Rewrite in simplest terms: -10f – 6(-9f +2)

Answer:

a)

Step-by-step explanation:

Y=k/x........(1)

Put y and x in (1) to get:

3=k/5

K=15

Now put k=15 in (1):

Y=15/x

b)

Y=k/x as x=45

Y=15/45

Y=1/3

Answer:

[tex]f'(x)=1+\ln x[/tex]

Step-by-step explanation:

[tex]f'(x)[/tex] is notation for the first derivative of [tex]f(x)[/tex].

Recall the product rule:

[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]

Therefore, we have:

[tex]\displaystyle \frac{d}{dx}(x\ln x)=\frac{d}{dx}(x)\cdot \ln(x)+\frac{d}{dx}(\ln x)\cdot x[/tex]

Note that:

[tex]\displaystyle \frac{d}{dx}(x)=1,\\\\\frac{d}{dx}(\ln x)=\frac{1}{x}[/tex]

Simplify:

[tex]\displaystyle \frac{d}{dx}(x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x, \\\\\frac{d}{dx}(x\ln x)= \ln x+1=\boxed{1+\ln x}[/tex]

The derivative is:

[tex] \bold{f(x) \: = \: x \: \times \: (In(x))}[/tex]

[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x \: \times \: In(x))}[/tex]

[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x) \: \times \: In(x) \: + \: x \: \times \: \frac{d}{dx} (In(x))}[/tex]

[tex] \bold{f'(x) \: = \: 1In(x) \: + \: x \: \times \frac{1}{x} }[/tex]

[tex] \bold{f'(x) \: = \: In(x) \: + \: x \: \times \: \frac{1}{x} }[/tex]

[tex] \boxed{ \bold{f'(x) \: = \: In(x) \: + \: 1}}[/tex]

The aspect ratio represents the ratio of the width to the height of a television.  

The size of a TV is calculated using Pythagoras theorem. Assume the length ratio of the older 25-inch [tex]4:3[/tex] TV is x.

The ratio is represented as:

[tex]Width : Height = 4:3[/tex]

Using Pythagoras theorem, we have:

[tex]Width^2 + Height^2 = 25^2[/tex]

[tex](4x)^2 + (3x)^2 = 25^2[/tex]

[tex]16x^2 + 9x^2 = 625[/tex]

[tex]25x^2 = 625[/tex]

Divide both sides by 25

[tex]x^2 = 25[/tex]

Take positive square roots

[tex]x = 5[/tex]

So, the height of the image is:

[tex]Height = 3x[/tex]

[tex]Height = 3 \times 5 = 15[/tex]

While the width is

[tex]Width = 4x = 4 \times 5 = 20[/tex]

Hence, the height of the image is 15 inches

The height of each black bar is calculated as follows:

[tex]Width : Height = 2.35 : 1[/tex]

Where

[tex]Width = 20[/tex]

So, we have:

[tex]20 : Height = 2.35 : 1[/tex]

Express as fraction

[tex]\frac{Height}{20} = \frac{1}{2.35}[/tex]

Make Height the subject

[tex]Height = \frac{20}{2.35}[/tex]

[tex]Height = 8.51[/tex]

The height of each black bar at the top and at the bottom is 8.51 inches

The percentage of the screen’s area that is occupied by the image is calculated using

[tex]\% Screen = \frac{A_1}{A_2} \times 100\%[/tex]

Where

[tex]A_1 \to[/tex] Area of black bars

[tex]A_2 \to[/tex] Area of the 25-inch 4:3 television

So, we have:

[tex]A_1 =8.51 \times 20 = 170.2[/tex]

[tex]A_2 =15 \times 20 = 300[/tex]

[tex]\% Screen = \frac{A_1}{A_2} \times 100\%[/tex] becomes

[tex]\% Screen = \frac{170.2}{300} \times 100\%[/tex]

[tex]\% Screen = \frac{170.2}{3} \%[/tex]

[tex]\% Screen = 56.73 \%[/tex]

Hence, the percentage of the screen area occupied is 56.73%

Consumers moved to TV with a wide screen because a TV with wide screen shows bigger pictures than smaller dimension TV screens,

When the pictures are bigger, the consumers will have a clearer view of what they're watching.

Read more about aspect ratios at:

brainly.com/question/17231027

The shaded region of a circle formed by one line as shown in the image is called a segment.

Answer: segment

Answer:

x = 2

Step-by-step explanation:

26-4x=9x

Add 4x to each side

26-4x+4x=9x+4x

26 = 13x

Divide each side by 13

26/13 = 13x/13

2 = x

Answer:

-26/5

Step-by-step explanation:

[tex]26 - 4x = 9x \\ 4x = 9x - 26 \\ - 5x = - 26 \\ \frac{ - 5x}{5} = \frac{26}{5} [/tex]

Answer:

ab = 144

Step-by-step explanation:

Assuming you mean a² + b² = 612, then

(a + b)² = a² + 2ab + b² , that is

30² = a² + 2ab + b²  , so

a² + 2ab + b² = 900

a² + b² + 2ab = 900 ← substitute a² + b² = 612

612 + 2ab = 900 ( subtract 612 from both sides )

2ab = 288 ( divide both sides by 2 )

ab = 144

Explanation:

We follow PEMDAS in reverse to undo every operation that is applied to variable x

Doing so will lead to the following

t = 0.4x + c

t - c = 0.4x

0.4x = t - c

x = (t - c)/(0.4)

The last equation is the same as writing [tex]x = \frac{t-c}{0.4}[/tex] which is what choice B shows.

