Given f(x) = 4/3 x + 1 determine f^-1 (x)

Answer:

0.43repeating

Step-by-step explanation:

You simply divide 30 by 13, and you get 0.43333333333333333

3 is repeating

Answer:

This is a one to one function

Step-by-step explanation:

From the function, we know that f(x) = x - 7 is a linear graph.

Using horizontal line test

the graph is one to one if the horizontal line only cross the graph at one point

[tex] \frac{3}{ \sqrt{5} - 2 } [/tex]

Rationalize the denominator by multiplying the numerator and denominator by the denominator. (Important: if the denominator has a minus sign, change to plus and vice versa)

[tex]⟹\frac{3 \times \sqrt{5 + 2} }{ (\sqrt{5} - 2 ) \times ( \sqrt{5} + 2) } [/tex]

[tex] ⟹ \frac{3 \sqrt{5} + 6 }{ \sqrt{25} + 2 \sqrt{5} - 2 \sqrt{5} - 4 } ⟹\frac{3 \sqrt{5} + 6 }{5 - 4} [/tex]

[tex] ⟹\frac{3 \sqrt{5} + 6}{1} ⟹3 \sqrt{5} + 6[/tex]

[tex] \frac{6 - \sqrt{12} }{ \sqrt{3} + \sqrt{10} } [/tex]

Rationalize the denominator.

[tex] ⟹\frac{(6 - \sqrt{12} ) \times ( \sqrt{3} - \sqrt{10} )}{ (\sqrt{3} + \sqrt{10} ) \times ( \sqrt{3} - \sqrt{10} } [/tex]

[tex]⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{ \sqrt{9} - \sqrt{30} + \sqrt{30} - \sqrt{100} } [/tex]

[tex]⟹ \frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{3 - 10} ⟹ \frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{ - 7} [/tex]

[tex] ⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + \sqrt{12 \times 10} }{ - 7}⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 4 \sqrt{3 \times 10} }{ - 7} [/tex]

[tex] ⟹ - \frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 2 \sqrt{30} }{7} [/tex]

Therefore:

1. [tex]3 \sqrt{5} + 6[/tex]

2. [tex] - \frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 2 \sqrt{30} }{7} [/tex]

Answer:

9

Step-by-step explanation:

because 8 gallons of lemonade will stand on charge $1.00 will add and answer will be 9

Answer:

(2,3)

Step-by-step explanation:

[tex]y=(2)^{2}-1=4-1=3[/tex]

when x = 2, y = 3

Hope this helps

Using Descartes's Rule of Signs:

There are four positive real zeros P can have.

There are zero negative real zeros P can have.

Descartes' rule of sign is used to determine the number of positive and negative real zeros of a polynomial function.

We have,

P(x) = 2[tex]x^{4}[/tex] - 7x³ + x² - 18x + 3

We have to look at the sign of the coefficient

Here,

  2[tex]x^{4}[/tex] - 7x³  +  x²  -  18x + 3

(+)---(-)(-)---(+)(+)--(-)(-)---(+)

There are 4 variations so there are 4 positive real zeroes.

For finding negative real zeroes we Put x = -x.

P(-x) =  2[tex]x^{4}[/tex] + 7x³ + x² + 18x + 3

   2[tex]x^{4}[/tex]  +  7x³  +  x²  +  18x  +  3

(+)---(+)(+)----(+)(+)--(+)(+)-- --(+)

There are no variations so there are zero negative real zeroes.

Thus,

a) Using Descartes's Rule of Signs, we know that there are four positive real zeros P can have.

b) Using Descartes's Rule of Signs, we know that there are zero negative real zeros P can have.

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Answer: 1/10 of a pound

Step-by-step explanation:

The total weight was 7/10 of a pound. Cutting the fudge into 7 pieces implies dividing the fudge by 7.

7 is the same as 7/1.

When dividing fractions, we can multiply by the reciprocal. Essentially, we just flip the second number.

