estimate 1624 divided by 23 using compatible numbers

f ⁻¹( x)= x^2+4 is the inverse of f(x)= [tex]\sqrt{x-4}[/tex]

what is an inverse function ?

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

write f(x)= [tex]\sqrt{x-4}[/tex] as an equation

y= [tex]\sqrt{x-4}[/tex]

interchange the variables

x= [tex]\sqrt{y-4}[/tex]

solve the equation for y we get

squaring both side ,we have

x^2 = y-4

this implies that

y= x^2 +4

replace y with f ⁻¹( x)  to show the final answer

f ⁻¹( x)= x^2+4

Hence, f ⁻¹( x)= x^2+4 is the inverse of f(x)= [tex]\sqrt{x-4}[/tex]

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Answer:

maximum at (0, 2 )

Step-by-step explanation:

the vertex is the turning point on the graph.

the graph increases on the left up to (0, 2 ) then decreases

this indicates the vertex is a maximum

Answer:

Step-by-step explanation:

The answer is just 5

f(5)=5

The vertex is (2,-3)So the Answer isY=(x-2)-3

The average quantity of juice that is consumed per person in this country is given as 3.84

We have the following data with which to answer this question

The consumption of juice = 1.92 billion

The population of the country = 500 million

The question wants us to calculate the amount of drink that the persons would consume on average in this nation.

we have average = quantity consumed / total number of persons

This would give us

average = 1.92 billion / 500 million

= 1, 920, 000, 000 / 500, 000 ,000

= 3.84

Hence the amount of juice that is consumed per person in this country is given as 3.84

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Solution of exponential equation  is , x=2

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa is also possible . The basic form of the exponential function can be written as   .

   [tex]a^n = x[/tex]

where, a = the base of function

            x = main expression

            n = exponential

Mathematically, if  [tex]log_ax = n[/tex] is an logarithmic function then, this can be converted to exponential function as    [tex]a^n = x[/tex] .

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

According to given statement,

2^3x = 4^(x+1)

the equation can also written as :

[tex]= > 2^{3x} = 2^{2(x+1)}\\= > 3x = 2(x+1)\\= > 3x = 2x +2\\= > x=2[/tex]

Thus solution for this equation is  x = 2.

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The complete question is :

Solve each equation.

[tex]2^{3x} = 4^{(x+1)}[/tex]

In the given expressions (f x g)(-4) is -8a³ - 8a² + 12a + 12.

So, (a+1)(2a²-3)(-4):

Therefore, in the given expressions (f x g)(-4) is -8a³ - 8a² + 12a + 12.

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Answer:

y =x - 3

Step-by-step explanation:

Here, m is the slope and b is the y-intercept.

 slope = m = 1

 y = 1x + b

Substitute the point (2,-1) in the above equation and find 'b'.

   -1 = 1*2 + b

   -1 = 2 + b

-1 -2 = b

     b = -3

Equation of the line:  y = x - 3

Answer:

85

Step-by-step explanation:

Consecutive numbers are numbers that follow each other in order. The two consecutive numbers are 42 and 43.

42+43=85

Answer:

42 & 43

Step-by-step explanation:

Let the two consecutive numbers be x and x+1 .

Here it is given that the sum of two consecutive numbers is 85.

So we get the equation,

x + (x+1) = 85

We get,

x + x + 1 = 85

2x + 1 = 85

Transposing +1 to RHS,

2x = 85 - 1

2x = 84

Transposing 2 to RHS,

x = 84 ÷ 2

Therefore, we get x = 42

Therefore, the two numbers are x and x+1, so they are: 42 and 43.

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Sam would need to drive for the two plans to cost the same is 130 miles.

Let, x = Number of miles driven

      y = Total cost

The first plan:

Initial fee = $65

Cost of 1 mile = $0.3

Cost of drive x mile = $0.3x

In total, you will pay

y = 0.3x + 65 for the first plan.

The second plan:

There are no initial costs, but

Cost of 1 mile = $0.80

y = 0.80x

Now we have two equations

y = 0.3x + 65

y = 0.80x

As we know that y is equal to both 0.3x + 65 and 0.80x, this means we can equate the right hand sides and solve for x.

