Find the inverse of the cubic function. Confirm the inverse relationship using composition.

f (x) = x^3 - 5/6

Slope-intercept form is −8x+9. One of the formulas used to get a line's equation is the slope-intercept formula.

Slope-intercept is a specific form of linear equations. The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = − 3 x + 5 , we see that the slope of the line is − 3 .

A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The y-intercept, or point where the line crosses the y-axis, is where the slope, or steepness, of the line is located.

-8x + y = -9

move y to right side

-8x = -9-y

Divide both sides by -8

-8x/-8x = -(9/-8) - (y/-8)

Simplify

-8x/-8x = -(9/-8) - (y/-8)

Simplify -8x/-8x : x

Simplify  -(9/-8) - (y/-8) : -9 - y / 8

x = -(-9 - y / 8)

y = mx + b.

y = −8x+9

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The length of the second side of the triangle is 18 m

What is the perimeter of a Triangle?

The perimeter of a triangle is given by the formula

Perimeter of a triangle = Sum of all three sides

Let the sides of the triangle be a , b , c

Perimeter of a triangle = a + b + c

Given data ,

Perimeter of the triangle = 51 m

Let the first side , second side and third side of the triangle be a , b and c respectively

So , a + b + c = 51 m

And , The second side is twice as long as the first

So , b = 2a

And , The third side is 3 meters less than three times the first

So , c = 3a - 3

Substituting the values of a , b and c in the perimeter equation , we get

a + 2a + 3a - 3 = 51

6a - 3 = 51

Adding 3 on both sides , we get

6a = 54

Divide by 6 on both sides , we get

a = 9 m

Substituting the value of a , we get

b = 2a

b = 2 x 9

b = 18 m

c = 3a - 3

c = 3 x 9 - 3

c = 27 - 3

c = 24 m

So the length of the first side , second side and third side is 9m , 18 m and 24 m respectively

Hence , the length of the second side is 18 m

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Answer:

[tex]x < \frac{17}{5}[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:9-0

Step-by-step explanation:sdwew

Answer:

x = 35 degrees

Step-by-step explanation:

3x-11+2x+16 = 180

5x +5 = 180

5x = 180 -5

5x = 175

5/5 x = 175/5

x = 35 degrees

The equation 56 ÷ 8 + 3² = 2⋅2³  is true which is the correct answer would be option (C).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

As per option (A),

39 − 3⋅6 = 6⋅10/4 + 4

39 - 18 = 6 × 5/2 + 4

11 = 30/2 + 4

11 = 15 + 4

11 = 19

This equation is not true.

As per option (B),

8²−5²=4²−7

64 - 25 = 16 - 7

39 = 9

This equation is not true.

As per option (C),

56 ÷ 8 + 3² = 2⋅2³

56 / 8 + 9 = 2 × 8

7 + 9 = 16

16 = 16

This equation is true.

Therefore, the equation 56 ÷ 8 + 3² = 2⋅2³  is true.

Hence, the correct answer would be option (C).

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Answer:

9q+7

Step-by-step explanation:

1. Add 6q+3q, which is 9q

2. Then add 2+5, which is 7

3. Then combine those answers and you get a final answer of 9q+7

Answer:

9q+7

Step-by-step explanation:

1. Group all like terms: 6q+3q  and 2+5

2. Add the like terms together. 6q+3q= 9q.         2+5=7

3. Rewrite the equation 9q+7

ANSWER : 9q+7

Answer:

This statement is False.

Step-by-step explanation:

It is not impossible, but on MOST occasions, you will get a decimal number.

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 15 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

20 sections per friend

Step-by-step explanation:

First find the total number of sections

5 * 12 = 60 sections

Divide by 3 friends

60/3 = 20

20 sections per friend

Answer:

30 every 5 days

Step-by-step explanation:

x = 10% solution

y = 15% solution

let's start at the beginning, without the equation just yet, so let's start off by making a table for the substances and let's use the decimal format for the percentages to get the actual amounts.

[tex]\begin{array}{lcccl} &\stackrel{mL}{quantity}&\stackrel{\textit{\% of mL that is}}{\textit{alcohol only}}&\stackrel{\textit{mL of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{10\% sol'n}&x&0.10&0.10x\\ \textit{15\% sol'n}&y&0.15&0.15y\\ \cline{2-4}&\\ mixture&50&12&6 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.10x+0.15y=6 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies y=50-x}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.10x+0.15(\underset{y}{50-x})=6} \\\\\\ 0.10x+7.5-0.15x=6\implies -0.05x+7.5=6\implies -0.05x=-1.5 \\\\\\ x=\cfrac{-1.5}{-0.05}\implies \boxed{x=30}\hspace{15em}\stackrel{50~~ - ~~30}{\boxed{y=20}}[/tex]

The given expression √3x²+√4x is defined for x > 0

By property |f(x)| < c

⇒ f(x) < 0   and  - f(x) < 0

⇒√3x²+√4x < 0 and -(√3x²+√4x) < 0

⇒ x < -√4/3   and  x < -√4/3

Therefore x should be greater than 0.

