Find the derivative.
y = x tanh^-1(x) + ln (√( 1 −x2))

Step-by-step explanation:

let, the ratio of boys and girls be 6x:5x

total student=550

now,

Answer:

hope it helps you have a good day

The sum of the greatest common factor (HCF) and least common multiple (LCM) of 3 and 6 is 9.

The H.C.F. defines the highest common factor present in between given two or more numbers, while L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers.

factors of 3 are 1 and 3

factors of 6 are 1, 2, 3, and 6

3 = 1 × 3

6 = 2 × 3

LCM = 2 × 3

LCM = 6

HCF = 3

sum of HCF and LCM of 3 and 6 = 3 + 6

sum of HCF and LCM of 3 and 6 = 9

Therefore, 9 is the sum of the greatest common factor HCF least common multiple LCM of 3 and 6.

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1) The formula for area is,

⇒ Area of rectangle = Length × Width

And, The formula for perimeter is,

⇒ Perimeter = 2 (Length + width)

2) An expression for the length of the south side of the yard is,

⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)

3) The simply expression for the length of the south side of the yard is,

⇒ Length =  2x² - 2x + 5

4) An expression for the perimeter of the pool area is,

⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )

5) 5) The simply expression for the perimeter of the pool area is,

⇒ Perimeter = 2x² + 16x + 36

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The Johnson family is redesigning their backyard this spring. They want to include a sandbox area, a swing set area, a patio area, a pool area and a grill area.

Now,

1) The formula for area is,

⇒ Area of rectangle = Length × Width

And, The formula for perimeter is,

⇒ Perimeter = 2 (Length + width)

2) An expression for the length of the south side of the yard is,

⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)

3) The simply expression for the length of the south side of the yard is,

⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)

                = 5x + 2 + x² - 9 + x² - 7x + 12

                = 2x² - 2x + 5

4) An expression for the perimeter of the pool area is,

⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )

5) The simply expression for the perimeter of the pool area is,

⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )

                    = 2 (x² + 10 + 8x + 8)

                    = 2 (x² + 8x + 18)

                    = 2x² + 16x + 36

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Answer:

6

Step-by-step explanation:

delta math

The required measure of the other leg will be 6 cm in the given right triangle.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

We have been given that one of the legs of a right triangle measures 8 cm and its hypotenuse measures 10 cm.

Let the measure of the other leg would be x cm.

According to Pythagoras's theorem,

⇒ c² = a² + b²  ....(i)

As per the given question, we have

c = 10cm, a = 8 cm and b = x

Substitute the values in the above formula, and solve for x

⇒ 10² = 8² + x²

⇒ 100 = 64 + x²

⇒  x² = 100 - 64

⇒  x² = 36

⇒  x² = 6²

⇒  x = 6

Therefore, the required measure of the other leg will be 6 cm in the given right triangle.

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Answer:

81π sq. in.

Step-by-step explanation:

A = 36π = [tex]\pi r^{2}[/tex]

[tex]r^{2}[/tex] = 36

r = 6 = radius of the mirror

Add 3 to the 6 to get the radius(R) including the frame

R = 9

A = [tex]\pi 9^{2}[/tex] = 81π sq. in.

As 200 is not a perfect square it is not possible to increase the dimensions of the park by the same number of miles.

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

We know the area of a rectangle is (length×width).

Given, Park rangers plan to expand the area of the park to 506 square miles.

Currently, the park has an area of (18×17) = 306 square miles.

Therefore, The amount of square miles they need to increase is (506 - 306)

= 200 miles.

Now, They also want to increase the length and the width by the same amount but 200 is not a perfect square so it is not possible to increase the dimensions by the same amount.

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No, It is not possible to have a complex number in the form of a + bi when b = 0.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Complex number.

It is in the form of a + ib.

Where a and b are real numbers.

Now,

If b = 0 then we can not have a complex number.

Example:

a + bi

a = 1 and b = 0

1 + 0i = 1 which is not a complex number.

