Simplify each expression using the imaginary unit i . 2 √-24+6 .

Each logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 8}{log \\3}[/tex]

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  [tex]a^N=x[/tex]  is an exponential function 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.

Some important formulas of logarithms are :

The given expression is,

[tex]log_38[/tex]

as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]

therefore ,

[tex]log_38[/tex] =  [tex]\frac{log \ 8}{log \ 3}[/tex]

Hence,  logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 8}{log \\3}[/tex]

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The solution for the radical equation 2√x =√(x+1) is x=1/3

The phrase "algebraic expression" refers to any arrangement of terms that have undergone operations like addition, subtraction, multiplication, division, etc. (or variable expression).. Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.

Eliminate the radical on the both sides by squaring on both sides-

Both sides must be raised to the second power

(2√x)²=(√x+1)²

After squaring we get 4x=x+1

Solving the equation-

We get rearranged equation as 4x=x+1

3x=1    x=1/3

Check if the  solution is correct by putting it in original equation-putting x=1/3 in the equation 2√x =√(x+1)

2×√1/3=√1/3+1

4/3=4/3

Therefore, the solution for the radical equation 2√x =√(x+1) is x=1/3.

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The biggest weight the person can be based on the recommendation by the doctor is 90 pounds.

From the information, it was stated that doctors recommend us to eat between 3 to 8 percent of our bodyweight each day and that one day someone eats 7.2 pounds.

It should be noted that based on the information given, the highest percentage which is 8% will be used for the calculation.

Therefore, the biggest weight the person can be will be:

8% of x <= 7.2

0.08x <= 7.2

x <= 7.2/0.08

x <= 90 pounds

Therefore, the biggest weight the person can be based on the recommendation by the doctor is 90 pounds.

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After evaluating the logarithm log₂ 2⁵, we get the result as 5.

The common logarithm is also known as the base 10 logarithm. It is represented by log10 or simply log.

For example, the common logarithm of 1000 is written as log(1000). The common logarithm defines how many times we need to multiply by 10 to get the required output.  The natural logarithm is called the logarithm of base e. The natural logarithm is represented by ln or loge. Here, "e" stands for Euler's constant which is approximately equal to 2.71828.

For example, the natural logarithm of 78 is written as ln 78. The natural logarithm determines how much we need to multiply "e" to get the required output.

We need to evaluate log₂ 2⁵Using the property logₐ (mⁿ) = n logₐ m log₂ 2⁵ can be written as

log₂ 2⁵ = 5 log₂ 2

We know that logₐ a = 15 log₂ 2= 5

Therefore, after evaluating the logarithm log₂ 2⁵, we get the result as 5.

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The correct option B: (-9/4 × 3/2)×(6/3 × 5/7) = -9/7×(3/2×6/3)×5/7 is the associative property of multiplication.

The formula for associative property of multiplication is-

a×(b×c) = (a×b)×c

For four digits;

(a×b)×(c×d) = a×(b×c)×d

Thus, from the given option the condition for associative law is only satisfied in option B.

(-9/4 × 3/2)×(6/3 × 5/7) = -9/7×(3/2×6/3)×5/7

Thus, the correct option for the associative property of multiplication s chosen.

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The expression of the mathematical statement given as "The perimeter of a rectangle is equal to two times the length plus twice the width" is P = 2l + 2w

The mathematical statement is given as

The perimeter of a rectangle is equal to two times the length plus twice the width

Represent the perimeter with P

So, we have

P is equal to two times the length plus twice the width

Represent the length and the width with l and w

So, we have

P is equal to two times l plus twice w

So, we have

P = 2l + 2w

Hence, the expression of the mathematical statement given as "The perimeter of a rectangle is equal to two times the length plus twice the width" is P = 2l + 2w

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Answer: I believe it is ZERO

Step-by-step explanation:

Answer:

No Solution

Source: cymath.com

Step-by-step explanation:

The equation which illustrates and meets the conditions given is 1.25 × 0.2

First number = 1.25

First number = 1.25Second number = 0.2.

Product = 0.25

First number, x = 1.25

First number, x = 1.25 Second number, y = 0.2

= first Number × second number

= 1.25 × 0.2

= 0.25

Evaluating the result : 0.25

Number of digits = 3

Non - zero digits = 2

There are several values of x and y that will satisfy the 3 conditions given.

