Unit 4 homework 7 part 2
Please help

Inverse of logarithm function is exponential function, undoing the effect of logarithm.

What is logarithm ?

A logarithm is a mathematical function that calculates the power to which a given number (the base) must be raised to produce a certain value. Commonly, logarithms are written with the notation log base b (x), where b is the base and x is the value for which we want to find the power. It can also be written as log x.

The reverse or inverse of a logarithm function is the exponential function. If f(x) = log_b x, then the inverse function, denoted as f^-1(x), is the exponential function with base b, denoted as b^x. This is because log_b (b^x) = x, and b^(log_b x) = x. The logarithm and the exponential function are inverse of each other, meaning that applying the logarithm function "undoes" the effect of the exponential function, and applying the exponential function "undoes" the effect of the logarithm function.

Inverse of logarithm function is exponential function, undoing the effect of logarithm.

To learn more about logarithm visit : brainly.com/question/30085872

#SPJ4

The domain of the function f(x) = (3 - 2x)/(9 - 4x) is equal to (-∞, 9/4) U (9/4, ∞) or (-∞, 2.25) U (2.25, ∞).

In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined.

In order to determine the domain of this rational function, we would use an online graphing calculator to plot it and then write its domain in interval notation based on the values on the x-coordinate of the graph as follows:

Domain = (-∞, 9/4) U (9/4, ∞) or (-∞, 2.25) U (2.25, ∞)

By using set builder notation, the domain of this rational function f(x) = (3 - 2x)/(9 - 4x) can be re-written as follows;

Domain = {x|x ≠ 9/4} or {x|x ≠ 2.25}.

Read more on domain here: brainly.com/question/4685947

#SPJ1

It will take 3750 minutes (62.5 hours) time for all the water to flow out of the tank.

1. Calculate the total volume of the tank: 4500 litres

2. Calculate the rate of flow: 1.2 litres per second

3. Calculate the total time it will take for all the water to flow out: 4500 / 1.2 = 3750 minutes (62.5 hours)

The tank contains 4500 litres of water and is flowing out of the tank at a rate of 1.2 litres per second. This means it will take 3750 minutes (62.5 hours) for all the water to flow out of the tank. To calculate this, we first had to determine the total volume of the tank which was 4500 litres. Then, we had to calculate the rate of flow which was 1.2 litres per second. Finally, using the total volume of water and the rate of flow, we were able to calculate that it would take 3750 minutes (62.5 hours) time for all the water to flow out of the tank.

Learn more about time here

https://brainly.com/question/28050940

#SPJ4

Answer:

x - 75 ≥ 420

Step-by-step explanation:

Answer:

16/52

8/26

4/13

As 13 cards are one suit or are hearts, and in that suit, there is one king, I just add 3 more cards for the other king cards as well and you get 16/52

Step-by-step explanation:

Therefore , the solution of the given problem of inequality comes out to be x<6 and x>9.

A connection of linear solutions or integers in mathematics that lacks an equal sign is known as an inequality. Inequity so follows an imbalance. There exists an inequality between two numerical values when they are not equal. Differences exist between equality and inequality. I've used the most typical symbol in cases where the variables aren't comparable or equal (). Regardless of how little or large the values are, there are numerous inequities that can be used to compare them. A variety of fundamental inequality issues can be solved by switching the two sides until variables represent everything that is left. There are numerous variables that could lead to inequality, including the conjunction or division of low values on both sides. Alternating sides

Here,

Given : 5x + 2 < 32

=> 5x < 32-2

=>5x < 30

=>x < 6

thus,

=> x-7>2

=> x>9

Therefore , the solution of the given problem of inequality comes out to be x<6 and x>9.

To know more about inequality visit:

https://brainly.com/question/29914203

#SPJ1

Answer:

B) m × 3 = 27

Step-by-step explanation:

Explanation:

m = 27 ÷ 3 = 9

E) q ÷ 3 = 27

Explanation:

q = 27 × 3 = 81

So, the equations with 9 as a solution are B and E.

