  (5,3)

We can say that it is a relation as for every input, there is an output.

But, it is not a function.

This is because the input 3 has 2 outputs as 1 and 4 which is not possible in a function.

Therefore, the set of points on this graph is a relation but not a function.

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Puja is not right to claim that any fraction can be thought of as a division problem and any division problem can be thought of as a fraction.

As seen by the definition of fraction, in terms of division problem, it involves only the the dividend and the divisor and not the quotient.

Hence, the two cannot be used inter-changeably, i.e., a fraction is not a division problem and vice versa.

Hence, Puja is not right to claim that any fraction can be thought of as a division problem and any division problem can be thought of as a fraction.

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Answer:

Step-by-step explanation:

yesterday

Answer:

V = 86.06

Step-by-step explanation:

V = u + 9.8t

V = 4.7 + 9.8(17)

V = 86.06

Answer:

2.89

Step-by-step explanation:

GPE = U * 1/2

GPE = 5.78 * 1/2

GPE = 2.89

The distance in feet between the ground and the top of the ladder  is 16.7 feet.

Let the distance in feet between the ground and the top of the ladder be x.

According to the given question.

Length of the ladder = 17 foot

The distance of the ladder from the base of the wall is 3 feet.

From the given data we can say that we have a right angle triangle in which the hypotenuse is the length of the ladder, base is the distance between the ladder and wall. And the distance between ground and ladder is our perpendicular.

Now according to the Pythagoras theorem,the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

Therefore,

17^2 = 3^2 + x^2

⇒ 289 = 9 + x^2

⇒ 280 = x^2

⇒ x = 16.7 feet

Hence, the distance in feet between the ground and the top of the ladder  is 16.7 feet.

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Answer:

The slope should be -1.

----------------------------------

Hope this helps!

Have a great day and God bless! :)

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

Work Shown:

[tex](x_1,y_1) = (1,-1) \text{ and } (x_2,y_2) = (2,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - (-1)}{2 - 1}\\\\m = \frac{-2 + 1}{2 - 1}\\\\m = \frac{-1}{1}\\\\\boldsymbol{m = -1}\\\\[/tex]

--------------------

Side notes:

Slope = rise/run

rise = change in y value = [tex]y_{2} - y_{1}[/tex]

run = change in x value = [tex]x_{2} - x_{1}[/tex]

Make sure you subtract in the same order each time.

The radius of the sprinkler is approximately 7 yards.

In this situation we find the case of a sprinkler that rotates until a complete revolution is done, that is, the area of complete circle is covered due to the rotation. That area can be found by using this formula:

A = (θ / 360) · π · r²

Where:

If we know that A = 171 yd² and θ = 360°, then the radius is approximately:

171 = π · r²

r = √(171 / π)

r ≈ 7.378 yd (approx. 7 yd)

The radius of the sprinkler is approximately 7 yards.

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Answer:

y = 12 + c

Step-by-step explanation:

Well, let's begin with what you're given, and that is that there are 12 clear ones, and there is a number of colored ones which succeeds that, which is represented by the variable c. So, we can use the equation:

y = 12 + c

To show the amount of colored ones that Vicky has in her collection, with y = number of colored crystals.

The linear function that gives the monthly cost E for x > 300 is given by:

E(x) = 44 + 0.04x.

A linear function is modeled by:

y = mx + b

In which:

When x > 300, we have that:

Hence the intercept is given by:

b = 8 + 0.12 x 300 = 44.

The slope is the cost per kWh of 4 cents, hence the function is:

E(x) = 44 + 0.04x.

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Step-by-step explanation:

it made £12,858.56.

the costs were £6,429.28

so, the profit was

12,858.56 - 6,429.28 = £6,429.28

since cost and profit are equal, that means they are both exactly half of the total income.

and half means 50%.

formally, to do the full % calculation :

100% = 12,858.56

1% = 100%/100 = 12,858.56/100 = 128.5856

how many % are 6,429.28 ?

as many % as times that 1% fits into 6,429.28 :

6,429.28 / 128.5856 = 50

so, it is 50%.

The actual width of Tyrone's patio using the scale drawing is 16 feet's

The scale from the backyard to the drawing is 2 ft to 1 inches.

The width of the patio on the drawing is 8 inches.

Therefore, the width of the Tyrone's actual patio is as follows;

Hence,

1 inches = 2 feet's

8 inches = ?

cross multiply

actual length of Tyrone's patio = 8 × 2

actual length of Tyrone's patio = 16 feet's

Therefore, using the scale drawing, the actual length of Tyrone's patio is 16 feet's.

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