Therefore, the product of the values 1.25 and 0.2 gives the required output

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2 log (x + 1) = 5 => x = 315.22, by properties of logarithm.

Given: 2 log (x + 1) = 5

=> log (x + 1) = [tex]\frac{5}{2}[/tex]

Raising both sides by 10, in order to remove the logarithm:

=> [tex]10^{log_{10}(x+1)} = 10^{2.5}[/tex]

=> x + 1 = 316.22 ( as [tex]a^{log_a(x)} = x[/tex])

=> x = 315.22

Hence, 2 log (x + 1) = 5 => x = 315.22, by properties of logarithm.

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Answer: 346.19

Step-by-step explanation:

So we know that the radius of the corner shelf is 10.5 inches. So first you write down the formula for finding the area of a circle. The formula for finding the area of a circle is:

A= pi x r squared

A= 3.14 x 10.5 squared

A= 3.14 x 110.25

A= 346.185 or 346.19

Hope that helps

When choosing a loan, the best scenario is lower APR, shorter loan, and extra principal payments.

A loan is a type of debt that a person or other entity incurs. The lender advances the borrower a certain amount of money, typically on behalf of a business, financial institution, or government. The borrower accepts a specific set of terms in return, which may include any financial costs, interest, a repayment schedule, and other requirements.

APR represents the total yearly cost of a loan to the borrower, including all fees. The APR is stated as a percentage, just like an interest rate. It does, however, contain other costs or fees such as mortgage insurance, the majority of closing costs, discount points, and loan origination fees, unlike an interest rate. It should be noted that the APR simply means the annual percentage rate which is the interest that's generated on the amount borrowed.

Therefore, it should be noted that when choosing a loan, the best scenario is a lower APR, shorter loan, and extra principal payments

This is important in order to reduce the value that the person will pay and make it easier to return the loan.

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The solution for the given logarithmic expression log₂4+3 log₂9 as a single logarithm is log₂ (2916).

A logarithmic equation is one that includes a logarithm in the variable x.

An exponential formula is one where the variable is represented by an exponent. To answer exponential equations, first determine whether both sides of the equation can be written as powers of the exact number. If you can't, take the common logarithm from both of the equation's sides and use property 7 to solve the problem.

Now, as per the stated condition in question;

The expressed equation is;

= log₂4+3 log₂9

Using the Power Rule in the second term.

= log₂4+log₂9³

=  log₂4+log₂729

As, the base of each log term is 2. We can use product rule to simplify the equation.

= log₂(4×729)

= log₂ (2916) [As a single log function]

Therefore, the simplification of the given logarithmic expression as the single logarithm is log₂ (2916).

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Answer:

undefined

Step-by-step explanation:

4x-32=4x+2

-4x

-32=2

undefined

Answer:

I think about 5

5+5+5+5+5

25.

The number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.

We are given that;

a represents the number of drinks purchased.

y represents the number of tacos purchased

He must buy a minimum of 11 drinks and tacos altogether. Thus, the inequality that describes this is;

2a + 4y ≤ 40

a + y ≥ 11

The inequality graph that represent the given system of inequalities is as shown in the atatched file.

From the given inequality graph, we can tell that one possible solution is; (a, y) = (2, 9)

Thus, the number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.

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The result of simplifying each number 64²/₃ 64²/₃  using the exponent rules is 256

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

64²/₃ * 64²/₃

The base number 64 is the same that: 4³, then we get:

(4)³ ⁽²/₃⁾ * (4)³ ⁽²/₃⁾

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

4⁽³*²/³⁾ * 4⁽³*²/³⁾

4⁽⁶/³⁾ * 4⁽⁶/³⁾

(4)² * (4)²

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

4⁽²⁺²⁾

4⁴

4*4*4*4

256

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:

see explanation

Step-by-step explanation:

substitute the values of x, situated inside the parenthesis into f(x)

f(- 1) = - 1 - 5 = - 6

f(0) = 0 - 5 = - 5

f(1) = 1 - 5 = - 4

f(2) = 2 - 5 = - 3

f(5) = 5 - 5 = 0

f(8) = 8 - 5 = 3

1) Substitute x = -1 into f(x) = x - 5

2) Substitute x = 0 into f(x) = x - 5

3) Substitute x = 1 into f(x) = x - 5

4) Substitute x = 2 into f(x) = x - 5

5) Substitute x = 5 into f(x) = x - 5

6) Substitute x = 8 into f(x) = x - 5

The two pages the boys are reading are pages 31, and 30. I'm not sure which is which. (would depend on who is reading the odd number page).