Answer:

-35 and 7

Step-by-step explanation:

7 - 35 = -28

35 has a (-) sign, and 7 has a (+) sign

Addition can be defined as the process of adding two numbers. The two integers with different signs that have a sum of -28 are -29 and 1.

Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.

An integer is a number that can be written without using a fractional component.

Given that the two integers with different signs have a sum of -28. Therefore, we can write,

Hence, the two integers with different signs that have a sum of -28 are -29 and 1.

Learn more about Addition here:

https://brainly.com/question/13167637

#SPJ2

Answer:

14th term is 16,384

Step-by-step explanation:

I. When [tex]a_{n} = a_{1}(r^{n-1} )[/tex]

If n = 14, a = 2 and r = 2

         [tex]a_{14} = 2(2^{14-1} )[/tex]

               = 2([tex]2^{13}[/tex])

         [tex]a_{14}[/tex]      = 16,384

Step-by-step explanation:

y=x+6.......(1)

y=-3X-6....(2)

from eq (1), we get,

x=y-6....(3)

sub eq (3) in eq (2), we get

y= -3(y-6)-6

y= -3y+18-6

y+3y-12=0

4y=12

y=3

sub value of y in eq (3)

x=3-6

x=-3

Answer: (3, 3)

Step-by-step explanation:

There are three general ways of solving a system of equations:

When solving systems of equations with graphing, look for points that overlap with each other or cross, and that will be the solution for the system. There might be one, two, or more than two solutions.

Please refer to the attachment below for the graph of the two equations.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

f(1) = 2 f(3) = 8 f(t) = 2^t

Step-by-step explanation:

you just plug in the number in the parenthesis next to f to x in the equation 2^x

Answer:

500 - 6r = t

Step-by-step explanation:

500 represents the amount of copper wire Lisa started with.

-6r represents how much copper wire (in yards) is used on the robot (9*2 / 3 = 6).

t represents the total wire left after Lisa builds r robots.

Step-by-step explanation:

4(1-3x)+7x-8

4-12x+7x-8

-12x+7x+4-8

-5x-4

Answer:

x = 8

Step-by-step explanation:

A common pythagorean triplet is 7, 8, 9

Answer:

11.4

Step-by-step explanation:

Pythagorean theorem

[tex]7^{2}[/tex] + [tex]9^{2}[/tex] = [tex]x^{2}[/tex]

49 + 81 = [tex]x^{2}[/tex]

130 = [tex]x^{2}[/tex]

11.4 = x

Answer:

167

812

Step-by-step explanation:

I think it's correct and helping you get a great day:)

Step-by-step explanation:

steps are in the picture above.

Note:if you need to ask any question please let me know.

Answer:

According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0. ... Also, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0. This proves the converse of the theorem.

Answer:

4x-2y =42 is the required equation

Step-by-step explanation:

given equation is,

4x-2y -7=0---------eqn1

parallel equation of given equation is

4x -2y+k =0-------eqn 2

now passing it through (9,-3), we get,

4×9 + 2×3 +k = 0

or,36+6+k =0

or,42+k =0

or, k= -42

putting the value of k in eqn2

4x-2y - 42=0

4x-2y = 42

simplify the expression below

(x 1/15) 5

Using the law of indices we multiply the power outside the parenthesis with the power inside the parenthesis.

Therefore,

1/15 x 5 = 5/15 = 1/3

After multiplying the power, we reduce the fraction to it lowest term. By doing so we get the fraction power of 1/3.

our final expression will be like

(xA 1/15) A 5 multiply the power

(xA 5/15) reduce the fraction power to it lowest term

(1/x3)

Answer:

[tex] {x}^{2} + x + xy + y + zx + z \\ = x(x + 1 + y + y + z) + z \\ = x(x + 2y + z + 1) + z[/tex]

Answer:

I am sorry I not no

this question

Step-by-step explanation:

sorry dear friend

Answer:

1

Step-by-step explanation:

The second power and square root cancel each other (second power means squared by the way)

Answer:

KL=63

Step-by-step explanation:

Answer:

Step-by-step explanation:

Kl=63

Answer:

12 hours

Step-by-step explanation:

each worker digs a hole and takes 4 hours doing so

2 workers dig 3 holes each, 3*4=12, 12 hours

Answer:

12 hours

Step-by-step explanation:

4 workers can dig 4 holes in hours=4

1   worker    ,,     ,,   4    ,,      ,,    ,,     =4×4=16

1      ,,           ,,     ,,    1   hole ,,    ,,     =16÷4=4

2     ,,           ,,     ,,    1     ,,     ,,    ,,    =4÷2=2

2     ,,           ,,     ,,    6 holes ,,    ,,    =2×6=12

Answer:

0.72 repeat

Step-by-step explanation:

              __

8 ÷ 11 =0.72

Answer:

7, 3, 0, -3, -5, -8, -14

Step-by-step explanation:

I know 7 is the greatest value you add the most because to get to 7 from 0.

I know -14 is the least value because I subtracted the most to get to -14 from 0.

Answer:

c=sqrt21

Step-by-step explanation:

angle c is the angle between a and b, so use the cos law

c^2=a^2+b^2-2*a*b*cosC

c^2= 16+25-2*4*5*1/2

c^2=21

c=sqrt21