What is the solution of each equation? Check your answers.

(a) e x-2=12

Answers

Answer 1

According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.

Therefore, the given expression is [tex]ex^{-2}=12[/tex]

The values get multiplied in addition. Therefore, the above expression can be written as by taking log on both the sides:

[tex]ln(ex^{-2} )=ln(12)\\-2(ln(e)+ln(x)) = ln(4)+ln(3)= 2ln(2)+ln(3)[/tex]

Using logarithmic definition, we can write:

The solution for the given expression is [tex]-2(1+ln(x)) = 2+ln(3)[/tex]

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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Related Questions

Which statement is true about the ray passing through points B and C?

Answers

Answer:

The ray extends infinitely in one direction.

Step-by-step explanation:

It starts at the point and the arrow at the ends mean it extends in that direction away from the point infinitely.


Evaluate each logarithm.
log₁₂ 144

Answers

The logarithmic equation log₁₂ 144 = 2

What is logarithmic equation ?

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

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

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

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

According to statement,

log₁₂ 144

this can be written as ,

log₁₂ (12²)

= 2 log₁₂ (12)

= 2 . 1                   (as, log a with base a = 1 )

= 2

Thus , log₁₂ 144 = 2

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Write 0.33 as a percentage.

Answers

Answer:

33%

Step-by-step explanation:

moving the decimal two places to the right


The expression 0.036m³/₄ is used in the study of fluids. Which best represents the value of the expression for m=46 x 10⁴ ?
(A) 636
(B) 1460
(C) 1660
(D) 16,600

Answers

The value of the expression 0.036m³/₄ is determined by algebraically substituting the value of m=46 x 10⁴ and solving the radical expression.

In the given radical expression, 0.036 is a constant and m is a variable with a power of ¾.

We will solve for the variable term first which will be written as a radical and multiply it with the constant.

Substituting m=46x10⁴ in the expression 0.036m³/₄.

0.036m³/₄=0.036(46x10⁴)³/₄

Now rewrite the expression as a radical,

0.036(46x10⁴)³/₄= 0.036∜(46*104)3

Multiply the exponents within radicand term,

= 0.036∜(463*1012)

Now simplify the expression,

= 0.036∜(463*(103)4

= 0.036*103 *∜463

= 0.036*103 *∜97,336

= 36 ∜97,336

= 36*17.66≈636

Hence, the correct answer is option A.

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Is 4 x 10³ or 2 x 10⁸ larger in value? Explain why.

Answers

First, you must solve for (4 x 10^3) and (2 x 10^8)

Think of the ^3 and ^8 as decimal places. Ten to the positive three means to move the decimal behind the 4, backwards the increase the number. So (4 x 10^3) would be equal to 4000. 3 decimal places back from 4.

Do the same thing for (2 x 10^8) and you get 200000000.

TLDR: (2 x 10^8) > (4 x 10^3) because (2 x 10^8) = 200000000 and (4 x 10^3) equals 4000.

-160=6x-8(5x+3) what is my answer

Answers

The answer to the expression -160=6x-8(5x+3)  is x = 4.

What is an expression?

An expression is written in the form of variables and constants combined with arithmetic operations. There are many types of expressions in mathematics they are algebraic expressions, logarithmic expressions, trigonometric expressions, and many more.

The given expression - 160 = 6x - 8(5x+3) can be writen as,

6x - 8(5x+3) = -160.

First, we will distribute what is inside the brackets.

∴ 6x - 40x - 24 = -160.

-34x = -160 + 24.

-34x = -136.

34x = 136.

x = 136/34.

x = 4.

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Please help me please please

Answers

Simplifying the problem, 4 - 9 + 5 - 1 - 6 + 11 would give the result of 4.

How to simplify equation?

In order to simplify the problem given of 4 - 9 + 5 - 1 - 6 + 11, you can put the numbers into brackets and then carry out math operation:
= (4 - 9) + (5 - 1) - (6 + 11)

Solving the numbers in the brackets gives:

= -5 + 5 - 1 - 6 + 11

= 4

In conclusion, the simplified form would be 4.

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she had to choose between two families to babysit for. the first family offers her 40 plus $5 per hour. The second family offers her $20 and $10 per hour. Which offer will make her more money and how much more will she make

Answers

The offer that will make her more money and how much more will she make is

The first offer$15 dollars more

This is further explained below.

Which offer will make her more money and how much more will she make?

Generally, the equation for the total made is  mathematically given as

T= flat rate +(hours worked*hourly pay)

Therefore, for the first family

T= 40 + (6+5)

T=$51

For the 2nd family

T'= 20 + (6+10)

T'=$36

In conclusion, the offer that will make her more money and how much more will she make is

T'=51-36

T'=$15

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CQ

Simone wants to babysit this weekend to make some extra money she changes a flat fee then changes per hour or part thereof that she babysits Saturday afternoon she will babysit for 6 hours she had to choose between two families to babysit for. the first family offers her 40 plus $5 per hour. The second family offers her $20 and $10 per hour. Which offer will make her more money and how much more will she make

Measure of each numbered angel m<1=38

Answers

The measures of the angles are <1 = 38, <2 = 142, <3 = 38 and <4 = 142

How to use the diagram to find the angle measures that satisfy each case?

The diagram that completes the question is added as an attachment

From the diagram, we have

<1 + <2 = 180 degrees --- supplementary angles

Given that

<1 = 38 degrees

We have

38 + <2 = 180

Evaluate

<2 = 142

Also, we have

<3 = <1

<4 = <2

This means that

<3 = 38

<4 = 142

Hence, the measures of the angles are <1 = 38, <2 = 142, <3 = 38 and <4 = 142

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Jordan's t-shirt business sells long sleeve shirts for $15 and short sleeve shirts for $10. he needs to make at least $300 to buy a new heat press machine. so far, fewer than 28 people have purchased shirts. which system of inequalities fits this scenario?

Answers

The system of inequalities fits in this scenario are x + y & lt; = 2815x + 10Y & lt;= 300.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including: The symbol a b indicates that an is smaller than b. When a & gt; b is used, it indicates that an is bigger than b. A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered. In the given questions the inequalities are x + y & lt;= 2815x + 10y & lt;= 300

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Simplify the expression.
164[3+2+ (9-7)] =

Answers

After thoroughly calculating the simplifying the expression 164[3+2+ (9-7)] is   1148

What is mathematical expression?

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.

The following are some examples of expressions and word phrases that they relate to:

Formula: 3 + 7

Expressions and equations are different from one another because an expression consists of a combination of numbers, variables, and operation symbols, whereas an equation consists of two different expressions joined together by an equals sign. This shows that the expression's two sides have the same value.

Simplification of the expression 164[3+2+ (9-7)]

⇒ 164[3+2+ (9-7)] =

⇒ 164[5+(2)] =

⇒ 164[5+(2)]

⇒ 164(7)

⇒ 1148

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There are 62 people at the commuter area waiting to catch carpool vans. Each van can fit 9 people. How many vanes will be needed to transport everyone so that no one is left behind?

Answers

Answer:

7 vans

Step-by-step explanation:

62 ÷ 9 = 6.86.8 is not a whole number, so when you round it to the nearest whole number you get 7.[Also, 9 × 7 = 63, which is close to 62]∴ 7 vans will be needed.

Answer:

7 vans

Step-by-step explanation:

Each van can take 62 people so you share the 62 among the vans, and each van is 9,therefore 62÷9=6.888889 and people cannot be in decimals so you round the figure to a whole number which is equal to 9.

wwwwwhat is a/-3-6=-1

Answers

-9=-1
I believe this is the answers


You have solved equations containing square roots by squaring each side. You were using the property that if a=b then a²=b² . Show that the following statements are not true for all real numbers.
a. If a²=b² then a=b .

Answers

If a² = b² , then a = b is not true for all real numbers.

We know that ' if a = b, then  a² = b²'.

We need to prove that the converse of this statement is not always true.

i.e., we need to show that if a² = b² , then a = b is not true for all real numbers.

To show that a statement is wrong we just need to find a counter example for the statement.

For this, let a = -5 and b = 5.

Clearly, a ≠ b

But -5² = 25 and 5² = 25

That is, a² = b² but a ≠ b.

Hence we proved that 'If a² = b² , then a = b is not true for all real numbers'.

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how do you know when a table is a function? explain

Answers

Answer:

You know a table is a function when each element inside the domain matches with only one element within the range.

Answer: You know a table is a function when each element inside the domain matches with only one element within the range.

Step-by-step explanation:  hope this helps


What is the solution of each system of equations? Solve using matrices.
b. [4x-6y=9 -10x+15y = 8]

Answers

The system of equations which is as represented in the task content above when solved by elimination, substitution or matrices has no solution.

This goes to say that the above given system of equations ultimately has no solution using matrices

What is the solution of the system of equations given in the task content?

It follows from the task content that the solution pair of the system of equation as given in the task content is to be determined.

Given system of equation;

4x-6y=9

-10x+15y = 8

By multiplying the first equation by 5 and the second equation by -2; we have;

20x - 30y = 45

20x - 30y = -16

Hence, it is evident that the system of equations above has equal slope but different intercept equations.

Consequently, subtract equation 2 from 1 so that we have;

0 = 61....an equality which doesn't hold true.

Ultimately, the system of equations has no solution.

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Need some help with this..

Answers

Answer:

Step-by-step explanation:cevaplandıında banada haber verin rez kardeşlerim

89 + 38 x 2 = ?
Giving crown

Answers

The answer is 165
Djdjxiwnsjxjdj

Answer: 254

Step-by-step explanation:

89 + 38 x 2

89 + 38 = 127

127 x 2 = 254


Let f(x)=x-4 and g(x)=x²-16 . Perform each function operation and then find the domain. f(x)=g(x)

Answers

The domain of the function h(x) = x² - x - 12 when the function operation f(x) = g(x) is performed is ( - ∞ , ∞ ).

A domain is a collection of potential input values. All input values visible on the x-axis make up the graph's domain. The collection of potential output values represented on the y-axis is known as the range.

Consider the two functions,

f(x) = x - 4 and g(x) = x² - 16

The function operation f(x) = g(x).

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

x² - 16 - ( x + 4 ) = h(x)

h(x) = x² - x - 16 + 4

h(x) = x² - x - 12

The collection of input or argument values for which a function is actual and defined is known as its domain.

So, the domain of the function h(x) is ( - ∞ , ∞ ) or - ∞ < x < ∞.

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2 1/6 + 3 4/9
Need help with this mixed number problem:)

Answers

Answer:

5.611 or 5 11/18

Step-by-step explanation:

hope this is helpful!

Answer:5/3

Step-by-step explanation:


Evaluate each logarithm. log₃ 1/9

Answers

According to the given  the given  logarithm log₃ 1/9 the value is = -2

What is Logarithmic functions?

Logarithmic functions are significant due of their link to exponential functions. Logarithms are useful for solving exponential equations and investigating the properties underlying exponential functions.

According to the given information:

log₃ 1/9

Can be written as:

log₃ (1/9) = x

using the log definition in exponential form. if x and b are positive real number and b dose not equal 1 then  log_b (x) = y is equivalent to b^y = x.

3^x = 1/9

creating equivalent expression in the equation that all have equal base.

3^x = 3^-2

if the base are the same, two expression are only equal if the exponential are also equal

x = -2

the variable x is equal to -2

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Solve. Check for extraneous solutions. 2(x-1)⁴/₁+4=36

Answers

No extraneous solution to the equation

The equation is

2[tex](x - 1)^{4/1}[/tex] + 4 = 36

We have to find the extraneous solution of the equation and for this first, we need to find the value of x.

2[tex](x - 1)^{4}[/tex] + 4 = 36

2[tex](x - 1)^{4}[/tex] = 32

[tex](x - 1)^{4}[/tex] = 16

x - 1= 2

x = 3

Now we will put the value of x in the equation.

2[tex](3 - 1)^{4}[/tex] + 4 = 36

2 [tex]2^{4}[/tex] + 4 = 36

2 × 16 + 4 = 36

32 + 4 = 36

36 = 36

Therefore we get that there is no extraneous solution to the equation, x = 3 is the solution of the equation.

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Can someone to help me answer this

Answers

I am pretty sure it is the top right graph

It’s the picture below left


Evaluate each logarithm.
log₅125

Answers

the answer to the given logarithm expression is log₃ 125 = 3

Another technique to explain exponents in mathematics is through logarithms. A base number's logarithm equals another number.

The power's inverse function is the logarithm. For instance, log10 100 = 2 if 102 = 100. A power to which a number must be increased in order to achieve another value is referred to as a logarithm.

This is the most practical method for displaying enormous numbers. Logarithms have several important properties that prove that multiplication and division of logarithms can  be written in terms of addition and subtraction logarithms. A second name for the common logarithm is the base 10 logarithm.. This is represented as log10 or simply log. The base 10 logarithm is another name for the common logarithm. The common logarithm specifies the number of times the number 10 must be multiplied in order to produce the desired result.. We need to evaluate log₃ 125

Using the property

logₐ (mⁿ) = n logₐ m

125 = 5³log₃ 125 can be written as log₃ 125= 3 log₅ 5

We know that logₐ a = 13 log₅ 5= 3

Therefore, we calculated the logarithm, which is log₃ 125 = 3

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the question is in the picture! i need help ASAP!

Answers

Answer:

The answer I think is

No points of intersection

Step-by-step explanation:

HELP PLEASEEEEEEEEEE

Answers

Answer:

11:50 AM

Step-by-step explanation:

We should first find the sum of the times it would take her to clean each room, along with the break time.

Kitchen = 80 minutes
Lounge = 40 minutes
Bedroom = 90 minutes
Bathroom = 35 minutes
Break = 45 minutes

[tex]\text{Total time (in minutes) } = 80 + 40 + 90 + 35 + 45 = 290.[/tex]
We should then divide this amount of minutes by 60 to find how many hours it took her.

[tex]\text{Total time (in hours) } = \frac{290}{60} = 4\frac56[/tex]
This means it took her 4 hours and 50 minutes to finish cleaning.

Therefore, if she started working at 7 AM and worked for 4 hours and 50 minutes, she was done by 11:50 AM.


In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.
magnitude 9.5 in Valdivia, Chile, in 1960

Answers

The intensity level of the earthquake in New Madrid, Missouri in 1812 was about 1.6 times less than the intensity level of the earthquake Valdivia, Chile, in 1960.

We use the following formula for comparing the intensity level of earthquakes-

Log (i1 / i2) = M1 - M2

where i = intensity level determined by a seismograph

M = magnitude on a Richter scale.

Now, from the given information-

magnitude of earthquake in New Madrid = 7.9

Thus, M1 = 7.9

Then intensity of the earthquake in New Madrid = i1

magnitude of earthquake in Chile = 9.5

Thus, M2 = 9.5

Then intensity of the earthquake in Chile = i2

⇒ log (i1 / i2) = 7.9 - 9.5

log (i1 / i2) = -1.6

This means that the intensity level of the earthquake in New Madrid, Missouri in 1812 was about 1.6 times less than the intensity level of the earthquake Valdivia, Chile, in 1960.

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A 1200 gram sample of radioactive matter will completely decay (be undetectable) in 10 hours. There exists a set of ordered pairs (t. m), where t is the amount of time in hours that the substance has been decaying, and m is the mass in grams that has decayed.

If t≥ 0, what is the range of m?​

Answers

Using it's concept, the range of the function is given as follows:

0 ≤ m ≤ 1200.

What is the range of a function?

The range of a function is the set that contains all possible output values for the function.

For this problem, we have to consider these two bullet points next, considering the mass is the output value of the function.

The smallest possible mass for the substance is of 0 grams, as after the substance decays to 0 grams, it will not assume a negative value, it will just disappear.The greatest possible mass for the substance is the initial mass of 1200 grams, as the substance does not adquire mass with time, it just loses it.

Considering these masses, the range of the function is given as follows:

0 ≤ m ≤ 1200.

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Mariam took a taxi from her house to the airport. The taxi company charged a pick-up fee of $2.90 plus $1.25 per mile. The total fare was $6.65, not including the tip. Write and solve an equation which can be used to determine m, the number of miles in the taxi ride.
Equation:
Answer: m =​

Answers

Answer:

are there options?

Step-by-step explanation:

In an arithmetic series, s40 = 1900 and u40 = 106. find the value of the first term and the common difference.

Answers

The first term and common difference of the arithmetic series are -11 and 3.

How to solve an arithmetic series?

In the arithmetic series, S₄₀ = 1900 and U₄₀ = 106

Hence,

Sₙ = n / 2 (2a + (n - 1)d)

S₄₀ = 20(2a + 39d)

S₄₀ = 40a + 780d

1900 =  40a + 780d

Uₙ = a + (n - 1)d

U₄₀ = a + 39d

106 = a + 39d

Combine the equation

a + 39d = 106

40a + 780d = 1900

20a + 780d = 2120

40a + 780d = 1900

20a = - 220

a = -220 / 20

a = -11

Hence,

106 = a + 39d

106 = -11 + 39d

106 + 11 = 39d

117 = 39d

divide both sides by 39d

d = 117 / 39

d = 3

Therefore, the first term and common difference of the arithmetic series are -11 and 3.

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