    0.3x + 65 = 0.80x

0.80x - 0.3x = 65

            0.5x = 65

                 x =  65÷0.5

                 x =  130

The cost of two plans will be same when Sam drive 130 miles.

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The four rational number between -5/6 and -4/9 are (-43/54, -37/54, -35/54 and -31/54).

First we will make the denominator of -5/6 and -4/9 same by multiplying the numerator and denominator of -5/6 by 9 and multiply the numerator and denominator of -4/9 by 6, we get

-5x9/6x9 = -45/54 and -4x6/9x6 = -24/54

Now, we have -45/54 and -24/54 whose denominator are same.

we can choose or pick any four integers as numerator in between -45 and -24 with denominator as 54.

-43/54, -37/54, -35/54 and -31/54 are the four rational number having numerator in between -45 and -24 with denominator as 54.

Therefore, -43/54, -37/54, -35/54 and -31/54 are the four rational number between -5/6 and -4/9.

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The logarithmic form of 1/4 = 4⁻¹ is log₄ 4⁻¹ = ₋1.

The fundamental logarithmic function has the notation f(x) = log(r) y = log(x), where a > 0. The exponential function ay = x's inverse is represented by this. The common logarithm (log) or natural logarithm (ln) are examples of log functions (log).

The exponential function of the type aˣ = N can be converted into the logarithmic function logₐN = x. A Napier logarithm table can be used to determine the logarithmic value of any number. Logarithms are often calculated using a base of 10, therefore it is possible to get the logarithmic value of any number.

we have the exponential form as aˣ = N

1/4 = 4⁻¹

now the logarithmic form is:

logₐ N = x

log₄ 4⁻¹ = ₋1

hence we get the logarithmic form  as log₄ 4⁻¹ = ₋1.

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Answer:

11429 (estimated)

Step-by-step explanation:

1. Combine like terms: 3x+4x=7x

7x=80,000

2. Divide 80,000 by 7, which is 11428.57

which can be rounded to 11429

Answer:

odd

Step-by-step explanation:

Not sure tho

The average rate of change of 2|x| on the interval [-3, 5] is 0.5

The function is given as

2|x|

Rewrite as

f(x) = 2|x|

The interval is given as

[-3, 5]

So, we have

f(-3) = 2|-3| = 6

f(5) = 2|5| = 10

The average rate of change of 2|x| on the interval [-3, 5] is then calculated as

Rate = (f(5) - f(-3))/(5 --3)

This gives

Rate = (10 - 6)/(5 --3)

Evaluate

Rate = 0.5

Hence, the average rate of change of 2|x| on the interval [-3, 5] is 0.5

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The result of simplifying the expression  x³/₅ / x³/₁₀  using the exponent rules is [tex]\sqrt[10]{}[/tex](x³)

To solve this exercise we have to resolve algebraic operations following the exponent rules.

[(x)³/₅ ] /  [(x)³/₁₀]

Using the quotient rule that indicates that: the exponent result will be the subtraction of these exponents, we have:

x⁽³/⁵ ⁻³/¹⁰⁾

(x)⁽⁶⁻³⁾/¹⁰

(x)³/¹⁰

As we have a fractional exponent, you must convert the exponent to root:

[tex]\sqrt[10]{}[/tex](x³)

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Answer:

15hw.

Step-by-step explanation:

Note 5wh is the same as 5hw, so we have:

7hw+5hw + 3hw

= 15hw.

Or, if you like, you could write it as 15wh.

The absolute value of the inequality is x < 6

Absolute value can be defined as the describing the distance of a number from zero on the number line, without considering direction.

It is also the value of the number with no consideration to it's sign.

Given the inequality;

| | x+4|-7 |< 5 | |

Take the absolute value and expand the bracket

(x + 4) + 7 < 5

expand the bracket

x + 4 + 7 < 5

x + 11 < 5

Make 'x' the subject

x < 5 - 11

x < -6

Take the absolute value

x < 6

Thus, the absolute value of the inequality is x < 6

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Answer:eighty four

Step-by-step explanation:

Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.