In order to have a complex number a can be any real number and 0 but b  can not be a zero.

Thus,

It is not possible to have a complex number in the form of a + bi when

b = 0.

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Answer:

X=32, y=-5

Step-by-step explanation:

Answer: -37

Step-by-step explanation: -11-26

Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method presented problem.

The term "unitary" refers to a single or separate unit or variable . As a result, this strategy's objective is to establish values in terms of a single unit. For instance, if a car travels 44 kilometres on two litres of gas, the unitary technique can be used to determine how many kilometers it will drive on one.

Here,

Given: Each box of bandages has three packs, with two bandages in each pack.

Now, determine how many bandages there are in two boxes.

Therefore, we solve using the unitary method:

One pack contains two bandages.

In 3 packs, there are therefore = 2*2 = 6 bandages.

One box contains three packs as stated.

Consequently, we multiply 2 by 6 to obtain the bandages in 2 boxes:

=> 2 * 6 = 12

Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method's presented problem.

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The student is testing each soil's permeability, and soil X is more permeable than soil Y. The correct option is A.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that has never been tried before. Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.

Porosity can be defined as the quality of the material having pores or holes. The permeability can be defined as the state or quality of a material that allows liquids or gases to pass through it.

The soil which does not hold much water can be considered of high porosity and high permeability. As it is only possible if the soil has a large number of pores and it is not in compact form.  

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Answer:

[tex]b = 90[/tex]

[tex]d = 100[/tex]

[tex]c = 80[/tex]

Step-by-step explanation:

The problem is asking for the values of the variables [tex]b[/tex], [tex]c[/tex], and [tex]d[/tex] in the given parallelogram with angles [tex]d\textdegree[/tex], [tex]c\textdegree[/tex], [tex](b-10)\textdegree[/tex], and [tex](b+10)\textdegree[/tex].

To solve for these variables, we can construct three equations using the knowledge that any two adjacent angles of a parallelogram are supplementary (their measures add to 180º).

The first equation shows that the top two angles are supplementary:

[tex]d\textdegree + c\textdegree = 180\textdegree[/tex]

The second equation shows that the bottom two angles are supplementary:

[tex](b-10)\textdegree + (b+10)\textdegree = 180\textdegree[/tex]

The third equations shows that the left two angles are supplementary:

[tex]d\textdegree + (b-10)\textdegree = 180\textdegree[/tex]

First, we can solve for [tex]b[/tex] in the second equation using simple algebraic manipulation.

[tex](b-10)\textdegree + (b+10)\textdegree = 180\textdegree[/tex]

[tex](b+b)\textdegree + (10-10)\textdegree = 180\textdegree[/tex]

[tex]2b\textdegree = 180\textdegree[/tex]

[tex]b\textdegree = 90\textdegree[/tex]

[tex]b = 90[/tex]

Using this [tex]b[/tex]-value, we can solve for [tex]d[/tex] by rewriting the third equation, plugging [tex]90[/tex] in for [tex]b[/tex]:

[tex]d\textdegree + (b-10)\textdegree = 180\textdegree[/tex]

[tex]d\textdegree + (90-10)\textdegree = 180\textdegree[/tex]

[tex]d\textdegree + 80\textdegree = 180\textdegree[/tex]

[tex]d\textdegree = 100\textdegree[/tex]

[tex]d = 100[/tex]

Finally, we can solve for [tex]c[/tex] in the first equation by plugging [tex]100[/tex] in for [tex]d[/tex]:

[tex]d\textdegree + c\textdegree = 180\textdegree[/tex]

[tex]100\textdegree + c\textdegree = 180\textdegree[/tex]

[tex]c\textdegree = 80\textdegree[/tex]

[tex]c = 80[/tex]

Answer:

Way too many

Step-by-step explanation:

(92)

Answer:

12,000 Litres

Step-by-step explanation:

From the measurements given in the figure, we can understand that the tank is cuboidal in shape.

