If f(x) = 5x, what is f¹(x)?

i) The coefficients of the equation of the line are a = 20 / 3 and b = 160 / 21.

ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.

iii) The x-intercept and y-intercept of the line are (- 3, 0) and (0, - 21 / 8).

iv) Two alternative solutions of the equation of the line are 20 · x + (160 / 7) · y = - 60 and 140 · x + 160 = 420.

In this problem we know that form of an equation of the line and two points, on which the line pass through. i) We determine the values of the coefficients a and b by solving the following system of linear equations:

5 · a - 7 · b = - 20

- 3 · a = - 20

Whose solution is a = 20 / 3 and b = 160 / 21.

ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.

iii) Now we find the coordinates of the intercepts of the line:

x-Intercept

(20 / 3) · x = - 20

x = - 3

y-Intercept

(160 / 21) · y = - 20

y = - 21 / 8

iv) We can find two alternative solutions by using multiples:

20 · x + (160 / 7) · y = - 60

140 · x + 160 = 420

To learn more on equations of the line: https://brainly.com/question/21511618

#SPJ1

Answer:

- (2x^2 - 13x + 6)

The above expression is in brackets and a negative sign is outside of the brackets. This means that when expanding the expression, we have to multiply each number with the negative sign (each number would switch their signs to the opposite one). Therefore, 2x^2 becomes -2x^2, -13x becomes 13x and 6 becomes -6.

The direction does the parabola open is right. Option C

It is important to note that the general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h

where

⇒ (h , k) denotes the vertex.

Also, the standard equation of a regular parabola is y² = 4ax.

From the equation given , we have

We know that when the vertex of the parabola is (0, 0) and the directrix is x = - a, the parabola will have the form;

y² = 4ax

It is important to note that ;

From this, we can see that the parabola would open in the right direction

Thus, the direction does the parabola open is right. Option C

Learn more about a parabola here:

https://brainly.com/question/4061870

#SPJ1

The amount of water in each mug is 2 / 5 litres

The water bottle has 4/5 litres of water.

The litre of water is poured equally in 2 mugs.

Therefore, the amount of water in each mug can be calculated as follows;

amount of water in each mug = 4 / 5 ÷ 2

amount of water in each mug = 4 / 5 × 1 / 2

amount of water in each mug =  4 / 10

amount of water in each mug = 2 / 5 litres

learn more on litres here: brainly.com/question/3920797

#SPJ1

The series converges to  1/(1-9x) for -1/9<x<1/9                  

Given the series is  ∑ [tex]9x^{n} x^{n}[/tex]

We have to find the values of x for which the series converges.

We know,                

∑ [tex]ar^{n-1}[/tex]    converges to  (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, ∑ [tex](9x)^{n}[/tex] is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for -1/9<x<1/9

And geometric series converges to a/(1-r)

Here, a = 1 and r = 9x

Therefore, a/(1-r) = 1/(1-9x)

Hence, the given series converges to   1/1-9x  for  -1/9<x<1/9

For more information about convergence of series, visit

https://brainly.com/question/15415793

#SPJ4

Answer:

Rs 400 is the cost of an article for Ram.....

Step-by-step explanation:

X - cost of an article for Ram

120% = 1.2

1.2*X - Ram’s selling price

5% = 0.05

1.2*X*0.05 - Shyam selling price

1.2*X*0.05 = 504

X = Rs 400 is the cost of an article for Ram

Hope it Helps!!!!

The side length of the original field is 19 feet.

What is square?

Suppose the original square is x feet wide. Since its the length and width are the same,

So, length of side of enlarged field = x+5

Area of new enlarged field =  side²  = ( x + 5 )²

So, the enlarged shape would be = ( x + 5 ) ( x + 5)

  Then ,  ( x + 5 ) ( x + 5) = 576

               ( x + 5 )²= 576

                x + 5 = √576

               x + 5  = 24

                 x = 24 - 5 ⇒ 19

Hence, The side length of the original field is 19 feet.

Learn more about square

brainly.com/question/22964077

#SPJ4

Answer:

5) 26

6) 18

Step-by-step explanation:

Substitute the value of the variables in the expression and evaluate.

x = 2 ; y = -3 and z = 1

Absolute value:  Absolute value of a real number is the non negative a value of x without regard its sign.

