0.25 (5 is recurring) decimal to fraction

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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After solving the given equation log₃x = 4, the value of x = 81.

So,

Then,

Therefore, after solving the given equation log₃x = 4, the value of x = 81.

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Answer:

your question is empty please give right questions to get answers

No extraneous solutions to this equation.

The equation is

[tex](5x- 4)^{1/2}[/tex] - x = 0

To find the value of x

[tex](5x- 4)^{1/2}[/tex] = x

Now square on both sides of the equation.

We get

5x - 4 =[tex]x^{2}[/tex]

[tex]x^{2}[/tex] - 5x + 4= 0

[tex]x^{2}[/tex] - 4x - x + 4 =0

x( x -4 ) - 1 ( x - 4) =0

( x- 4 ) ( x - 1)= 0

x = 4, 1

We get the value of x as 4 and 1

Now we have to put the value of x in the equation

First, put 4

[tex](5x - 4)^{1/2}[/tex] -x =0

[tex](5 * 4 - 4)^{1/2}[/tex] - 4= 0

[tex](20 - 4)^{1/2}[/tex] - 4 =0

[tex]16^{1/2}[/tex] - 4 = 0

4-4 =0

0 = 0

Now put 1

[tex](5 * 1 - 4)^{1/2}[/tex] - 1 = 0

[tex](5 -4)^{1/2}[/tex] - 1=0

1 - 1=0

0=0

Hence we get that both the value of x is not an extraneous solution.

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Answer: A quadrilateral that has 4 sides is known as a rectangle.

Answer:

Step-by-step explanation:

This is either a rectangle or a square.

(A square is a special type of rectangle, with 4 equal sides).

Answer:

-18k

Step-by-step explanation:

-> -8k+ 10k

-> minus and plus is = minus

-> 8k+10k

-> -18k(ans)

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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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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I think the answer is x=4

Answer: x=4

Step-by-step explanation:

2x+3(5x-7)=47

2x+15x-21=47

17x-21=47

  +21  +21

17x= 68

17     17

x=4

The value of the expression log 10,000 is 4.

The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.

Log a to the base b can be written as- log a/ log b.

Moreover, log [tex]a^{k}[/tex] = k log a, for all non negative values of a

Here, we are given a logarithmic expression- log 10,000

As the base is not given, we always assume it to be 10.

We can expand this as-

log 10,000 = log 10,000/ log 10

= log [tex]10^{4}[/tex]/ log 10

= 4 log 10/ log 10

= 4

Thus, the value of log 10,000 is 4.

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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 )

The value of x is 12.

What is triangle proportion?

According to the Triangle proportion rule, When a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

In the diagram;

The side with x is a reflexive side of both triangles and as such from triangle proportionality theorem we can say that;

⇒6/x = 3/6

⇒ 36 = 3x

⇒ x = 12

Hence, The value of x is 12.

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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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The quadratic function of graph given characteristics vertex(1,\9); passes through (4,\6) is y=1/3x2+2/3x+26/3.

A quadratic function is a polynomial function with one or more variables where the highest exponent of the variable is two. Due to the fact that the biggest degree term in a quadratic function is of second degree, it is sometimes referred to as the polynomial of degree 2. There must be a quadratic function with at least one second-degree term. It performs algebraic operations.

Assum:y=ax2+bx+c

Point (1,9)(4,6) into it:{9=a+b+c/6=16a+4b+c} (point 1and 2)

Therefore, vertex(1,9) –b/2a=1→-b=2a

Point 3 into 1 and 2={9=-a+c/b=8a+c}

a=1/3, b=2/3, c=26/3

y=1/3x2+2/3x+26/3

For: y=ax2+bx+c

The graph intersects the x axis at x1 and x2,

X1= -b+√b2-4ac/2a , X2= -b-√b2-4ac/2a

The x-coordinate of the vertex must be in the middle of x1 and x2.

Assume the x-coordinate of the vertex as x

So : x=x1+x2/2 = -b+√b2-4ac/2a + -b-√b2-4ac/2a / 2 = -b/2a

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The slope of the line that passes through  (8, 0) and (-4, -8) is calculated as: m = 2/3.

The slope (m) formula is given as:

Slope (m) = change in y/change in x = y2 - y1/x2 - x1.