The solution to the system of linear equation x, y are -6, 6

A system of linear equations is a collection of two or more linear equations that contain the same variables. Linear equations are equations of the form ax + by = c, where a, b, and c are constants and x and y are variables.

There are different methods to solve a system of linear equations, such as substitution, elimination, and graphing. Each method has its own advantages and limitations, and the choice of method depends on the form of the equations and the type of solution.

In this problem, we have two system of equations which are given as;

Combining both equations and solving via substitution method, the values of x and y are -6 and -6

Learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

There are 126 different selections possible if at least 3 balls must be blue.

Total number of red balls: 8

Total number of blue balls: 8

Also, a woman selects 4 balls

And also at least 3 balls off the 4 must be blue

So the first combination is 3 blue and 1 red remember the woman picks up 4 balls.

And the second combination is 4 blue and 0 Red remember at least 3 blue balls

So the equation is as given below:

[tex]^nC_{r} =\frac{n(n-1)(n-2)(n-3)..... r terms.}{1*2*3..... r terms.}[/tex]

Now substitute values in the formula:

(8C3*8C1 + 8C4*8C0)=(56+70)=126 selections.

Hence, There are 126 different selections are possible if at least 3 balls must be blue.

To know more about Combinations:

https://brainly.com/question/11732255

#SPJ4

The statement angle 8=85, because 180-115=65 , 180-(65+30)=85 is true.

A triangle is a three-sided polygon that consists of three edges and three vertices.

In the given triangle one measure is given which is 30 degrees.

The angle 7 we calculate because the other side angle is 115 degrees.

The sum should be 180 degrees

115+angle 7=180

angle 7=180-115

angle 7=65 degrees

Now we know that the sum of interior angles of a triangle are 180 degrees.

65+30+angle 8=180

95+angle 8=180

Angle 8=85

Hence, the statement angle 8=85, because 180-115=65 , 180-(65+30)=85 is true.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ1

The logarithm function can be used to calculate the log values. So the value of log 3 is 0.4771.

Logarithmic functions, also referred to as log functions, are the opposite of exponentiation. According to its definition, a logarithm is a measurement that depicts the degree to which a base (fixed number) is raised to generate a specific number.

The logarithmic function is typically expressed as:

f(x) = [tex]log_ax[/tex]

[tex]log_an=x[/tex] can be expressed as an exponential function in accordance with the definition of the logarithm function:

[tex]a_x = n[/tex]

In general, there are two types of logarithmic functions, namely:

1. Frequently Used Logarithmic Function

2. Natural Logarithmic Function

To learn more about finding the value of log link is here

brainly.com/question/78585

#SPJ4

Although the examples referenced are note given, the subject or principle of Quadratic Equations and the Quadratic formula are universal principles and hold true regardless of what examples are used.

Thus, two tings that one can learn about solving quadratic equations by using the Quadratic formula are:

In mathematics, almost every student encounters the quadratic formula, which is a popular method for determining the roots of a quadratic problem. In practice, the quadratic formula may be used to calculate the size of a place, the speed of a moving item, the value of profit earned on a product, and other things.

We've shown that a quadratic equation is a degree 2 equation. A quadratic has the standard form y = ax² + bx + c, where a, b, and c are integers and a cannot be zero. All quadratic equations graph into some form of curve. All quadratics have two solutions, although not all of them are real.

Learn mroe about Quadratic Formula:
https://brainly.com/question/9300679
#SPJ1

The 7 rules of logarithms are as: 

1. Rule of product.

2. Rule of division.

3. The Power/Exponential Rule.

4. A new fundamental rule.

5. Rule of the base swap.

6. Log derivative.

7. Log integral.

The alternate format for writing exponents is with logarithms. A number appears base-based logarithm is approximately equivalent to another number. A logarithm performs exponentiation's exact opposite function.

