Use natural logarithms to solve each equation.
ex/₅+4=7

Answer:

-85

Step-by-step explanation:

(-60) + (-25) = (-85)

Answer:

Step-by-step explanation:

the fish is 85 feet bellow the surface

explanation 60+25 is 85 so therefor -60-25 would be -85

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:

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

Answer:

I used desmos graphing calculator

Step-by-step explanation:

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!

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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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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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

Answer: 8c + 40

Step-by-step explanation: i did this on OW

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]

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

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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The equation of the line in slope intercept form is y = 1 / 6 x - 11

The equation of a line can be represented in a slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line is parallel to y =  1 / 6 x + 7 .

This means the equation of the line have the same slope with  y =  1 / 6 x + 7 .

The equation passes through (12, -9).

Therefore, let's find b

y = 1 /6 x + b

-9 = 1 / 6 (12) + b

b = -9 - 2

b = - 11

Therefore, the equation of the line in slope intercept form is y = 1 / 6 x - 11

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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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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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If Lily is sitting 40 feet away from a beautiful waterfall that is 1,000 feet high. The angle of inclination from Lily's location to the top of the waterfall is: 87.7°.

Given data or information:

Feet away=40 feet away

Feet high=1,000 feet high

Now let find or determine  the angle of inclination rom Lily's location to the top of the waterfall

Hence,

tanФ=1,000/40

Ф=tan^-1 (1,000/40)

Ф=87.70°

Therefore If Lily is sitting 40 feet away from a beautiful waterfall that is 1,000 feet high. The angle of inclination from Lily's location to the top of the waterfall is: 87.7°.

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Answer: 1.7

Step-by-step explanation:

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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Answer:

In the first image, the triangles are congruent because each side measures equally to the other. The circles are not because they are not the same size. The big circle is 4 by 4 squaes and the small circle is 2 by 2.

In the second image the first image is congruent, and in the second image the figures are not congruent because the image to the right is thinner than the left.

Step-by-step explanation:

Hope it helps! =D

Answer: Ok for the first screen shot (the one with the triangles) its yes then the circles no

the upside down L 's yes

and the quadrilaterals no

Step-by-step explanation: congruent means the same or identical.

Hope it helped :D

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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The simplification of the given logarithmic functions ln (2x-1)² = 7 is 17.055.

The logarithm of a number is the exponent by which a fixed value referred as the base should always be raised to generate a certain number. For instance, because 1000 is 10 to the third power, a log of 1000 to base 10 is 3.

Some properties of the logarithmic functions are defined as-

As, for the stated log or ln function ln (2 x-1)²=7

Use the power rule on the left side of the equation.

2 ln (2 x-1) = 7

Simplifying the equation.

ln (2 x-1) = 7/2

ln (2 x-1) = 3.5

Using the exponential property of the log.

e∧[ln (2 x-1)] = e∧3.5

2x-1 = 33.11

2x = 33.11 + 1

2x = 34.11

x = 34.11/2

x = 17.055

Therefore, the value of the x for the stated logarithmic functions ln (2x-1)² = 7 is calculated as 17.055.

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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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[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]

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:Student A

Step-by-step explanation:

1. -(3)

2.-19

20

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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The answer to the present question is: log(a²b³/c⁴) = 2log(a) + 3log(b) - 4log(c)

For solving this kind of question, we are going to use these three identities:

log(x*y) = log(x) + log(y)   ....(1)

log(x/y) = log(x) - log(y)    ....(2)

log(xⁿ) = nlog(x)                ....(3)

So, using (2), log(a²b³/c⁴) may be written as: log(a²b³) - log(c⁴)  ....(4)

Again, using (1), log(a²b³) are often written as: log(a²) + log(b³)  ....(5)

Now, Putting equation (4) in equation (3), we get:

log(a²) + log(b³) - log(c⁴)   ....(5)

Now, using (3), expanding all the terms, we get:

log(a²) = 2log(a)log(b³) = 3log(b)log(c⁴) = 4log(c)

Putting of these in equation 5, we get:

2log(a) + 3log(b) - 4log(c)

Therefore,  log(a²b³/c⁴) = 2log(a) +3log(b) - 4log(c)

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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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