The length of a rectangle exceeds its width by 4
inches, and the area is 60 square inches. What
are the length and width of the rectangle?

The differentiation of the function y = sin(2 sin⁻¹x) is; dy/dx = d√(1 - y²)]/(√1 - x²)

1) We want to differentiate the function;

[tex]\frac{\sqrt{x + 1} + \sqrt{x - 1}}{\sqrt{x + 1} - \sqrt{x - 1} }[/tex]

Differentiating this gives;

dy/dx = [tex]\frac{[(\frac{1}{2\sqrt{x + 1}} - \frac{1}{2\sqrt{x - 1}}) * \sqrt{x + 1} + \sqrt{x - 1}]}{(\sqrt{x + 1} - \sqrt{x - 1})^{2} }[/tex]

That can be simplified to get;

dy/dx = [tex]\frac{\sqrt{x + 1} + \sqrt{x - 1} }{(x - 1)\sqrt{x + 1} + (-x - 1) \sqrt{x - 1}}[/tex]

2) We want to differentiate the function;

y = sin(2 sin⁻¹x)

Differentiating the function gives;

dy/dx = [2cos(2 sin⁻¹x)]/√(1 - x²)

We know from trigonometric identity that;

cos²x = 1 - sin²x

Thus;

1 - sin²(2 sin⁻¹x) = cos²(2 sin⁻¹x)

But sin²(2 sin⁻¹x) = y²cos²(2 sin⁻¹x)

Thus; √(1 - y²) = cos(2 sin⁻¹x)

dy/dx = d√(1 - y²)]/(√1 - x²)

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The change is decay and the percentage rate of decrease will be 95%.

An exponential function is a function where a number is raised to the variable i.e. base is raised to the exponent times.

Here given the exponential function is y= 4300(0.042)ˣ

Now we have to identify if the change in exponential function represents growth or decay, and have to determine the percentage rate of increase or decrease.

Here in the exponential function, the base is less than 1 so the change is decay.

The equation represents exponential decay because the decay factor is lesser than 1.

The general form of the exponential equation is:

y(x)= a(1-r)ˣ such that r is the decay.

equating with the equation

y= 4300(0.042)ˣ

a= 4300

and 1-r=0.042

⇒r= 1-0.042

⇒r= 0.958

the perecentage of decay will be r*100= 0.958*100= 95%

Therefore the change is decay and the percentage rate of decrease will be 95%.

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Answer:

C, D and E

Step-by-step explanation:

The numbers which are greater than given number are : -2, -1.5, and 1.25.

A fraction represents a part of a whole or, more generally, any number of equal parts.

Here, given number: -7/3

or we can write this as -2.33

Now, Converting option fraction value into decimal

A). -3

B) -5.5

C). -2

D). -1.5

E). 1.25

On comparing options from the given value we get

the number which are greater than -2.33;   -2, -1.5, and 1.25

Thus, the numbers which are greater than given number are : -2, -1.5, and 1.25.

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The transformation is nonrigid because the segment lengths are not preserved.

The image related to the question cannot be found. However, the question can still be solved

The given parameters are:

From the question, we understand that the side lengths are not equal.

This means that the triangles are dilated.

And the scale factor of dilation is

Scale factor = 6/3 = 10/5 = 8/4

Scale factor = 2

The scale factor of dilation is 2

Dilation is a non rigid transformation.

Hence, the transformation is nonrigid because the segment lengths are not preserved.

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Answer:

The transformation is nonrigid because the segment lengths are not preserved.

Answer:

6.6

Step-by-step explanation:

the "mean" of a data set is what we commonly refer to as the average. We find this estimate of values by adding up all of the values of the data set, and then dividing by the number of values we added together.

{for example: the mean [average] of 1, 5, 6:

1 + 5 + 6 = 12

12 ÷ 3 [we have 3 numbers] = 4}

our values:

6.1 ; 5.9 ; 4.2 ; 5.9 ; 10.7

> 6.1 + 5.9 + 4.2 + 5.9 + 10.7 = 32.8

[we have 5 numbers]

32.8 / 5 =  6.56

when rounding a number, we look to the digit one place to the right. If it is greater than or equal to 5, we "round up" our digit [we move it up to the next digit]

if it is less than 5, we keep our digit the same

(the tenths place =  _  . _ _ _  ones. tenths)

so if we round 6.56 to the nearest tenth:

6.56

[6 > 5]

6.6

So, the mean of this data set rounded to the nearest tenth is 6.6

hope this helps!!