1. Rule of product: According to this rule, adding the individual logarithms of two logarithmic values results in the multiplication of those values.

[tex]Log_b (mn)= log_b m + log_b n[/tex]

2. Rule of division: The difference between each logarithm is equivalent to the division of two logarithmic values.

[tex]Log_b \left(\frac{m}{n}\right)= log_b m - log_b n[/tex]

3. The Power/Exponential Rule: According to the exponential rule, the exponent times the logarithm of m's logarithm is equivalent to m's logarithm with a reasonable exponent.

[tex]Log_b (m^n) = n log_b m[/tex]

4. A new fundamental rule:

[tex]Log_b m =\frac{log_a m}{log_a b}[/tex]

5. Rule of the base swap:

[tex]log_b (a) = \frac{1}{log_a (b)}[/tex]

6. Log derivative: If f (x) = [tex]log_b (x)[/tex], then the derivative of f(x) is given by;

[tex]f'(x) = \frac{1}{(x ln(b))}[/tex]

7. Log integral:

[tex]\int{log_b(x)dx} = x\left(log_b(x) - \frac{1}{ln(b)}\right) + C[/tex]

To learn more about rules of logarithms link is here

brainly.com/question/29258754

#SPJ4

Answer:

$40. If she bought 3 for $30, then each shirt must be equal to $10 each.

4 times 10 = 40

Step-by-step explanation:

Hope it helps you! =D

The relationship between two equal amounts is described by the characteristics of equality

The relationship between two equal amounts is described by the characteristics of equality. To maintain balance, each mathematical operation that is done to one side of an equation must also be applied to the opposing side.

a = 2b, then a-c = 2b - c

This is Subtraction Property of Equality

According to the Subtraction Property of Equality, if two equal things have an equal value subtracted from them or deleted, the outcome is a new equal quantity. When two equivalent sides of a mathematical statement are separated by an equal sign, an equation is being expressed. The subtraction property has the expression if a = b, then a - c = b - c.

X = X

This represents the Reflexive Property

In algebra, a number is always equal to itself according to the reflexive property of equality.

3(p-7) = 3p - 21

This represent distributive property.

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

-7k = -42 then k= 6

This is Division Property of Equality

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.

m + n = 15 and n = 2, then m + 2 = 15

This represent Substitution Property

x/4 = -5 then x = -20

This is Multiplication Property of Equality

w² = 2x and 2x = y, then w² = y

This is Transitive Property

c-9 = -1, then c = 8

This is Addition Property of Equality

n = -3, then -3 = n

This is Symmetric Property

To learn more about Properties of Equality refer to :

https://brainly.com/question/5217895

#SPJ1

The wingspan of the airplane in the scale drawing  is equal to 6.67 inches.

The wingspan of an airplane in a scale drawing can be calculated using the scale factor. If the wingspan of the real airplane is 60 feet and 1 inch represents 9 feet, then the wingspan of the airplane in the scale drawing is 60/9 = 6.67 inches. Knowing the dimensions of the real airplane and the scale factor of the drawing, it is possible to accurately calculate the wingspan of the airplane in the scale drawing. This calculation is important for accurately measuring and drawing scale models of aircraft.

To know more about scale drawing on below link:

https://brainly.com/question/17388747?#

#SPJ4

It could be challenging to remove blocks from the middle and bottom of the pile in order to draw a basic random sample. Take 10 blocks off the top of the pile to represent convenience as an example.

A non-probability sampling technique called convenience sampling includes selecting a sample from the nearest area of the population. Pilot testing makes the most use of this kind of sampling. Convenience sampling enables researchers to acquire data that would not otherwise be possible in the absence of a sample frame.

Convenience sampling can assist you in collecting data for exploratory research that can be utilised to develop a compelling hypothesis or research topic. Convenience sampling has several benefits, but its main benefits are that it is affordable, effective, and straightforward to use. The main drawback of convenience sampling is the sample's unclear generalizability.