Given the following points on the line:

(8, 0) = (x1, y1)

(-4, -8) = (x2, y2)

Plug in the values into the slope formula, x = y2 - y1/x2 - x1:

Slope (m) of the line = (-8 - 0) / (-4 - 8)

Slope (m) of the line = (-8) / (-12)

Slope (m) of the line = 2/3

Thus, the slope of the line that passes through  (8, 0) and (-4, -8) is calculated as: m = 2/3.

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The Magnitude of earthquake that hit Texas is 5.8; With the help of the logarithmic equation so found, we can get the value of M, with which we can get the magnitude of the Texas earthquake.

Given:

To find: Magnitude of earthquake that hit Texas.

Finding:

=>  [tex]\frac{I_2}{I_1}[/tex] =  [tex]30^M[/tex]

For  [tex]\frac{I_2}{I_1}[/tex] = 74900, the above expression becomes:

=> 74900 = [tex]30^M[/tex]

Taking logarithm on both sides, with base 10 gives:

=> log (74900) = log ([tex]30^M[/tex])

As [tex]log_b(a)^m = m(log_b(a))[/tex],

=> log (74900) = M ( log (30))

=> [tex]\frac{log(74900)}{log (30)}[/tex] = M

=> M ≈ 3.3, i.e., the increase in magnitude difference is approximately 3.3.

Thus, the magnitude of the earthquake that hit Texas = 9.1 - 3.3 = 5.8.

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The composite discount = 32%

The store offers 15% which  on all items and employees get a 20% discount.

The composite discount formula is:

 -x - y + ( x ×y / 100)

Here x = 15% and y = 20%

So by putting the value of x and y we get

- 15 - 20 + ( 15 × 20 /100)

- 15 -20 + 3

- 35+ 3

-32  

Therefore we get the composite discount i.e., 32%

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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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The unknown angle in the triangle is as follows:

m∠A = 52°

External angle theorem states that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Therefore,

m∠D = m∠A + m∠B

m∠D = 116°

m∠A =  (2x)°

m∠B = (x + 38)°

Hence,

116 = 2x + x + 38

116 = 3x + 38

3x = 116 - 38

3x = 78

divide both sides by 3

x = 78 / 3

x = 26

Therefore,

m∠A = 2(26)

m∠A = 52°

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Answer:

8.25 Hours she worked last week

Step-by-step explanation:

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

The new coordinates after transformation of the original coordinates using the transformation rule (x, y) → (x, -y) are;

P(6, -4) → P'(6, 4)

Q(2, -2) → Q(2, 2)

R(2, -6) →  R(2, 6)

S(6, -6) → S(6, 6)

The given reflection transformation of (x, y) → (x, -y) simply means a reflection across the x-axis.

Thus, the new coordinates after undergoing the above transformation are;

P(6, -4) → P'(6, 4)

Q(2, -2) → Q(2, 2)

R(2, -6) →  R(2, 6)

S(6, -6) → S(6, 6)

Thus, we conclude that the new coordinates after transformation of the original coordinates using the transformation rule (x, y) → (x, -y) are;

P(6, -4) → P'(6, 4)

Q(2, -2) → Q(2, 2)

R(2, -6) →  R(2, 6)

S(6, -6) → S(6, 6)

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Answer:

p = 2/5

Step-by-step explanation:

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

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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ANSWER- X is  2.52083333 or 2.52083 rounded

265-23 is 242. 242 divided into 96 is 2.52083333

(96 x 2.52083333)+23 = 265

This means our X is 2.52083...

HOPE THIS HELPS & GOOD LUCK

Answer:

[tex]\displaystyle \frac{121}{48}[/tex]

or

[tex]2.5208\bar3[/tex]

To begin, subtract 23 from both sides of the equation. This will move the constants to the right side.

[tex]96x=242[/tex]

Then, divide both sides of the equation by 96. This will isolate the unknown, x, and allow you to solve the equation.

[tex]\displaystyle \frac{96x}{96}=\frac{242}{96}[/tex]

[tex]\displaystyle x=\frac{121}{48}[/tex]

There are two different answers that are equivalent but will depend on what you are looking for.

For a fraction answer, your final answer is [tex]\displaystyle \frac{121}{48}[/tex].

For a decimal answer, your final answer is [tex]2.5208\bar3[/tex].