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The value of logarithmic expression 1/2 (logx4 + logx y) - 3 logx z as a single logarithm is (log4x^2y)^1/2/logx z^3

By considering the given  logarithmic expression

1/2 (logx4 + logx y) - 3 logx z

=1/2 (log4x^2y)-3 logx z

=(log4x^2y)^1/2- logx z^3

=(log4x^2y)^1/2/logx z^3

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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The value of a is 2/√7.

The given quadratic equation is x² ₋ 3ax ₊ a² = 0

sum of the roots of the equation  = 4

here, A = 1

B = 3a

C = a²

Let α and β be the roots of the equation.

α ₊ β = ₋B/A

= ₋3a/1

= ₋3a

⇒ α×β = C/A

= a²/1

= a²

⇒α² ₊ β² = (α ₊ β )²  ₋ 2αβ

= (₋3a)² ₋ 2(a²)

= 9a² ₋ 2a²

therefore, 7a² = 4

a² = 4/7

a = √4/7

a = 2/√7

Hence we found the value of a as 2/√7.

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The value of the variable x in the equation 2log₂(x) - log₂(2x) = 3 is x =16

The equation is given as

2log₂(x) - log₂(2x) = 3

Apply the power rule of logarithm

So, we have

log₂(x²) - log₂(2x) = 3

Apply the quotient rule of logarithm

So, we have

log₂(x²/2x) = 3

Apply the change of base of logarithm

So, we have

x²/2x = 2^3

Evaluate the exponent

So, we have

x²/2x = 8

Evaluate the quotient

So, we have

x/2 = 8

Multiply both sides by 2

So, we have

x =16

Hence, the value of the variable x in the equation 2log₂(x) - log₂(2x) = 3 is x =16

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Answer:

8,1 is the correct answer

Answer: I think this is it

Step-by-step explanation:

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list. This is what is most often meant by an average. The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

Answer:  115

Step-by-step explanation: because   if you subtract 120 - 5 you get 115 so its 115

The equation for the value of the painting of the years is y = 3000 + 330.4(x).

The estimated worth of the painting in 2030 is $7956.

In 2016, the worth of the painting is $3000.

In 2021, the worth of the painting is $4652.

The increase in worth in 5 years from 2016 to 2021 is:

= $4652 - $3000 = $1652

Hence, the increase in painting worth per year will be:

= $1652 / 5 = $330.4

Now, if x is in years and y is the worth of the painting in $.

Then, the equation for the worth of a painting is:

y = 3000 + 330.4(x)

From 2015 to 2030 the span is 15 years.

Then, the value of the painting in 2030.

So,

y = 3000 + 330.4(x)

y = 3000 + 330.4 × 15

y = 3000 + 4956

y = $7956

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Answer:

your question is empty please give right questions to get answers

The quotient should have four significant digits, which is the number of significant digits required to divide the numbers into equal parts.

Consider the two numbers,

2.058 × 10⁹ and 3.0571 × 10⁻⁴

Now, let x = 2.058 × 10⁹ and;

y = 3.0571 × 10⁻⁴

When we dived these two equations.

( x / y) = [ 2.058 × 10⁹ / 3.0571 × 10⁻⁴ ]

The significant digits in the number with the smaller number of significant digits should be used to determine the number of significant digits in a quotient where two numbers are divided by one another.

Here, 2.058 × 10⁹ is the figure with the fewer significant digits.

Since 0 comes after non-zero numerals, this number has four meaningful digits.

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Tt would take 15 minutes for there to be exactly 60 gallons in the hot tube.

Proportion can be defined as the mathematical comparison of two numbers.

It is also known as an equation defining that the two given ratios are equivalent to each other.

From the information given, we have the following deductions;

To determine the time taken for 60 gallons to be left in the hot tube, we have to subtract the number from the total number of gallons, we have;

= 150 - 60

Find the difference

= 90 gallons

Now,

If 6 gallons are drained in 1 minute

Then 90 gallons are drained in x minutes

cross multiply

x = 90/ 6

x = 15 minutes

Thus, it would take 15 minutes for there to be exactly 60 gallons in the hot tube.