Josiah is reading page 31. The page he is reading is an odd-numbered page is 31 by factorizing number.

Step 1: Determine the factors of 930.

The factors of 930 are 1, 2, 3, 5, 6, 10, 15, 31, 62, 93, 155, 186, 310, 465, and 930.

Step 2: Identify the factors that correspond to odd-numbered pages in the book.

Since Josiah is reading an odd-numbered page,  eliminate the even factors.

This leaves  with the odd factors:

1, 3, 5, 15, 31, 93, 155, and 465.

Step 3: Determine which odd factor corresponds to a page number within the range of the book.

Since the book has 50 pages,  eliminate the odd factors greater than 50. This leaves us with the odd factors: 1, 3, 5, 15, and 31.

Step 4: Identify the odd factor that, when multiplied by its complement, equals 930, that is:

31 × 30 = 930,

so Josiah is reading page 31.

Therefore, Josiah is reading page 31 of the book.

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Julia = 10 miles in 30 minutes

Jasmine = 3 miles in 12 minutes

Julia= 10/30 *2 = 20/60. Julia drove 20 mph

Jasmine= 3/12*5= 15/60. Jasmine drove 15mph

Julia drive faster.

Answer:

Step-by-step explanation:

I think it´s the polygamous

Answer: Option D is correct.

Step-by-step explanation:

Given: 7 and 11

We need to find the geometric mean of 7 and 11.

Geometric series whose common ratio is equal.

The geometric mean of two numbers is the square root of the product of two numbers.

If a, b and c are in GP then the geometric mean is b

The geometric mean of any two numbers a and b is

The given numbers are 7 and 11

Geometric mean is [tex]\sqrt 7x11\\[/tex]

Geometric mean: [tex]\sqrt{x} 77[/tex]

Answer:

[tex]z=\frac{s}{h-4c^4}[/tex]

Step-by-step explanation:

Switch the subject

[tex]s=zh-4zc^4\\zh-4zc^4=s[/tex]

Factor

[tex]zh-4zc^4\\=z\left(h-4c^4\right)\\z\left(h-4c^4\right)=s[/tex]

Divide: remember that h - 4c^4 is not equal to zero

[tex]\frac{z\left(h-4c^4\right)}{h-4c^4}=\frac{s}{h-4c^4}[/tex]

Simplify your solution where z is the redefined subject

[tex]z=\frac{s}{h-4c^4}[/tex]

Step-by-step explanation:

s=zh-4zc^4

we will factorise

s=z(h-4c^4)

we will divide both sides by (h-4c^4)

s/(h-4c^4)=z

z=s/(h-4c^4)

pls rate as brainliest

The expression for y months is 15y and the number of books is 135

The rate is given as

Rate = 15 books in a month

The number of month is given as

Months = y

The total number of books is

Total = Rate * Months

So, we have

Total = 15 * y

Evaluate

Total = 15y

When y = 9, we have

Total = 15 * 9

Evaluate

Total = 135

Hence, the expression for y months is 15y and the number of books is 135

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Answer: 21

Step-by-step explanation:

When it comes to finding the range, you must take the biggest number and subtract it from the smaller number, therefore in your question the answer is

25 - 4 = 21

Hope it helped :D

Answer:

$92

Step-by-step explanation:

32+4x where x is 15

32+(4*15)=?

32+60=92

Answer:

Step-by-step explanation:

hi

The amount that should be put into account is $6171.88

The formula for the compounded continuously is

              [tex]A = P(1 + {r}/{n})^{tn}[/tex]        (1)

    where , A  = future amount or the final amount

                  P = principal amount to be invested

                 r = annual interest rate

                 t = time

                 n = number of compounding in a year

According to the question we have been given that

              A = $8000

              r = 0.052

               t = 5

              n = 12

putting the required values in equation (1) we get

     8000 = P(1 + 0.052/12)^(5*12)

     8000 = P (1.004)^60

     8000 = P*1.27

            P = 8000/1.27

            P = $6171.88

Thus the amount that should be put into account is $6171.88

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