Example: I-3I = 3

               I 3I = 3

5) 24 + Ix - 4I =24 + I 2 - 4I

                      = 24 + I-2I

                      = 24 + 2

                      = 26

6) 13 + I 8 +y I = 13 + I 8 + (-3)I

                       = 13 + I 5 I

                       = 13 + 5

                       = 18

Under the assumption of simple harmonic motion, the package will be at x = 4.50 centimeters at a time of 0.805 seconds.

Simple harmonic motion is a kind of periodic motion represented by sinusoidal functions. Physically speaking, it is a good approximation for periodic motion due to small perturbations and with absence of frictions and viscous forces on the system.

The position of an object under simple harmonic motion is described by the following equation:

x (t) = A · cos (2π · t / T + Ф)      (1)

Where:

If we know that T = 5 s, A = 8.50 cm, Ф = 0 rad and x = 4.50 cm, then the time when the package will reach x = 4.50 cm is:

4.50 = 8.50 · cos (2π · t / 5)

9 / 17 = cos (2π · t / 5)

0.322π = 2π · t / 5

t = 0.805 s

Under the assumption of simple harmonic motion, the package will be at x = 4.50 centimeters at a time of 0.805 seconds.

To learn more on simple harmonic motion: https://brainly.com/question/17315536

#SPJ1

Answer:

x > 6

Step-by-step explanation:

2x - 7 > 5

2x > 5 + 7

2x > 12

x > 6

Answer:[tex]\Large\boxed{First~choice.~y\leq \frac{1}{2}x+2 }[/tex]

Step-by-step explanation:

Given function form

Point-Slope form : y = mx + b

Given the information from the graph

Since the graph crosses (0, 2), b = 2

Find the slope

Choose any two points from the graph

(x₁, y₁) = (0, 2)

(x₂, y₂) = (2, 3)

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (3 - 2) / (2 - 0)

Slope = 1 / 2

m = 1 / 2

Therefore, the equation form of the inequality is y = (1/2)x + 2

Since it is a solid line, the values on the line are also included. Thus, it must be either greater than or equal to, or less than or equal to.

The shaded region is below the solid line, therefore, it is ≤

Therefore, the inequality is [tex]\Large\boxed{y\leq \frac{1}{2}x+2 }[/tex]

To double-check the sign, we can substitute (0, 0) into the inequality to see whether it is true.

y ≤ (1/2) x + 2

0 ≤ (1/2) 0 + 2

0 ≤ 2              TRUE

Hope this helps!! :)

Please let me know if you have any questions

Answer:

(a)

(b) range of sample means =0.6

(c)

A statement which best defines an output is: B. an output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).

In Mathematics, there are different types of functions and these include the following;

In this context, we can infer and logically deduce that a statement which best defines an output is that it's the result of a relation or the function rule, which usually are the y-values in a set of ordered pairs, on a table or a graph.

Read more on function here: https://brainly.com/question/9315909

#SPJ1

Complete Question:

Which of the following best defines an output?

A. An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.

B. An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

C. An output is a special type of relation for which there is a rule that pairs each input with exactly one output.

D. An output is a set of ordered pairs in which no y-value repeats.

Debido a restricciones de extensión y la características del ejercicio, recomendamos leer la explicación de esta pregunta para mayores detalles sobre la adición de números enteros.

En este ejercicio tenemos un grupo de sumas con números enteros positivos y negativos, en las cuales se prueba la capacidad del estudiante para realizar varias operaciones en serie (adición, sustracción) y comprender las diferencias entre números positivos, negativos y neutros. Ahora procedemos a determinar el resultado de cada una de las expresiones:

20 + 50 + 30 + 7 = 107

30 + 5 + 2 = 37

- 200 - 50 - 70 - 8 = - 328

- 500 + 100 - 20 + 50 = - 370

10 - 5 = 5

20 + 50 - 25 - 10 = 35

- 100 + 20 = - 80

- 30 + 5 + 4 - 20 + 8 = - 33

- 258 + 8 = - 250

- 10 + 20 + 520 - 100 + 8 = 438

- 20 - 5 - 42 + 3 = - 64

1000 - 200 + 50 + 30 - 45 + 75 - 87 + 90 + 50 - 100 + 50 - 10 = 903

- 400 + 500 - 200 - 50 + 48 + 8 - 47 - 50 = - 191

300 + 20 - 50 + 30 - 84 + 35 - 7 + 20 - 40 + 10 - 45 + 65 + 8 - 55 = 207

800 + 50 - 69 + 8 - 35 + 85 - 54 + 40 + 85 + 74 - 32 - 8 + 65 - 27 = 982

Para aprender más sobre sumas: https://brainly.com/question/1456841

#SPJ1

The solution for the initial value problem is [tex]y_{g} = e^{-2x} (-12cos(x) + 5sin(x)) + 7e^{-4x}[/tex]

Given,

y" + 4y' + 5y = 35[tex]e^{-4x}[/tex]

y(0) = -5

y'(0) = 1

Solve this homogenous equation to get [tex]y_{h}[/tex]

According to differential operator theorem,

[tex]y_{h}[/tex] = [tex]e^{ax}[/tex]( A cos (bx) + B sin (bx)), where A and B are constants.

Therefore,

y" + 4y' + 5y = 0

([tex]D^{2}[/tex] + 4D + 5)y = 0

D = -2± i    

[tex]y_{h} = e^{-2x} ( A cos (x) + B sin (x))[/tex]

Now, solve for [tex]y_{p}[/tex]

A function of the kind [tex]ce^{-4x}[/tex] is the function on the right, we are trying a solution of the form [tex]y_{p} =ce^{-4x}[/tex], here c is a constant.

[tex]y_{p} " + 4y_{p} ' + 5y_{p} = 35e^{-4x} \\=16ce^{-4x} -16ce^{-4x} +5ce^{-4x} = 35e^{-4x} \\= 5ce^{-4x} =35e^{-4x} \\c=\frac{35}{5} =7\\y_{p} =7e^{-4x}[/tex]

Then the general solution will be like:

[tex]y_{g} =y_{h} +y_{p} \\[/tex]

    = [tex]e^{-2x} (Acos(x)+Bsin(x))+7e^{-4x}[/tex]

[tex]y_{g}(0)=-5=A+7=-12\\y_{g} '(0)=e^{-2x} (-Asin(x)+Bcos(x))-2e^{-2x} (Acos(x)+Bsin(x))-28e^{-4x} \\y'_{g} (0)=1=B-2A-28\\[/tex]

       B = 1 - 24 + 28 = 5

Then the solution for the given initial value problem is

[tex]y_{g} =e^{-2x} (-12cos(x)+5sin(x))+7e^{-4x}[/tex]

Learn more about initial value problem here: https://brainly.com/question/8599681

#SPJ4

We might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.

Recursive formulas are commonly used to compute the nth term of a sequence, where a(n) is the sum of all the preceding values.

Using its position, explicit formulas can compute a(n).

Therefore, we might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.

Know more about sequences here:

https://brainly.com/question/6561461

#SPJ4

Answer: (D)

Step-by-step explanation:

took quiz

Answer:

Step-by-step explanation:

integer and rational

The Option A is correct that tells us that the There is a common ratio between the terms which represent the Characteristics of the G.P. Series.

According to the statement

we have to explain the characteristics of the Geometric Sequence.

So, For this purpose

We know that the

A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

From its definition it is clear that the

There is a common ratio between the terms.

And this point represent the characteristics of the Geometric Sequence not all other points.

Now, The option A is the correct rather than the other options.

So, The Option A is correct that tells us that the There is a common ratio between the terms which represent the Characteristics of the G.P. Series.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Which statements describe characteristics of a geometric sequence? Check all that apply.

a.There is a common difference between terms

b.Each term is multiplied by the same number to arrive at the next term.

c.The sequence increases or decreases in a linear pattern

d.There is a common ratio between terms

Learn more about G.P. Series here

https://brainly.com/question/24643676

#SPJ4

Answer:

[tex]\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]

Step-by-step explanation:

We are given the expression:

[tex]\displaystyle{\dfrac{3}{x^2-9} + \dfrac{5}{x+3}}[/tex]

First, factor the denominator [tex]\displaystyle{x^2-9}[/tex] to [tex]\displaystyle{(x+3)(x-3)}[/tex] via difference of two squares:

[tex]\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5}{x+3}}[/tex]

Next, multiply the expression 5/(x+3) by [tex]\displaystyle{x-3}[/tex] both denominator and numerator:

[tex]\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5(x-3)}{(x+3)(x-3)}}[/tex]

Add both together since they have same denominator now:

[tex]\displaystyle{\dfrac{3+5(x-3)}{(x+3)(x-3)} }[/tex]

Simplify the numerator:

[tex]\displaystyle{\dfrac{3+5x-15}{(x+3)(x-3)} }\\\\\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]

Therefore, the sum is:

[tex]\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]

Answer:

  ln(5/3)

Step-by-step explanation:

The desired limit represents the logarithm of an indeterminate form, so L'Hopital's rule could be applied. However, the logarithm can be simplified to a form that is not indeterminate.

We can cancel factors of (x-1), which are what make the expression indeterminate at x=1. Then the limit can be evaluated directly by substituting x=1.

  [tex]\diplaystyle \lim\limits_{x\to1}{(\ln(x^5-1)-\ln(x^3-1))}=\lim\limits_{x\to1}\ln{\left(\dfrac{x^5-1}{x^3-1}\right)}\\\\=\lim\limits_{x\to1}\ln\left(\dfrac{x^4+x^3+x^2+x+1}{x^2+x+1}\right)=\ln{\dfrac{5}{3}}[/tex]

The correct option is B.

The enrollment capacity be 3 years from now is 2410

A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.

The formula for determining the nth term is used to locate a specific term in an arithmetic sequence. Step 1: An = a + (n - 1)d determines the nth term of an arithmetic series. Add the variables a = 2 and d = 3 to the formula in order to find the nth term.

At = a1 + (n - 1) x d is an equation that can be used to express the number of applications each year.

N equals 4 based on the information provided above. This corresponds to the term, which begins in three years.

At = 2200 + (4 - 1) x 70 = 2410

Thus, 2410 students could enroll at one time.

To know more about arithmetic sequence visit:

https://brainly.com/question/1450708

#SPJ4

Answer:

4x=90

X=90÷4

X=22.5

5x-27=90

5x=90+27

5x=117

X=117÷5

X=23.4

So 23.4 is a larger angle

Answer:

Step-by-step explanation:

3x + 1 < 7...subtract 1 from both sides

3x < 7 - 1

3x < 6 ...divide both sides by 3

x < 6/3

x < 2

which means the second answer choice is correct!

Answer: Second Graph

Step-by-step explanation:

Given inequality

3x + 1 < 7

Subtract 1 on both sides

3x + 1 - 1 < 7 - 1

3x < 6

Divide 3 on both sides

3x / 3 < 6 / 3

x < 2

Apply the inequality to the graph

Since it is less than, the circle should be hollow

Since it is less than 2, the line should point to the left

Therefore, it should be the Second Graph

Answer:

[tex] \blue{b < 8}[/tex]

Answer 1 is correct

Step-by-step explanation:

[tex] \frac{3}{2} b + 5 < 17[/tex]

Take 5 to the right side.

[tex] \frac{3}{2} b < 17 - 5 [/tex]

[tex]\frac{3b}{2} < 12 [/tex]

Multiply both sides by 2.

[tex]3b <12 \times 2[/tex]

[tex]3b < 24[/tex]

Divide both sides by 3.

[tex]b < 8[/tex]

Answer:

C.  Cube 2.

Step-by-step explanation:

Using PEMDAS  the first operation to be done is E (Exponent)  which is

2³.

Answer:

c  0.5⁻ˣ

Step-by-step explanation:

The slowest rate is:

0.5⁻ˣ

The equation of the line is b = am + c

Linear equations are equations that have a constant slope, average rate of change or gradients

The point is given as

(x, y) = (a, b)

The slope is given as

Slope = m

A linear equation is represented as

y = mx + c

Where me represents the slope

Substitute (x, y) = (a, b)

b = am + c

Hence, the equation of the line is b = am + c

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

In order to solve a problem that begins with a negative number and is divided by a positive number, the answer must also be negative.

Divide 21 ÷ 7

we get = 3

Mark it as negative number = -3

Hope this helps :)