What is the next fraction in this sequence? Simplify your answer.

9
14
,
4
7
,
1
2
,
3
7
,

Differentiation of the function [tex]f(x) = (-x^{2} - 4)x^{5}[/tex] with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].

What is the differentiation of the function?

A function differentiation is a method of displaying the rate of change of a function at a given moment. It is the slope of the tangent line at a point on a graph for real-valued functions.

We have,

                                     [tex]f(x) = (-x^{2} - 4)x^{5}[/tex]

By simplifying the given function, we get

                                      [tex]f(x) = -x^{7} - 4x^{5}[/tex]

Now, we will differentiate the given function with respect to [tex]x[/tex].

                                    [tex]\frac{d}{dx} f(x) = \frac{d}{dx} (-x^{7} - 4x^{5})[/tex]

                                    [tex]f'(x) = \frac{d}{dx} (-x^{7}) - \frac{d}{dx} (4x^{5}))[/tex]

                                     [tex]f'(x) = -7x^{6} - 20x^{4}[/tex]

Hence, differentiation of the given function with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].

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The derivative of the natural log function y = e^(-1/x^2) is

The given function is

y = e^(-1/x^2)

The given function is rearranged as

y = e^(-1/x^2) = e^u such that u = (-1/x^2)

Applying chain rule

y = e^u

y' with respect to u = e^u

u = (-1/x^2) = -x^(-2)

u' with respect to x = 2x^(-3)

(y' with respect to u) *  (u' with respect to x)

= e^u * 2x^(-3)

plugging in the value of u

=  e^(-1/x^2) * 2x^(-3)

= 2x^(-3)e^(-1/x^2)

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The area of the circle with the circumference 18 units is 25.80 square units

The given parameters are

Circumference = 18 units

As a general rule, circumference are represented by the variable C

So, we have the following representation equation

C = 18

The circumference of the circle can be calculated as

C = 2πr

Next, we substitute the value of the variable C in the above equation

i.e. C = 18

So, we have the following equation

2π * r = 18

Divide both sides by 2π

r = 9/π

The area of the circle can then be calculated using the following area formula

A = πr²

Next, we substitute the value of the variable r in the above equation

i.e. r = 9/π

A = π * (9/π)²

Evaluate the exponents

This gives

A = π * 81/π²

Evaluate the products

So, we have

A = 81/π

As a general notation, π = 3.14

So, we have the following equation

A = 81/3.14

Evaluate the quotient

A = 25.80

Hence, the area is 25.80 square units

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Answer:

Step-by-step explanation:

1. List out the numbers and divide

-1/6/2/9=

2. In division for fractions, the number or numbers on the right of the division side flip and change to multiply!

-1/6/2/9= -1/6*9/2= -9/12

3. Simplify!

-9/12= -3/4

Answer:

-3/4

Step-by-step explanation:

so you leave -1/6 but then you change the sign to multiply and the other fraction change it so if you had 2/9 it will be 9/2

so we get -1/6×9/2.

if you don't know how to multiply fractions i can explain just ask.

Answer:

Step-by-step explanation:

Thanks

For the given points (6, y) and (-8, 4) having slope = 1/7 the value of y = 10.

What is the slope of a line?

A line's slope, also known as its gradient, is defined as the value of a line's steepness or direction in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.

If P(a, b) and Q(c, d) are two given points on a coordinate plane, then the slope of line PQ can be computed using the formula

                      [tex]Slope(m)=\frac{d - b}{ c - a}[/tex]

The given points are (6, y) and (-8, 4).

and the slope of the line is given as m = 7.

By using the slope of a line formula, we get

                       [tex]m = \frac{8-y}{-8-7}\\\\ \frac{1}{7}= \frac{8-y}{-8-7}\\\\\frac{1}{7}= \frac{8-y}{-14}\\\\\\8-y=-2\\y=8+2\\y=10[/tex]

Hence,  the value of y is 10.

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Yes, Wilson is right since "negative numbers" don't exist when you find the absolute value.

Therefore, Wilson is correct as there is no negative term in absolute value.