Answer:

The answer should be 3.3/4

Step-by-step explanation:

Answer:

1) X² + 1 - 2X

2).x² + 4 - 4x

3) 9 + x² - 6x

4) y² + 16 - 8y

5) 4x² + 1 - 4x

6) 9 + 4y² - 6y

7) 4x² + y²- 8y

8) 1 + 16a² - 8a

9) 9x²+ 4y² - 12xy

10) -x²- 16y² + 8y

11) -x²- 25y + 10xy

The measure of angle D to the nearest tenth of a degree is 47 degrees

This theorem is used to determine the measure of sides and angles of a triangle.

According to the theorem

tan theta = opp/adj = 1.055

theta = arctan(1.055)

theta = 46.53 degrees

Hence the measure of angle D to the nearest tenth of a degree is 47 degrees

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The statement is given as the distance between points (x₁, y₁) and (4, 8) is the square root of (x₁ - 8)² + (₁-4)². Hence, the given statement is false, it is  √[(x₁-4)² + (y₁-8)²].

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]  

WE have been given two points.

So,

The distance between points (x₁, y₁) and (4, 8)

D = √[(x-p)² + (y-q)²]  

D = √[(x₁-4)² + (y₁-8)²]  

But the statement is given as the distance between points (x₁, y₁) and (4, 8) is the square root of (x₁ - 8)² + (₁-4)².

Hence, the given statement is false, it is  √[(x₁-4)² + (y₁-8)²].

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The given expression is equivalent to [tex]\frac{p^{7}q}{160}[/tex]

What are indices?

An index is a small number that tells us how many times a term has been multiplied by itself.

The plural of index is indices.

Below is an example of a term written in index form :[tex]4^{3}[/tex]

4 is the base and 3 is the index.

We can read this as ‘4 to the power 3’

Another way of expressing [tex]4^{3}[/tex] is

4 x 4 x 4 = 64

Indices can be positive or negative numbers.

Given expression can be written as [tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]

Now to simplify the given fractional expression :[tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]

=   [tex]\frac{4^{-2}p^{8}q^{-2}}{10pq^{-3}}[/tex]                    By using the property of exponents is given by:

                                    [tex](a^{m})^{n}=a^{m n}[/tex]

=[tex]\frac{p^{7}q}{10 .16}[/tex]                              By using the property of exponents given by

                                       [tex]a^{m}a^{n}=a^{m + n}[/tex]  and  [tex]a^{-m}= \frac{1}{a^{m}}[/tex]

= [tex]\frac{p^{7}q}{160}[/tex]

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Answer:

To order decimals, you first need a range of values.

Step-by-step explanation:

For example, if there are 5 values: 0.25, 0.87,0.19,0.89 and 0.98

First, look at the first digit after the decimal. The smallest digit is the smallest so far. In this case, it is 0.19 as '1' was the smallest digit. Second would be 0.25 because 2 is the second smallest digit here.

Now, we have 3 remaining numbers: 0.87, 0.89 and 0.98

You can notice that both 0.87 and 0.89 have the same first digit after the decimal.

Do fix this problem, look at the second digit and decide the smallest one. In this case, it is 0.87.

This means the order will go like this if it is smallest to largest: 0.19, 0.25, 0.87, 0.89, 0.98.

If it is largest to smallest, do it the other way around.

Hope this helped!

Answer:

See below ~

Step-by-step explanation:

a) Forming the equation :

⇒ We start with a number, x

⇒ Now we double it so : 2(x) = 2x

⇒ Then we add 11 to it : 2x + (11) = 2x + 11

⇒ It is equal to 25 : 2x + 11 = 25

b) Solving the equation :

Subtract 11 from both sides :

⇒ 2x + 11 - 11 = 25 - 11

⇒ 2x = 14

Divide 2 on both sides :

⇒ 2x/2 = 14/2

⇒ x = 7

Let unknown number be x

Double it

Add eleven

You got 25

Lets solve the equation

Using translation concepts, it is found that the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

From triangle X′Y′Z′ to triangle X′′Y′′Z′′, the rule is given by:

(x,y) -> (x, -y)

Hence the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.

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Step-by-step explanation:

here I have done you can check it out

Answer:

D

Step-by-step explanation:

The vertex is at (-2,4), so substituting into vertex form, only C and D match.

Also, the graph opens down, so the coefficient of x² is negative.

This eliminates C, leaving us with D

Answer:

⇒   Let marked price be Rs.x.

⇒  Discount = 20% of marked price.

⇒  Discount=  

100

20

​  

×x=  

100

20x

​

⇒  Selling price = Marked price - Discount.