Thus,

Volume of a cuboid = Width*Length*Height

Volume of Oil in the tank = 5 * 2 * 1.2

                                          = 12 cubic metres

1 cubic metre = 1000 litres

12 cubic metres = 12,000 litres

Hope it helps (:

Answer:

B

Step-by-step explanation:

1500 * 0.07 = 105

105 + 1500 = 1605

Answer:

5, 9, 13, 17, 21, 25

Step-by-step explanation:

Given a₁ = 5 and d = 4

Add d = 4 to the previous term, that is

a₁ = 5

a₂ = a₁ + 4 = 5 + 4 = 9

a₃ = a₂ + 4 = 9 + 4 = 13

a₄ = a₃ + 4 = 13 + 4 = 17

a₅ = a₄ + 4 = 17 + 4 = 21

a₆ = a₅ + 4 = 21 + 4 = 25

Answer:

C

Step-by-step explanation:

q3 - q1

7 -1 = 6

Answer:

6 is the IQR

Step-by-step explanation:

To determine the IQR, you need to evaluate the box. The first quartile starts at 1, and the third quartile ends at 7. To calculate IQR, subtract Q1 (1) from Q3 (7). So it would be 7 - 1 = 6

So your answer is 6.

Amelie needed 335 cups of flour for the recipe.

Given data :

She is making 2 1/2 or 2.5 times the original recipe.

Cups in original recipe= 134 cups

cups Amelie will need= 2.5 × 134

                                     = 335 cups

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Answer:

32.10

Step-by-step explanation:

25% of 62.80 is 15.70

62.80- 15.70 = 47.10

47.10- the 15 dollar giftard = 32.10

(Hope this helps! Please ask questions in the comments) :D

Answer:

[tex] log_{s}6 - log_{s}2 \\ = log_{s}( \frac{6}{2} ) \\ = log_{s}3[/tex]

Answer:

isosceles triangles have two congruent acute angles

Answer:

4 sweets per friend

Step-by-step explanation:

so first you want to minus 10 sweets since she ate 10 leaving her with 40 sweets. then she gives 8 sweets to her brother leaving her with 32 sweets left. If you divide the remaining sweets ( 32 ) by 8 you get 4 sweets per friend

Step-by-step explanation:

S = { 1, 2, 3, 4, 5, 6 7, 8 }

n ( S ) = 8

Let A be the event of getting 4,

A = { 4 }

n ( A ) = 1

P ( A )

= n ( A ) / n ( S )

= 1 / 8

Therefore, the probability of spinning a 4 is 1 / 8.

S = { A, B, A, C, A, B }

n ( S ) = 6

Let Y be the event of getting C,

Y = { C }

n ( Y ) = 1

P ( Y )

= n ( Y ) / n ( S )

= 1 / 6

Therefore, the probability of spinning a C is 1 / 6.

Answer:

Step-by-step explanation:

Let the number be x then,

1) 4 * x + 11

2) 8 * (x + 7)

3) 2x - 1

4) x+ 3x

5) 5x + 12

6) 16 + 1 + x = 17 + x

7) 20 - ( x - 5) = 20 - x + 5 = 25 - x

8) x - 6 + 15 = x +9

Answer:

Step-by-step explanation:

1) The domain is related to the behaviour of the x

the graph started when x is -11 and finish when x is 1

so

D : [-11 ; 1]

or -11 ≤x ≤ 1

the range is related to the behavior of y

the graph start when y is -7 and finish when y = 0

Range : [-7;0]

or -7≤ y ≤ 0

The equation is 80x + 1200 = 3800. And the numbers of at least 30 recliners and 32 sofas the company can have in the shipment.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A company is loading recliners and sofas onto a trailer that has a volume of about, 3800 cubic feet.

Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet.

The company wants the shipment to have at least 30 recliners and more than 25 sofas.

The equation that represents the situation is,

80x + 40y = 3800,

where x is the volume of a sofa and y is the volume of a recliner.

If y = 30 then,

80x + 1200 = 3800

80x = 2600

x = 2600/80

x = 32.5

x ≈ 32

Therefore, 30 recliners and 32 sofas.

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