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The require angle of x is 52.4°

Given is a quadrilateral

The given diagonal divides the quadrilateral in two parts

the first part is a right angled triangle

Thus to find the side BD

we will use the Pythagoras theorem ;

So according to this theorem

AB² + AD² = BD² [ because BD is the hypotenuse ]

Given AB = 8 cm and AD = 6 cm

8² + 6² = BD²

this implies 64 + 36 = BD²

100 = BD which implies BD = 10 cm

To find x

we know that in triangle BCD

BD = 10 cm and CD = 13 cm

tan theta = [tex]\frac{13}{10}[/tex]

this means theta = [tex]tan^{-1}[/tex] [tex]\frac{13}{10}[/tex]

theta = 52.4°

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Answer:

39.07

use pythagros to find bd then use the sine rule substitute in the values

bd=10

beacuse a²+b²=c²

substitute in 8²+6²=c²

Answer: They resold them for $30 more than the original price.

Answer: 37.5%

Step-by-step explanation:

$80 - $50 = $30,

$30/$80 = 0.375 > 37.5%

x = 32

Step-by-step explanation:

[tex]{ \tt{p(x) = \frac{x + 7}{3} }}[/tex]

If p(x) = 13, then

[tex]{ \tt{13 = \frac{x + 7}{3}}} [/tex]

[tex]{ \tt{13 \times 3 = x + 7}}[/tex]

[tex]{ \tt{39 = x + 7}}[/tex]

[tex]{ \tt{39 - 7 = x}}[/tex]

[tex]{ \red{ \boxed{ \blue{ \sf{x = 32}}}}}[/tex]

Answer:

78°

Step-by-step explanation:

∠M=∠Q

∠N=∠S

∠P=∠T

Answer:

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

Given

We know that corresponding angles of congruent triangles are congruent (vertices in same order as name of triangle):

Angle S corresponds to angle N, hence their values are equal:

I hope this helps. Have a great rest of your day!

The speed of the car is 40mph

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

Distance covered by car = 160 miles

distance covered by plane = 840 miles

let the time taken to cover 160 miles by car be x

speed of car = 160/x

speed of plane which is 170mph faster than speed of car = 170 + 160/x

time taken to cover 840 miles by plane,

time = distance/speed = [tex]\frac{840}{170 + \frac{160}{x} }[/tex]

By simplifying,

time taken by plane = [tex]\frac{840x}{170x + 160}[/tex]

since it takes same time for both to get to their destination,

Then,

x =  [tex]\frac{840x}{170x + 160}[/tex]

By cross multiplying

x( 170x + 160) = 840x

divide both sides by x, it reduces to

170x + 160 = 840

170x = 840 - 160

170x = 680

x = 680/170

x = 4

Speed of car = 160/x

speed of car = 160/4

speed = 40mph

In conclusion, the care moves at the speed of 40mph

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The range of the given function is:

Range: {-9,-3,0,5,7}

We are given ordered pair of set (x,y)

where, first value of ordered pair shows domain of function and second value of ordered pair shows range.

Range: It is output value of function.

Ordered pair: {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}

We can write as:

f(-2)=0,     f(-4)=-3,   f(2)=-9,   f(0)=5,    f(-5)=7

The values of f(x) are the range of function.

We will make a set of second value of all ordered pair of given set.

Range: {-9,-3,0,5,7}

Hence we get the required range of the function.

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Step-by-step explanation:

that is the same as calculating the perimeter of the rectangle (the way 1 time around the rectangle).

the perimeter of a rectangle is

2×length + 2×width

in our case that is

2×11 + 2×4 = 22 + 8 = 30 ft

the stripping costs $5 per foot, and we have 30 ft.

so, the total costs are

5 × 30 = $150

Applying angle relationships, the measures of the numbered angles are:

m∠1 = 90°

m∠2 = 68°

m∠3 = 112°

m∠4 = 112°

m∠5 = 68°

m∠6 = 56°

m∠7 = 124°

m∠8 = 124°

To calculate angle measurements that are formed by a transversal and parallel lines, we can apply the knowledge of the angle relationships that exist between the angle pairs in concerned. Some angle relationships are:

m∠1 = right angle [corresponding angles is the angle relationship]

m∠1 = 90°

m∠2 = 180 - m∠1 - 22 [triangle sum theorem]