⇒  192=x−  

100

20x

⇒  192=  

100

80x

⇒  x=  

80

19200

=Rs.240

Answer:

S.p = 992

discount = 20%

marked price = S. p + discount

= 992 + 20/100*992

= 992 + 198.4

= 1190.4

Answer:

b = 81

Step-by-step explanation:

given a² and b are directly proportional then the equation relating them is

a² = kb ← k is the constant of proportionality

to find k use the condition a = 2 when b = 9 , then

2² = 9k

4 = 9k ( divide both sides by 9 )

[tex]\frac{4}{9}[/tex] = k

a² = [tex]\frac{4}{9}[/tex] b ← equation of proportion

when a = 6 , then

6² = [tex]\frac{4}{9}[/tex] b

36 = [tex]\frac{4}{9}[/tex] b ( multiply both sides by 9 to clear the fraction )

324 = 4b ( divide both sides by 4 )

81 = b

Answer:

i's 20 because it seems that it is the most successful

Answer:

second branch..................

Answer:

b

Step-by-step explanation:

eq y=x+4 is for x>=2 inclusive

Answer:

Answer x=2/3, -1
Option B

Step-by-step explanation:

Answer:

B) x =( 2/3, -1)

Step-by-step explanation:

Equation:

[tex]6x {}^{2} + 2x = 4[/tex]

Solution:

We know that,

[tex] \rm \: Quadratic \: formula (x)=\cfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

According to the problem,

Plugging them on the formulae,we obtain,

Choice B is accurate.

Answer:

They are parallel because their slopes are equal.

Step-by-step explanation:

See attached image.

There are 315 number of different pairs

The given parameters are:

Men = 15

Women = 21

The number of different pairs is calculated as:

Pair = Men * Women

So,we have:

Pair = 15 * 21

Evaluate

Pair = 315

Hence, there are 315 different pairs

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Step-by-step explanation:

1)Take the time he is traveling divided by the speed to get the time.

2)Subract the time you have got from the average time,then subtract the average distance from the traveling distance,then divide the two to get the speed.

3)Take the total distance, divide it by the total time to get the average speed.

Answer:

Since both of the coordinates are positive, we have:

Find the hypotenuse of the right triangle using values of both legs:

Find sine:

Find cosine:

The simplest form of the square root of 48 is 4√3

Given the following rational function √48

The correct prime factorization is given as;

√48 = √3×16

√48  = √16 × √3

Since the square root of 16 is 4, hence;

√48 = 4√3

Hence the simplest form of the square root of 48 is 4√3

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The simplified product of [tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5}[/tex] is [tex]\frac{(b+3)}{2}[/tex]

The products can be simplified as follows;

Multiplying fraction,

[tex]\frac{x}{y} . \frac{a}{b} = \frac{xa}{yb}[/tex]

Therefore,

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)}[/tex]

Hence,

Let's reduce the fraction by dividing

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)}[/tex]

Therefore,

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b}[/tex]

Hence,

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b} = \frac{b+3}{2}[/tex]

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Answer:

A, b+3/2

Step-by-step explanation:

Answer:

-32/21

Step-by-step explanation:

First, we can convert -0.35 into a fraction: -35/100, which could be further simplified to -7/20.
Dividing a fraction by another is the same thing as multiplying a fraction by the reciprocal (denominator over numerator) of the fraction. Therefore, we can rewrite this expression as: 8/15 * -20/7
To find the answer to that, you simply multiply the numerators together and the denominators together separately. The final answer is -32/21.

Answer:

-1 11/21

First step:

First, you change the decimal into a fraction. To do that you look at the decimal place at the end of -0.35. The decimal place is hundredths. That means the fraction form of -0.35 is -35/100.

Now to simplify it just find out what both the numbers can be divided by. In this case, 35 and 100 can be divided by 5. If you divide them both by 5 you get -7/20

Fraction form: -7/20

Second step:

Now you just plug it in to the equation.

8/15÷(-7/20)

To solve this you need to change it to multiplication and flip the second fraction.

8/15×(-20/7)

Final step:

Now you multiply the fractions.

8/15×(-20/7)= -32/21 or -1 11/21

Final answer: -1 11/21

Answer:

[tex]\fbox {Perimeter = 37.92}[/tex]

Step-by-step explanation:

Finding the missing side :

⇒ Take the tan value of the listed angle

⇒ tan 60° = √3 = 6/x

⇒ x = 6/√3 × √3/√3 = 2√3 = 2(1.73) = 3.46

Solving :

⇒ Perimeter = 10 + 2(6 + 3.46)

⇒ Perimeter = 10 + 2(9.46)

⇒ Perimeter = 19 + 18.92

⇒ Perimeter = 37.92