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Answer:

y = 3/2x + 2

Step-by-step explanation:

The x axis runs by 2.

The y axis rises/drops (depends on which you are using) by 3.

The format is rise over run.

So its 3/2

With respect to the proportional relationship table, Harry can run 2.6 miles in 28.6 minutes

What is the proportional relationship?

If all of the ratios of the variables are equal, then there is a proportional link between the two variables. In a proportional relationship, one variable is, in other words, always a constant value multiplied by the other variable. In other words, a relationship is proportional if it can be explained by multiplying each pair of data values by a certain amount.

Solution Explained:

A/Q, the table shows the proportional relationship between distance and time.

Given,

Distance                   Time
0.7                             7.7
1.4                              15.4
x                                 28.6

We know, the ratios are equivalent in a proportional relationship
If we divide, 0.7 and 7.7, we get 11
so taking 11 as the constant of proportionality, we get

x X 11 = 28.6
x = 28.6 / 11
x = 2.6

Therefore, Harry can run 2.6 miles in 28.6 minutes.

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Answer:

Harry can run 2.6 miles in 28.6 minutes

Step-by-step explanation:

A/Q, the table shows the proportional relationship between distance and time.

Given,

Distance                   Time

0.7                             7.7

1.4                              15.4

x                                 28.6

We know, the ratios are equivalent in a proportional relationship

If we divide, 0.7 and 7.7, we get 11

so taking 11 as the constant of proportionality, we get

x X 11 = 28.6

x = 28.6 / 11

x = 2.6

Therefore, Harry can run 2.6 miles in 28.6 minutes.

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Answer:

Step-by-step explanation:

Assuming that a linear function can be in all different directions, but remain straight. It might be B. Because the answer shows (0,-1) and the other solutions don't have a y-intercept with a 0 x-intercept...?

By using the given chart, the value of h'(4) would be -16.

What is a chain rule in calculus?

According to the chain rule, the derivative of f(g(x)) is f'(g(x)).g' (x). In other words, it aids in the differentiation of 'composite functions'.

Sin(x²), for example, is a composite function because it can be written as f(g(x)) where f(x)=sin(x) and g(x)=x².

The given function is

                                h(x) = f(g(x))

            Now differentiating the above function with respect to x, we get

                               h'(x) = f'(g(x)) * g'(x)

                     Now find h'(4), so put x = 4, we get

                               h'(4) = f'(g(4)) * g'(4)

                     By using the given table, we can write

                                h'(4) = f'(-1) * 8

                                h'(4) = (-2) * 8

                                h'(4) = -16

Hence, by using the given chart, the value of h'(4) would be -16.

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Ed’s profit on “Good Luck” cards in 2017 is $450.

Given that, Ed's profit on “Good Luck” cards in 2018 was £360. This was a decrease of 20% on his profit in 2017.

The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.

Let x be the profit on "Goodluck" card in 2017.

Now, x - 20% of x=360

⇒ x - 20/100 × x = 360

⇒ x - 0.2x = 360

⇒ 0.8x = 360

⇒ x = 360/0.8

⇒ x = 450

Therefore, Ed’s profit on “Good Luck” cards in 2017 is $450.

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"Your question is incomplete, probably the complete question/missing part is:"

Ed's profit on “Good Luck” cards in 2018 was £360.This was a decrease of 20% on his profit in 2017.Work out Ed's profit on “Good Luck” cards in 2017.

Answer: -18

Step-by-step explanation:

((-3)2)3

((-3) x 2) x 3

Apply rule (-a) = - a

(-3) = -3

-3 x 2 x 3

-6 x 3

= -18

Answer:

Step-by-step explanation:

Vector:

AB = { 2 - 5;  7 - 3;  -1  - (-1) } = { -3; 4; 0 }

Vector modulus:

| AB | =  √ ( (-3)² + 4² + 0² ) = √ (9 + 16 + 0 ) = √ 25 = 5

Unit vector:

U = -(3/5)·i + (4/5)·j + 0/5·k

U = -(3/5)·i + (4/5)·j

The length of the curve is 2.0036.

The equation of the curve is y = e^(x). The interval is 0 ≤ x ≤ 1. A curve is a smoothly drawn figure or line in a plane that has a bend or twist in it. A curve is defined as a continuous and smooth flowing line with no sudden twists. A curve is an abstract concept in mathematics that describes the path of a continuously moving point. The arc length of a curve y = f(x) in the increasing interval from a to b is given below.

[tex]L = \int\limits^a_b {\sqrt[]{ 1 + (\frac{dy}{dx})^{2}} \, dx[/tex]

dy/dx = d(e^x)/dx = e^x

(dy/dx)² = e^(2x)

The length of the given curve is calculated below.

[tex]L = \int\limits^1_0 {\sqrt[]{ 1 + e^{2x}}, dx[/tex]

L = [√(1+e^2x) + (1/2)ln(√(1+e^2x) - 1) - (1/2)ln(1 + √(1+e^2x))] from limits 0 to 1.