[tex]\frac{7}{10}/7 =\frac{7}{10} / \frac{7}{1} =\frac{7}{10} *\frac{1}{7}[/tex]

We can multiply this out to 7/70 and then simplify to 1/10,

or we could first cross simplify by dividing the 7s out of the numerator and denominator before multiplying. Either way, your answer ends up being 1/10 of a pound.

Hope this helps!

The  slope of the line y-3= 4(x+8) is  4 and (-8, 30 is a point on line y - 3 = 4(x + 8).

According to the given question.

We have a equation of a line y-3= 4(x+8).

Here, we have to find the slope of a line y-3= 4(x+8) and a point on the line.

Since we know that, the equation of a lines through a point (x1, y1) is given by y - y1  = m(x - x1), where m is the slope of the line.

And the equation of slope intercept form for a line is y = mx + c.

So, compare the given equation of line y-3= 4(x+8) with the standard equation of line y - y1  = m(x - x1)  which passes through the point (x1, y1), we get

point ( -8, 3) on line y-3= 4(x+8).

Now, the slope intercept form of the line y-3= 4(x+8) is

y - 3 = 4x + 32

⇒ y = 4x + 32 + 3

⇒ y = 4x + 35

Thereofore, the slope of the line y-3= 4(x+8) is  4.

Hence, the  slope of the line y-3= 4(x+8) is  4 and (-8, 30 is a point on line y - 3 = 4(x + 8).

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Answer: Does it specify how long his short bumper stickers are?

Step-by-step explanation:

Answer:

40 degrees

Step-by-step explanation:

Substitute f = 104:

[tex]C = \frac{5(f - 32)}9 \\\\\to C = \frac{5(104 - 32)}9 \\\\\to C = \frac{5 \times 72}9 \\\\\to C = 5 \times 8 = 40 \text{ degrees}[/tex]

Answer:

{x|x>5}

Explanation:

4(x-3)-2(x-1)>0

4x-12-2x+2>0

2x-10>0

2x>10

x>5

Answer:

-1/9

Step-by-step explanation:

Answer:

3.1kg

Step-by-step explanation:

4.7+5.6+6.4+2.8+3.5+4.4+4.5 = 31.9

4.375 x 8 = 35

35 - 31.9 = 3.1

For the given geometric sequence, we have that:

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

For the series given by:

8, 12, 18, 27, ...

We have that:

When a geometric series is infinite and has a common ratio greater than 1, it diverges.

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4,12
represents that jorge takes 4 steps to walk 12 feet
or represents number of steps that it takes to walk 12 feet either is right

Complex fraction 4²/₃ + 1/3 – 4¹/₃ = 2/3

A fraction defined as the part of the whole thing. For example, a pizza is divided into four equal pieces, then each piece is represented by ¼. Fractions help to distribute and judge the numbers easily and make the calculation faster.

Some steps to solve a fraction -

Step 1: Write the factors of numerator and denominator.

Step 2: Determine the highest common factor of numerator and denominator.

Step 3: Divide the numerator and denominator by their highest common factor (HCF). The fraction so obtained is in the simplest form.

For example -

4²/₃ + 1/3 – 4¹/₃

= (4 × 3 + 2)/3 + 1/3 – (4× 3 + 1)/3

= 14/3 + 1/3 – 13/3

= (14 + 1 - 13)/3

= (15 - 13)/3

= 2/3

Hence , in the mathematics problem can be solved by using the fractions.

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Answer:

Function 3 is less steep.

Step-by-step explanation:

The steepness of a linear function is determined by its coefficient of x.

Since the coefficient of x in [tex]f_3(x)[/tex], 0.5, is smaller than that of [tex]f_1(x)[/tex], 2, function 3 is less steep than function 1.

Significance of the coefficient of x

We can think of the function as an equation of a line in the slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.

Steepness and value of x

The larger the numerical value of m, the steeper the line is.

