4.

Which inequality describes all the solutions to 11(3 - x) < -2x + 6?
x < -27
x > 3
x < -3
x > 4 1/3

Answer:

8,1 is the correct answer

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:  115

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

Answer:

8.25 Hours she worked last week

Step-by-step explanation:

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

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

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 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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Answer:

p = 2/5

Step-by-step explanation:

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

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 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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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:

your question is empty please give right questions to get answers

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- 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].

Answer:

No

Step-by-step explanation:

If you substitute, you get

2(5) - 10 >= 3

10 - 10 >= 3

0 >= 3, which is false!

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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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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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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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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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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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 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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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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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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