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Answer:

No

Step-by-step explanation:

If you substitute, you get

2(5) - 10 >= 3

10 - 10 >= 3

0 >= 3, which is false!

The solution of the given equation by rounding off it to the nearest ten-thousandth is 0.5185.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation 9²x = 42

As given equation is 9²x = 42

81x = 42

x = 42 / 81

= 14 / 27

= 0.5185

Hence, the solution of the given equation is 0.5185.

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Answer: 1 and 7 over 10

Step-by-step explanation:

Answer:

[tex]\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]\frac{9}{10} + ( -\frac{4}{5} )[/tex]

change the fraction  [tex]( -\frac{4}{5} )[/tex] to[tex]( -\frac{8}{10} )[/tex]

I multiplied both the denominator and numerator by 2

[tex]\frac{9}{10} + ( -\frac{8}{10} )[/tex]

simplify the negative

[tex]\frac{9}{10} -\frac{8}{10}[/tex]

subtract the numerator not the denominator

[tex]\frac{1}{10}[/tex]

The number of bleacher seats that the stadium will include will be 8000 seats.

In this situation, the The team's policy is to have a 3:2 ratio of premium seats to bleacher seats.

Therefore, the total number of premium seats are:

= 4500 + 7500

= 12000

The number of bleachers will be:

= 2/3 ×12000

= 8000

Therefore, the number of bleacher seats that the stadium will include will be 8000 seats.

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What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given:

y = x³ + 2x +5

z = x² + 7x + 1

To find: Value of 2y + z in terms of x

Finding:

Now, 2y = 2 (x³ + 2x + 5) = 2x³ + 4x + 10

Then, 2y + z =  2x³ + 4x + 10 + x² + 7x + 1

=> 2y + z = 2x³ + x² + 11x + 11

Hence, Option C is the correct option.

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If a 2 N and 6 N pull on an object to the right and a 4 N force pulls to the left a 0.5 kg object. The net force on the object  is: 4N.

First step is to calculate the force to the right

Force to the right = 2N+6N

Force to the right = 8N

Second step is to calculate the net force on the object using this formula

Net force= Force to the right- Force to the left

Where:

Force to the right = 8N

Force to the left = 4N

Let plug in the formula

Net force= 8N - 4N

Net force= 4N

Therefore if a 2 N and 6 N pull on an object to the right and a 4 N force pulls to the left a 0.5 kg object. The net force on the object  is: 4N.

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Answer:

The absolute value of -5 is 5, it's positive opposite.

Have a fantabulous day <3

Answer:

5

Step-by-step explanation:

the only real math to absolute value is if it negative make it not.

The inverse of the function will be:

if x is an integer, then f⁻¹ (x) = x - 1

for all other x , f⁻¹ (x) = x - 2

We are given the function as:

if x is an integer, then f (x) = x + 1

for all other x , f (x) = x + 2

Now, we need to find the inverse of the function.

We will do it in 2 parts.

First we will find the inverse of f (x) = x + 1 and then of f (x) = x + 2.

For f (x) = x + 1:

y = x + 1

y - 1 = x

x = y - 1

f⁻¹ (x) = x - 1

For f (x) = x + 2

y = x + 2

y - 2 = x

x = y - 2

f⁻¹ (x) = x - 2

Therefore, the inverse of the function will be:

if x is an integer, then f⁻¹ (x) = x - 1

for all other x , f⁻¹ (x) = x - 2

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Answer:

If the state is 0, then Alberto's is -3 and Rebecca's is +2 or 2

The distance between Alberto's and Rebecca's: 2 - (-3) = 2 + 3 = 5

Step-by-step explanation:

If the state is 0, then Alberto's is -3 and Rebecca's is +2 or 2

The distance between Alberto's and Rebecca's: 2 - (-3) = 2 + 3 = 5

We're given:

First, we must identify the pattern:

This is our written pattern statement. To convert this into an expression, we can use the following format:

[tex]mn+b[/tex]

In this case, m is 6, and b is 2 - 6, or -4. Plug these numbers into the expression:

[tex]6n+(-4)\\6n-4[/tex]

To find the 42nd term, plug in 42 as n:

[tex]6n-4\\6(42)-4\\248[/tex]

The 42nd term is 248.

a₄₂= 248.