Significance of the sign of x

The sign (positive or negative) of m tells us the direction in which the line is sloping towards. A positive m value gives us a line sloping upwards from left to right, while a negative m value gives us a line that is sloping downwards from left to right.

Additional:

For a similar question on the steepness of functions, do check out the following!

Answer:

it cannot be simplified anymore

Answer:

0.648148

Step-by-step explanation:

it is already in its simplest form but in decimal it is 0.648148(rounded up to six decimal places.

If a sports fan believes that, the probability of the red team winning is 0.35 and that of the blue team winning is 0.40, then the fan expects the red team to win 9 matches less than the blue team in a season of 180 games.

As per the question statement, based on the records for the past several​ seasons, a sports fan believes that, the probability of the red team winning is 0.35 and that of the blue team winning is 0.40.

We are required to calculate the number of games, the fan expects the red team to win, lesser than the blue team in a season of 180 games.

As per the probability record, maximum number of games, the fan believes that the blue team can win all over the season of 180 games = [tex](0.40*180)=(\frac{40}{100}*180)=(4*18)=72.\\[/tex]

Similarly, maximum number of games, the fan believes that the red team can win all over the season of 180 games = [tex](0.35*180)=(\frac{35}{100}*180)=(7*9)=63.\\[/tex]

Hence, the fan expects the red team to win [tex][(72-63)=9][/tex] matches less than the blue team in a season of 180 games.

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The least natural number that has exactly 6 factors and is not divisible by 2 is 75.

It should be noted the factors of 75 include 1, 3, 5, 15, 25, and 75.

Therefore, it should be noted that 2 isn't among the factors based on the information given in the question.

Therefore, the least natural number that has exactly 6 factors and is not divisible by 2 is 75.

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Answer:

10

Step-by-step explanation:

Ordered pairs are listed in this format: (x,y).

In the pair (10,5):

10 = x

and 5 = y

Answer:

In an ordered pair you will find (#,#) number one equals x and number two is y. So the answer is 10.

Step-by-step explanation:

(x,y)

Answer: step by step

Step-by-step explanation:

not totally sure what you're asking but in this equation p=2

If we assume that I = E(R + r), then I/I = R/E + r/E​.

The inverse of a value of a number is known as the reciprocal of the number. The reciprocal can be found out by replacing the numerator with the denominator and vice versa. For example, reciprocal of a number x will be 1/x and vice versa.

Here, we are given that I = E/(R + r)

Taking reciprocals of both sides we get-

Reciprocal of I will be- 1/I

Reciprocal of E/(R + r) will be- (R + r)/ E

Thus,

1/I = (R + r)/ E

Simplifying the equation further, we get-

1/I = R/E + r/E

Hence, proved

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The image of the point after a 180∘ counterclockwise rotation about the origin is (-1, 4)

The given parameters are

Point = (1, -4)

Transformation: 180∘ counterclockwise about the origin

The rule of 180∘ counterclockwise about the origin is

(x, y) = (-x, -y)

When this rule is applied to the given point, we have the image to be

Image = (-x, -y)

This gives

Image = (-1, 4)

Hence, the image of the point after a 180∘ counterclockwise rotation about the origin is (-1, 4)

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Answer:

False.

Step-by-step explanation:

Whole numbers can be described as the integers greater than and including zero. 56 has no fractional or decimal part, and is positive, so it is a whole number and an integer!

Considering the definition of an inequality, the inequality that can be used to determine p, the maximum number of people who can go to the amusement park, is:

17.25 + 37.25×p ≤ 605

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "p" the number of people who can go to the amusement park, the inequality that expresses the previous relationship is

17.25 + 37.25×p ≤ 605

Finally, the inequality that can be used to determine p, the maximum number of people who can go to the amusement park, is:

17.25 + 37.25×p ≤ 605

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https://sis-union.tnk12.gov/scripts/wsisa.dll/WService=wsUNIStu/seplog01.w

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

ya it of course sachi ta