You may also hear the simplest form called "lowest term."

In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:

Input:

32^ (-3/5)

Exact Value:

1/8

Decimal Form:

0.125

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Answer:

r = -10

Step-by-step explanation:

1. Distribute

1-(r+2)=9

1-r-2=9

2. Subtract the numbers

1-r-2=9

-1-r=9

3. Rearrange the terms

-1-r=9

-r-1=9

Solution: r = -10

The bone is approximately 16384 years old, as solved by basic algebra and logarithm.

The properties of logarithms and exponents so used are:  [tex]log_b(a)^m=m(log_b(a))[/tex], [tex]log_e(e) = 1[/tex]

Let 'a' be the original amount of the object.

Then, according to question, for y = amount of carbon in the object, y = 0.14(a) (as the bone contains 14% of its original carbon-14).

We are also given that: y = a [tex]e^{-0.00012t}[/tex]

On substituting the value of y, we get: 0.14a = a [tex]e^{-0.00012t}[/tex]

By basic algebra, we can solve it as:

=> 0.14 = [tex]e^{-0.00012t}[/tex]

=> ln (0.14) = ln ([tex]e^{-0.00012t}[/tex]) (taking natural logarithm on both sides)

=> ln (0.14) = - 0.00012t (as [tex]log_b(a)^m=m(log_b(a))[/tex]; further  [tex]log_e(e) = 1[/tex])

=> [tex]\frac{ln(0.14)}{-0.00012}[/tex] = t

=> t = 16384 years (approx.)

Hence, the bone is approximately 16384 years old, as solved by basic algebra and logarithm; The properties of logarithms and exponents so used are:  [tex]log_b(a)^m=m(log_b(a))[/tex], [tex]log_e(e) = 1[/tex].

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Answer:

Each pack of gum was 1.69

Step-by-step explanation:

20 - 2.50 = 17.50

17.50 - 12.43 = 5.07

5.07/3 = 1.69

The approximate length is 12.755 year or 4653.75 days.

A year is the time it takes for a planet, moon, or other celestial body to make one orbit around the Sun. ( when we take our solar system as an example). In the case of other exoplanets, the celestial bodies, moon and other planets orbit around the main star. The period of the moon's orbit around the earth is related to the moon.

The reference point is very important in determining the exact length of a year. The length is dependent upon the reference point used for the orbital movement.

Jupiter completes a Single orbit once every 4333 days, due to which one Jupiter year is equivalent to 11.86 earth years.

The complete calculation is done below. (Image Attached)

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Answer:

back view

Step-by-step explanation:

You are very very very correct

Answer:

You want to start off my isolating the y onto one side:

2y-10x=14 ---> 2y=14+10x

then you remove the coefficient from the left side:

2y=14+10x -----> y=7+5x

Then all you want to do is rearrange the equation to match slope intercept:

y=7+5x ----> y=5x+7

Answer:

You want to start off my isolating the y onto one side:

2y-10x=14 ---> 2y=14+10x

then you remove the coefficient from the left side:

2y=14+10x -----> y=7+5x

Then all you want to do is rearrange the equation to match slope intercept:

y=7+5x ----> y=5x+7

Step-by-step explanation:

The value of BC the nearest hundredth is 15.01 .

From the image , we are able to see that CA = seven and angle A = 65°

Using ,Trigonometric Ratios , we get

Tan A = Perpendicular / Base

Tan 65° = BC / CA

2.144 =BC / 7

2.144 ×7 = BC

15.011 = BC

On rounding off to the closest hundredth , we have a tendency to get BC = 15.01

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Answer: It is correct.

The first step here is to distribute the numbers

4 times 2x is 8x

4 times -5 is -20

Therefore, you're left with 8x-20

I hope this helps!

For any function, we call x the numerator value and y is the denominator value.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

In Mathematics, a fraction comprises two (2) main parts and these include the following:

For any function in Mathematics, we call x the numerator value while y is the denominator value.

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Answer:

7 14/15

Step-by-step explanation: