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The equation can be expressed in Logarithmic form as log₃ 81 = 4

logarithmic form is a method to write equations when solving for a variable in an exponent.

Any exponential equation can be written as a logarithm. The logarithmic form is used to calculate an exponent of an equation.

The logarithmic form is a rearrangement of the exponential form. Exponential form: aᵇ = c

Logarithmic form: logₐ c = b

Comparing this with our equation, a=x, b=4, c=y

Therefore, we get the logarithmic form as log₃ 81 = 4

Hence, the Conversion from exponential form to logarithmic form gives the final answer as log₃ 81 = 4

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Answer:

I used desmos graphing calculator

Step-by-step explanation:

Answer:Student A

Step-by-step explanation:

1. -(3)

2.-19

20

The required function based on the given conditions is y = 13 / x.

What is a function?

A function is defined as an expression or rule that specifies the relationship between two variables or objects, out of which one is dependent and the other is an independent variable. The image of each and every element is unique.

Examining the function which satisfies the given conditions

Given values of x = 52 and y = ¼

Consider a function such that x and y vary inversely with each other,

y = k / x, where k is a constant         —-- 1

Putting values of c and y, we get,

¼ = k / 52

52 / 4 = k

k = 13

Put the value of k in equation 1, we get,

y = 13 / x

Hence, the required function is given by, y = 13 / x.

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[tex] \large \bf \implies{(x - 6)^{2}(x + 1) }[/tex]

[tex] \sf \longrightarrow\frac{1}{ {x}^{2} - 5x - 6} \: and \: \frac{1}{ {x}^{2} - 12 + 36 } \\ [/tex]

[tex] \sf \longrightarrow \frac{1}{ {x}^{2} - 5x - 6 } = \frac{1}{(x - 6)(x + 1)} \\ \\ \sf \: and \\ \\ \sf \longrightarrow \frac{1}{ {x}^{2} - 12x + 36 } = \frac{1}{(x - 6)(x - 6)} [/tex]

Step 1) : First of all notice that term is in standard form.

For eg :- 6x + 2x² + 5 = 2x² + 7x + 5

Step 2) : Multiply with first and last term.

2 × 5 = 10

Step 3) : Next we have multiply got the answer 10 and subtract or add we have got the answer 7.

Now, we have got the term. We have multiply 2 and 5 got the answer 10 and we have add got the answer 7.

Step 4) : Attach the factor into the removal of 7x

2x² + 5x + 2x + 5

Step 5) : Simplify it

Step 6) : We have got the answer

[tex]\sf \longrightarrow(2x + 5)(x + 1)[/tex]

Answer:

slope = - [tex]\frac{12}{5}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (9, - 1 ) and (x₂, y₂ ) = (4, 11 )

m = [tex]\frac{11-(-1)}{4-9}[/tex] = [tex]\frac{11+1}{-5}[/tex] = - [tex]\frac{12}{5}[/tex]

The least sum of money can be made up of an exact number of 25 pieces or 50  pieces is 50.

So, the least sum:

Therefore, the least sum of money can be made up of an exact number of 25 pieces or 50 pieces is 50.

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Answer:

Find out the number of video games that Jasmine can buy with her savings .

To proof

Let us assume that the number of video games Jasmine can buy  be x .

As given

Jasmine wants to use her savings of $1128 to buy video games and music CDs.

The total price of the music CDs she bought was $72. The video games cost $43 each.

Than the equation becomes

72 + 43× x = 1128

simplify

72 + 43x = 1128

43x = 1128 - 72

43x = 1056

x = 24.6 (approx)

Take

x = 24

Therefore the maximum number of video games that Jasmine can buy with her savings be 24 .

Step-by-step explanation:

The maximum number of video games that Jasmine can buy with her savings is... 24 ✅

Allow me to explain...

First, subtract $72 from $1,128

1,128 - 72 = 1,056

       ⬆️         ⬆️

Then, divide $1,056 by $43

1,056 ÷ 43 = 24.5581...

        ⬆️            ⬆️

Coming to the conclusion that Jasmine only has enough money for a maximum of 24 video games. ✅

I hope this was helpful! (✿◠‿◠)

After solving the given equation 1/3lnx+ln 2- ln3=3, the value of

x = 3(In+3)/In.

So,

Then,

Therefore, after solving the given equation 1/3lnx+ln 2- ln3=3, the value of x = 3(In+3)/In.

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Answer:

15

Step-by-step explanation:

First mutiply both sides with 3

(x/3x3)+(10x3)=15x3

x+30=45

the add -30

x+30-30+45=30= 15

We need to know about logarithm to solve this problem. The exponential form of the logarithm is [tex]2^{7} =128[/tex].

Logarithm is the exponent that is raised to a base to get a certain number.There are a few rules of logarithm, log a+ log b can be written as log ab, log a -log b can be written as log a/log b, when the number whose logarithm is being calculated is raised to a power, then the power can be multiplied to the log itself. Logarithm when written as log without base mentioned, the base is 10, the log of a number that is same as the base is always 1, the log of 1 is always 0 because a nonzero number raised to 0 is always 1. To write a logarithm in exponential form we have to raise the value of the logarithm to the base which is equal to the number whose logarithm we found.

[tex]log_{2} 128=7[/tex] can be written as [tex]2^{7} =128[/tex]

Therefore we found the exponential form of the logarithm to be [tex]2^{7} =128[/tex]

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Answer:

Step-by-step explanation:

The formula for annual compound interest, including principal sum, is:

A = P (1 + r/n) (nt)

where

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for

here

we have to found semianually

P= 2000

r= 11% =0.11

n=2   .... for semiannual

t =5

A = 2000( 1 +0.11 /2 )(2*5)

 = 2000(1 +0.055)10

= 2000(1.055)10

= 2000(1.708)

=3416

The movie earned $1.21×10^7 in revenue per minute.

Revenue was earned per minute

we get,

we can divide the total revenue by the number of minutes.

When numbers are in scientific notation, we can divide in two separate steps.

First, let's divide the powers of ten, then we will divide the other numbers.

Because of the properties of exponents, we can subtract the exponent in the denominator from the exponent in the numerator to divide the powers of 10.

Now we can divide the numbers that are not powers of 10.

The problem asks us to round to two decimal places, so our final answer will have three digits including the ones place. Let's round

so the final answer will have three digits.

first number is 1.109 and

second number is .109

Now let's put the two results back together.

we get, $1.21

we get number after scientific notation

The movie earned $1.21×10^7 in revenue per minute.

Scientific Notation is the expression of a number n in the form

a∗10b

where a is an integer such that

1≤|a|<10

and b is an integer too.

Multiplication: To multiply numbers in scientific notation, multiply the decimal numbers. Then add the exponents of the powers of 10. Place the new power of 10 with the decimal in scientific notation form. If your decimal number is greater than 10, count the number of times the decimal moves to the left, and add this number to the exponent.

Division: To divide numbers in scientific notation, first divide the decimal numbers. Then subtract the exponents of your power of 10. Place the new power of 10 with the decimal in scientific notation form. If the resulting decimal number is less than 1, move the decimal point to the right and decrease the exponent by the number of places that the decimal point moved.

Large Numbers in Standard Form

n=101325=1.01325∗105

(Move the decimal point 5 places to the right)

Express Small Numbers in Standard Form

n=0.00092=9.2∗10−4

(Move the decimal point 4 places to the left.)

Multiplication:

(2.3∗104)∗(6.6∗107)

First Step -

2.3∗6.6=16.38

Second Step -

104∗107=1011

Because the new decimal number in step one is greater than 10, count the number of places the decimal moves to put the number between 1 and 10. Add this number to the exponent. In this case, the decimal point moves one place, so add 1 to the exponent.

1.638∗1012

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Answer:1.21*10^7

Step-by-step explanation:

i did kahn academy and this was the correct answer:)

Based on the vertical angles theorem, the step 2 was completed in the proof incorrectly by Latonya.

When two straight lines intersect to form a pair of two angles that share the same vertex but are non-adjacent to each other, both angles are called vertical angles, and based on the vertical angles theorem, they are congruent to each other.

In the the diagram given, angles JKN and IKL are vertical angles, and they are congruent to each other based on the vertical angles theorem.

Therefore, based on the vertical angles theorem, the step 2 was completed in the proof incorrectly by Latonya.

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Answer: 2 laps four minutes

explanation:

The correct option is B that is square root of 16 i.e., 4 is a rational number.

What is a rational number ?

If p and q are any two numbers where q is not equal to 0, then the fraction in form p/q is called as rational number.

Let's check which of the given numbers are rational numbers.

A.

The number is √15.

= 3.8729

As , the number has non - terminating decimal , so , √15 is an irrational number.

B.

√16

= 4

As , this number is an integer and we can write it in form of fraction as [tex]\frac{4}{1}[/tex] , so , √16 is a rational number.

C.

√17

= 4.12310

As , the number has non - terminating decimal , so , √17 is an irrational number.

D.

√18

= 4.2426

As , the number has non - terminating decimal , so , √18 is an irrational number.

Therefore , the correct option is B that is square root of 16 i.e., 4 is a rational number.

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Answer: 2 6/7

Step-by-step explanation:

Answer:

Answer is 75/32

Step-by-step explanation:

Convert the mixed number to an improper fraction so 7 1/2 changes to 15/2 divided by 2x5/8 but then you change the 2 to 1/2 so 15/2 x 1/2 x 5/8

then you multiply the fractions then you get 75/32

When Todd says that he used 718 feathers to make the cat toys, it does not sound right.

To solve this problem, we have to state the equations using the information of the problem

Information about the problem:

Calculating how many feathers Todd should use to made 198 cat toys:

Total feathers = No. of toys * No. feather per toy

Total feathers = 198 toys  * 6 feather/ toy

Total feathers = 1188 feathers

With the calculate we can confirm that Todd's calculate is not right because:

Total feathers > Todd's calculated

1188 feathers > 718 feathers

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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The decimal number will be 0.248.

So, decimal number less than 1:

Therefore, the decimal number will be 0.248.

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The sum of (-3) + (-1) is -4.

The addition expression (-3) + (-1) on a number line is : (-4).

Here, we have,

To represent the addition expression (-3) + (-1) on a number line,

we would start at -3 and move to the left by 1 unit.

Here's how we can explain it step by step:

Start at -3 on the number line.

Since we have a negative sign in front of both numbers, we will move to the left (in the negative direction) on the number line.

The first number, -3, indicates that we will start at -3 on the number line.

The second number, -1, indicates that we will move to the left by 1 unit from -3.

When we move to the left from -3 by 1 unit, we will reach -4 on the number line.

So, (-3) + (-1) represented on the number line means starting at -3 and moving to the left by 1 unit, resulting in -4.

The sum of (-3) + (-1) is -4.

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If Arturo lives in colorado, which has a state income tax rate of 4.63% and he earns $1,345 biweekly, then the amount of state income tax withheld from each of his paychecks is equal to $62.27.

The state income tax withheld from each of his paychecks can be determined by the percentage formula;

P% × x = y

Here,

P% is the state income tax rate

x is the dollars earned biweekly

y = state income tax withheld from each of his paychecks

As the state income tax rate is equal to 4.63% and the amount earned biweekly is equal to $1345, therefore;

P% × x = y

4.63% × 1345 = y

4.63% can be converted into decimal form as follows,

4.63% = 4.63 / 100 = 0.0463

Therefore,

0.0463 × 1345 = y

y = 62.27

Hence, the state income tax withheld from each of his paychecks is calculated to be $62.27

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Answer:

[tex] \sf \large \: x = -1[/tex]

Step-by-step explanation:

4x + 7 = 3

Substract 7 from both sides

4x + 7 - 7 = 3 - 7

4x = -4

Divide both sides by the coefficient of x

4x/4 = -4/4

calculate

x = -1

The inequality to represent how much taller he must be to drive a bumper car is written as 4 1/3 + x ≥ 4 3/4 and he must be 0.42 feet taller or more to drive a bumper car.