To learn more about sample of convenience: https://brainly.com/question/6078134

#SPJ4

Mountain View received at least 4000 visits 66.67% of the time during their busy season.

Calculating the percentage of times Mountain View received at least 4000 visitors is the task at hand in this exercise. According to the data plot, we can see that they had no visitors the first weekend, 2000 the following weekend, 4,000 the third week, 6,000 the fourth, 8,000 the following week, and 10,000 the last week of their busy season. We can see that starting in week 3, they had more than 4,000 visits, making the total number of weeks within our 6-week study period that had more than 4,000 views equal to 4 weeks. Therefore, (4/6)*100, or about, 66.67% represents the percentage of visitors of at least 4,000 at Mountain View.

Learn more about percentage here:

https://brainly.com/question/26511030

#SPJ4

The given line segment which is divided into the ratio 3 : 4  shows line is divided into 7  parts.

As given in the question,

Let us consider the given line segment be PQ .

And take point R between the given points AB such that it get divided in the ratio 3 : 4.

From the given ratio PR is divided into 3 equal parts.

And RQ  is divided into 4 equal parts.

Total number of parts PQ  is divided is given by

= PR + RQ

= 3 + 4

= 7  parts  which are equal to each other.

Therefore,  the given ratio 3 : 4 represents that the line segment is divided into 7 equal parts.

Learn more about ratio here

brainly.com/question/13419413

#SPJ4

On solving the provided question we can say that equation will be as follows  6x + 55y = 13.15 => x = coins = 2 and y = nickels = 12

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

jesse has  = $6.55 worth of quarters and nickels

the number of nickels is five more than two times the number of quarters

so

let coins be x

and nickels be y

now equation will be as follows

6x + 55y = 13.15

x = coins = 2

y = nickels = 12

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The value of constant of proportionality is, 9,400

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The local dam lets 75,200 gallons pass through it over the course of 8 hours on Wednesday.

And, On Thursday, the dam lets 141,000 gallons pass through it over the course of 15 hours.

Now, We know that;

By the definition of proportionality,

⇒ y = kx

Where, k is constant of proportionality.

Let y represent the number of gallons and x represent the number of hours.

So, We get;

For The local dam lets 75,200 gallons pass through it over the course of 8 hours on Wednesday.

⇒ y = kx

⇒ 75,200 = k × 8

⇒ k = 9,400

And, On Thursday, the dam lets 141,000 gallons pass through it over the course of 15 hours.

⇒ y = kx

⇒ 141,000= k × 15

⇒ k = 9,400

Learn more about the proportion visit:

https://brainly.com/question/1496357

#SPJ1

His total profit is  13130. Your remaining cash balance (also known as your net profit) is the sum of all your business expenses.

The answer is given below :

Sum = Rs 40000

We know that,

Interest = (Sum × Time × Rate)/100

So, for the 1st year when profit is 5%,

Interest

= Rs (40000 × 1 × 5)100

= Rs 2000

So, according to the question,

Rs (40000 + 2000) = Rs 42000 be the Sum for the 2nd year.

So, for the 2nd year, when profit is 10%,

Interest

= Rs (42000 × 1 × 10)/100

= Rs 4200

Again, for the 3rd year, Sum

= Rs (42000 + 4200)

= Rs 46200

Thus, for the third year, when profit is 15%,

Interest

= Rs (46200 × 1 × 15)/100

= Rs 6930

So, now amount is total

= Rs (46200 + 6930)

= Rs 53130

Hence, total profit

= Rs (53130 - 40000)

= Rs 13130

To learn more about total profit refer to:

https://brainly.com/question/21613450

#SPJ1

The inverse of the logarithmic function 3 is 1000 for base 10.

The index or power to which the base must be raised in order to reach the given number is represented by the logarithm of any positive number, whose base is a number that is larger than zero but not equal to one.

mathematical form: [tex]log_ab=x[/tex].

Here for inverse of given function is derived by given formula.