An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.

If the initial term of an arithmetic progression is a and the common difference of successive members is d, then the n-th term of the sequence  

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

6

to the previous term in the sequence gives the next term. In other words,

aₙ= a₁+ d (n-1)

substitute  in the values of a₁=2 and d=6

simplify each term

aₙ= 6n-4

substitute and calculate you will get

a₄₂= 248.

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Answer:

8.25 Hours she worked last week

Step-by-step explanation:

Answer:

CD ≈ 10.8

Step-by-step explanation:

calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1} )^2 }[/tex]

with (x₁, y₁ ) = C (- 5, 4 ) and (x₂, y₂ ) = D (5, 8 )

CD = [tex]\sqrt{(5-(-5)^2+(8-4)^2}[/tex]

     = [tex]\sqrt{(5+5)^2+4^2}[/tex]

     = [tex]\sqrt{10^2+16}[/tex]

     = [tex]\sqrt{100+16}[/tex]

     = [tex]\sqrt{116}[/tex]

     ≈ 10.8 ( to the nearest tenth )

Answer:

1 3/4

Step-by-step explanation:

Answer: Option D

Step-by-step explanation: Explanation:

7/4 is an improper fraction. Let's take the numerator and divide it by the denominator.

Divide 7 by 4. The quotient digit is 1.

Multiply the quotient digit 1 by the divisor 4.

Subtract 4 from 7.

The result of 7 divided by 4 is 1 with a remainder of 3.

Thus, 7/4 as a mixed number can be written as 1 3/4.

Answer:

p = 2/5

Step-by-step explanation:

[tex]7p+8=12-3p \\ \\ 10p+8=12 \\ \\ 10p=4 \\ \\ p=2/5[/tex]

The possible pairs when rewriting the position and sequence values are (d) (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)...

The sequence is given as

1, 4, 9, 16, 25...

The position and sequence values of the above sequence are

1, 2, 3, 4, 5...

1, 4, 9, 16, 25...

When represented as an ordered pair, we have

(1, 1), (2, 4), (3, 9), (4, 16), (5, 25)....

Hence, the possible pairs when rewriting the position and sequence values are (d) (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)....

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Answer:

its b:0.0333! (srry if its wrong)

Step-by-step explanation:

[tex]{\huge\color{green}{\boxed{\fcolorbox{white}{black}{꧁ANSWER꧂}}}}[/tex]

15+4a=7a

15=3a

3a=15

a=15/3=5

The solution of the linear equation with single variable 7a = 15 + 4a will be 3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

15 + 4a = 7a

Simplify the equation, then we have

7a = 15 + 4a

7a - 4a = 15

3a = 15

a = 15 / 3

a = 3

The solution of the linear equation with single variable 7a = 15 + 4a will be 3.

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If the inverse of f exists, it is represented by f⁻¹ and exists only if f is a bijective function.

The value of this function is h⁻¹(4) = 2.

The inverse function of a function f is a function that reverses the operation of f. The inverse of f exists if and only if f is bijective, and it is denoted by f⁻¹ if it exists.

Because they allow mathematical operations to be reversed, inverse procedures are essential for solving equations. When introducing a mathematical procedure, one of the most important questions is how to invert it.

Inverse operations are mathematical manipulations in which one operation reverses the action of the other, such as addition and subtraction, multiplication and division. In most cases, the inverse of a number is its reciprocal, i.e. x - 1 = 1 / x. A number and its inverse (reciprocal) product equals one.

Let the function be h(x)= 1/x+2  

h(x) = 1/x + 2 then

y = 1/x + 2

x = 1/y + 2

simplifying the equation, we get

x-2 = 1/y

x-2 = y⁻¹

h⁻¹(x) = x - 2

substitute the value of x = 4,

h⁻¹(4) = 4 - 2

h⁻¹(4) = 2

The value of this function is h⁻¹(4) = 2.

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