Substitute

m∠2 = 180 - 90 - 22

m∠2 = 68°

m∠3 = 180 - m∠2

Substitute

m∠3 = 180 - 68

m∠3 = 112°

m∠4 = m∠3

m∠4 = 112°

m∠5 = 180 - m∠4

m∠5 = 180 - 112

m∠5 = 68°

m∠6 = 1/2(180 - m∠5)

m∠6 = 1/2(180 - 68)

m∠6 = 56°

m∠7 = 180 - 56

m∠7 = 124°

m∠8 = m∠7 [alternate interior angles is the angle relationship]

m∠8 = 124°

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Answer:

Her sister has 9032 beads

Step-by-step explanation:

All you have to do is Tina's beads plus the extra number of beads that her sister has

5345 + 3687 = 9032

There are '5n' computers set up if they each set up the same number of computers.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Ching and his 4 brothers set up computers at their family company.

Now,

Let the number of computers for each person = n

The total number of persons = 5

So, We can formulate;

⇒ The number of computers set up if they each set up the same number of computers = 5n

Thus, There are '5n' computers set up if they each set up the same number of computers.

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The height of the cone given the volume of 2411.52 cubic millimeters and a radius of 12 millimeters is 16 millimeters.

Volume of a cone = 1/3πr²h

2411.52 = 1/3 × 3.14 × 12 x 12 × h

2411.52 = 1/3 × 3.14 × 144h

2411.52 = 452.16h / 3

7,234.56 = 452.16h

h = 7,234.56 / 452.16

h = 16 millimeters

In conclusion, the height of the cone is given by 16 milliliters.

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The mean score of all the students is 79.5 and it is round off into one decimal place.

Mean

Mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Given,

In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test and their mean score is 67.7.

Here we need to find the mean score of all students.

In order order to find the mean score, we have to calculate the total score of the students by multiplying the mean score by the number of students then we get,

=> 30 x 87.7 = 2631

Similarly, the total score for 21 students is,

=> 21 x 67.7 = 1421.7

So, the 51 students, cumulative score is

=> 2631 + 1421. 7 = 4052.7

Therefore, the mean score is calculated as,

=> 4052.7/51

=> 79.464

When we round off the value into one decimal place then we get

=> 79.5

Therefore, the mean value of all the students is 79.5.

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Answer:

Step-by-step explanation:

201.06ft²

Answer:

Step-by-step explanation:

Step-by-step explanation:

A boy paid $11 for a bottle with a cork. A bottle costs $10 more than a cork. How much does a cork cost?

cork: c

bottle: 10c

c + 10c = 11

11c = 11

c = $1

A cork costs $1

Answer:

124 km

Step-by-step explanation:

Wanda walked 43.4 km in 14 days. At this rate, how far would she walk in 40 days? She would walk__km in 40 days.

First, figure km per day:

43.4/14 = 3.1 km per day

3.1 * 40 = 124 km

She would walk 124 km in 40 days.

The required length of the pieces is given as 20 ft, 16ft, and 14ft.

Given that,
An electrician cuts a 50 ft piece of wire into 3 pieces. The first piece is 4 ft longer than the second piece and the third piece is 2 feet shorter than the second piece. How long are the pieces is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
according to the question,
Length of the first, second, and third  be x, y and z,
According to the question,
x + y + z = 50 - - - - - - - - (1)
x = y + 4
z = y - 2
put x and z in equation 1
y + 4 + y + y - 2 = 50
3y = 50-2
y = 48/3
y = 16 ft
Now,
x = 16 + 4 = 20 ft
z = 16 - 2 = 14 ft

Thus, the required length of the pieces is given as 20 ft, 16ft, and 14ft.

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Answer:

5736

Step-by-step explanation:

calculator

Answer:          5736

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

I hope this helps!

Answer: x < 3

Explanation: Once you reach step 3, you divide -2 on both sides. -2x cancels out, and -6 divided by -2 is 3

Answer:

A:

Answer:65Step-by-step explanation:C^2= A^2 + B^2C^2 = (60)^2 + (25)^2 C^2 = 4225Take the square root of CC = 65