[tex]a^x=b[/tex]

There are two types of logarithm function:

Natural Logarithm and common logarithm.

[tex]log_{a}b=x\\log_{10}b=3\\a^x=b\\10^3=b\\b=1000[/tex]

So inverse of logarithmic function 3 is 1000.

Know more about logarithm function:

https://brainly.com/question/30085872

#SPJ4

The dimensions that will minimize the cost of the metal to manufacture the can is r = 5.42 dm and h = 10.84 dm.

To minimize the cost of the metal to manufacture the can, minimize the surface area of the can. The surface area of a cylinder can be found using the formula 2πr(r + h) where r is the radius and h is the height.

The volume of the cylinder is given by the formula πr²h, and it is known that it needs to be equal to 1000 l or 1000 cubic dm.

Set the volume equation equal to 1000 and rearrange it in terms of r.

πr²h = 1000 cubic dm

h = 1000/(πr²)

Substitute this value of h back into the surface area equation and minimize it with respect to r.

2πr(r + h) = 2πr(r + 1000/(πr²))

To minimize the surface area, take the derivative of this expression with respect to r and set it equal to zero, then solve for r.

d(2πr(r + 1000/(πr²)))/dr = 0

d(2πr² + 2000πr/(πr²))/dr = 0

d(2πr² + 2000/r)/dr = 0

4πr - 2000/r² = 0

4πr = 2000/r²

r³ = 2000/4π

r = ∛(500/π)

r = 5.42 dm

Substitute it back into the equation for h and find the corresponding value of h.

h = 1000/(πr²)

h = 1000/(π(∛(500/π))²)

h = 10.84 dm

So, the dimensions that will minimize the cost of the metal to manufacture the can are r = 5.42 dm and h = 10.84 dm.

Learn more about cylinder here: https://brainly.com/question/9554871

#SPJ4

hi there! the slope for those two points is 10/5

Answer:

B

Step-by-step explanation:

B.B.B.B.B.B.BB.B.B.B.B.B.B.B.B

The total length of wood in meters is 9.65m .

To convert mm to meter

There are 1000mm per meter so divide number of mm by 1000 to convert to meters

The sizes of the pieces of wood are

Add the number of pieces of wood:

1.5m + 2.5m + 0.85m + 4.8m = 9.65m

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units (SI) system.

Most people understand length to refer to an object's longest dimension. However, depending on the object's position, this is not always the case.

Learn more about Length of wood:

https://brainly.com/question/21172438

#SPJ4

The required  temperature of the oven 17 and t minutes after being turned on are 245º and 75º + 17t.

The formula R = D/T, or rate of change equals the distance travelled divided by the time required to do so, can be used to approach rate of change problems in general.

The initial temperature of the oven is 75º and temperature will increase at a rate of 10° per minute after being turned on.

Total temperature after 17 minutes,

75º  + 17(10º )

75º + 170º

245º

And

Temperature after oven t minutes after being turned on

75º + 17t

Thus, required temperature of oven is 245º and 75º + 17t.

To know more about Rate change visit:

brainly.com/question/29518179

#SPJ4

Between these two integers the square roots lie

a)√ 56=7 < √56 < 8

b)-√78= 8 < -√78 < 9

c) -√43=-7 < -√43 < -6

d)√99= 9 < √99 < 10

Find the square of the two integers that are immediately adjacent to the square root. For instance, we would discover the square of 7 and 8, which is 49 and 64, respectively, for 56.

The surd should be compared to the square of the adjacent numbers. The surd is said to be between two integers if it is bigger than the square of the lower integer and less than the square of the higher integer.

This approach allows us to see that √56 is between 7 and 8 as 49 < √56 < 64.

Similarly,

b) -√78 lies between 8 and 9 because 64 < -√78 < 81

c) -√43 lies between -7 and -6 because 49 > -√43 > 36

d) √99 lies between 9 and 10 because 81 < √99 < 100

To learn more about square roots refer to

https://brainly.com/question/29286039

#SPJ1