Inequality can be defined as a relationship between two numbers or algebraic expressions in which one is either greater than, greater than or equal to, less than or equal to the other.

As the height must be at least 4 3/4 or more to drive a bumper car, an inequality equation can be given as,

4 1/3 + x ≥ 4 3/4

The sign "≥" represents that the height must be equal to or greater than 4 3/4.

Solving for x,

x ≥ 4 3/4 - 4 1/3

x ≥  4.75 - 4.33

x ≥  0.42

Therefore the friend must be at least 0.42 feet taller or more to ride the bumper car.

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Answer:

3.5 hours

Step-by-step explanation:

divide 10.5 by 3 since there is 3 days to get 3.5

Let me know if this was helpful

The unit price for the tape is $0.38 or 38 cents per yard.

The unit price is the price of one unit of measurement for a particular substance.

The unit price of a substance is used to calculate the total cost of a particular substance or the cost of a fraction of a substance.

Unit price is calculated by dividing the total cost by the total quantity of the product.

The given price of the product is $3.04 for a 8-yard roll of tape.

So to find the unit price we divide the total cost by the total length to find the cost of 1 yard of tape.

Unit price = $3.04 ÷ 8

or, Unit price = $ 0.38

Therefore the unit price of the tape is $0.38 or 38 cents.

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The given expression can be solved by finding the square root of the terms if possible and expressing the terms in the simplest form.

The square root of a number is the factor (number) that can be multiplied by itself to get that number (within the square root sign). Finding the square root of a number can be seen as the opposite of squaring a number. In the general form, √a*a=a.

In the given expression, the numerator √6 cannot be further simplified.

√6=√2*3

We cannot take square root as the number is not multiplying itself.

In the denominator √36 can be further simplified.

√36=√6*6=6

We can take square root as the number is multiplying itself.

Hence,

√6/3√36=√6/(3*6)=√6/18

The product or quotient of √6/3√36 is √6/18

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Answer:

a

Step-by-step explanation:

the complement of R is 90 - R , then

R = 5(90 - R) - 6

R = 450 - 5R - 6

R = 444 - 5R ( add 5R to both sides )

6R = 444 ( divide both sides by 6 )

R = 74°

complement = 90° - 74° = 16°

Option(a) 16 is correct option, the measure of the complement of R is 16

Two angles are complementary if their sum is 90°.

Let x be an angle and y be its complement of x then x + y = 90°.

Let the measure of the complement of R be x

Given that the measure of angle R is 6 less than 5 times its complement

Then 5 times the complement of R = 5x

And 6 less than 5 times the complement of R  = 5x-6

Thus, R = 5x -6

∴ R + complement of R = 90°

⇒5x-6 + x = 90

⇒6x = 96

⇒x = 96/6 = 16

Therefore, the measure of the complement of angle R is 16 and option (a) is correct option.

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Answer:

the harvester costs 1200 a day.

54 hectares / 12 per day = 4.5 days.

Step-by-step explanation:

if she can rent the harvester for half a day, it will cost her 4.5 * 1200 = 5400.

if she can only rent the harvest for full days, it will cost her 5 * 1200 = 6000.

Answer:

A. (0, 4), (4, ∞)

B. (-∞, -4), (4, ∞)

C. (-∞, 0), (0, ∞)

Step-by-step explanation:

1

p(x) = -------- ; m(x) = x² - 16

√x

a.

p(x)

-------

m(x)

1 1

-------- --------------

√x √x

------------------------------ = ---------------------

x² - 16 (x + 4)(x - 4)

Domain: (0, 4), (4, ∞)

----------------------------------------------------------------------------------------------------------

B.

P(m(x))

1 1 1

------- = ----------------- = ----------------------

√x √(x² - 16) √(x - 4)(x + 4)

Domain: (-∞, -4), (4, ∞)

----------------------------------------------------------------------------------------------------------------------------

C.

M(p(x))

x² - 16

1 1

( ------- )² - 16 = ------- - 16

√x x

Domain: (-∞, 0), (0, ∞)

----------------------------------------------------------------------------------------------------------------------------

I hope this helps!