L = [√(1+e²) + (1/2)ln(√(1+e²) - 1) - (1/2)ln(1 + √(1+e²))] - [√(1+1) + (1/2)ln(√(1+1) - 1) - (1/2)ln(1 + √(1+1))]

L = [√(1+e²) + (1/2)ln(√(1+e²) - 1) - (1/2)ln(1 + √(1+e²))] - [√2 + (1/2)ln(√2 - 1) - (1/2)ln(1 + √2)]

L ≈ 2.0036

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The conversion of 30 miles per second into miles per minute is 1800 miles per minute and Mercury will travel 5400 miles in 3 minutes at this rate.

According to the question,

We have the following information:

Mercury travels at a rate of approximately 30 miles per second.

We know that there are 1/60 minutes in 1 second.

So, we have the following expression for conversion:

30/(1/60) miles per minute

30*60

1800 miles per minute

Now, we know that following formula is used to find distance:

Distance = speed*time

Distance = 1800*3

Distance = 5400 miles

Hence, the conversion of 30 miles per second into miles per minute is 1800 miles per minute and Mercury will travel 5400 miles in 3 minutes at this rate.

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The two relationships between the two triangles QRS and TUV is that they are similar triangles.

Option b is correct.

What is a similar triangle?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are described as items with the same shape but varying sizes, such as two or more figures. The polygon with three sides is a triangle. The prerequisites for a triangle's resemblance are that the corresponding angles on both triangles must be identical, and the corresponding sides must be proportional to one another.

In the given question, we have:

The two triangles: QRS and TUV;

and we have the measure of the angles;

∠Q = 76°

∠R = 26°

∠S = 76°

∠T = 76°

∠U = 26°

∠V = 76°

and the sides measure:

RQ = 4cm;

RS  = 2cm;

SR = 4cm;

UT = 12cm;

TV = 6cm;

UV = 12cm;

So, when we find the proportion of the corresponding sides, we get:

The ratio of sides is as [tex]\frac{1}{2}[/tex];

and all the corresponding angles are equal;

So, we can say that the two triangles are similar;

Hence, The two triangles are similar;

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The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.

Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

O and R are the subsets of a Universal set, U, such that

U = {22,23,24,25,26,27,28,29,30}

O = {prime numbers} = {23, 29}

R = {even numbers} = {22, 24, 26, 28, 30}

The elements of (OUR)' will be given as,

(OUR)' = {23, 29}

The elements of (O∩R)' will be given as,

(O∩R)' = {22, 23, 24, 26, 28, 29, 30}

The elements of O∩R will be given as,

O∩R = 0

The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.

The Venn diagram is given below.

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The equivalent expression of 4(5+y)  by distributing is 20 + 4y.

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, two mathematical expressions are said to be equivalent if they yield the same result upon solving them.

Therefore, let's find the equivalent expression of 4(5 + y) by distributing it.

Hence,

4(5 + y)  = 20 + 4y

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The value of the function at x = -1, 0, 1, 2, and 3 will be -4, 3, 2, -1, and 0, respectively.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

From the graph of f(x), then the value of the function at x = -1, 0, 1, 2, and 3 will be given as,

x             f(x)                        Feedback

-1             -4               Point is in the fourth quadrant

0              3                      Point is in the y-axis

1               2               Point is in the first quadrant

2             -1               Point is in the second quadrant

3              0                      Point is in the x-axis

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The total number of red roses sold by the florist is 455.

A Fraction represents the parts of a whole or collection of objects. The first and most common form of representing a fraction is [tex]\frac{a}{b}[/tex].

Here, a is the numerator, and b is the denominator.

Number of Roses sold by The florist = 715

Fraction for the number of red roses sold = [tex]\frac{7}{11}[/tex] (7 out of 11 roses)

We have to find the number of red roses sold by the florist.

Now,

The number of red roses sold by the florist will be

[tex]\frac{7}{11} \ of\ 715[/tex]

[tex]=\frac{7}{11}*715[/tex]

[tex]=\frac{7*715}{11}[/tex]

[tex]=\frac{5005}{11}[/tex]

[tex]=455[/tex]

Hence, the total number of red roses sold by the florist is 455.

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Answer: Sir in what way would you like me to explain this

Step-by-step explanation:

Answer

3x−2y=12y=1−2x

re

Based on the information given; there are outliers in the data and this can be attributed to the relatively large standard deviation relative to the mean.

Outliers as the name implies are data values which significantly deviate from the measures of central tendency such as mean and median.

On this note, the major outliers in the scenario are; the minimum and maximum whose values are $18,000 and $350,000 respectively.

It is noteworthy to also know that the relatively large standard deviation with respect to the mean is an indicator of the presence of outliers in the data.

Ultimately, there are outliers in the data given and this follows from the fact that the mean, Q1, Q3 all range between 50,000 - 58,000 while the outliers can register for them LAS

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The image of (-8, 7) after dilation by a scale factor of 1/3 centered at the origin is : (-8/3, 7/3)

Given point P (-8, 7)

The point is dilated by a scale factor of 1/3 centered at the origin is equivalent to multiplying the point by 1/3 for both the co-ordinates.

Therefore, the new point is given by :

P' = (-8×(1/3), (7)×(1/3))

P' = (-8/3, 7/3)

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