Arrange the steps to show how to solve for x.

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.

To know more about the Extraneous solution refer to the link given below:

https://brainly.com/question/2959656

#SPJ4

Answer:

8.25 Hours she worked last week

Step-by-step explanation:

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.

Learn more about the Triangle proportion rule visit:

https://brainly.com/question/24804474

#SPJ1

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.

Learn more about net force here:https://brainly.com/question/11556949
#SPJ1

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:

p = 2/5

Step-by-step explanation:

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

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.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

#SPJ4

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)

Read more about reflection transformation coordinates at; https://brainly.com/question/12992962

#SPJ1

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.

Learn more about logarithms here-

https://brainly.in/question/6663314

#SPJ4

Answer:

The dimensions of the rectangle are length = 22 meters and width = 13 meters.

Step-by-step explanation:

It is given that the length of a rectangle is 4 meters less than twice the width and if the area of the rectangle is 286 square meters we need to calculate the dimensions.

Firstly, let us look at the dimensions of the rectangle;

=> Let 'l' be the length and 'b' be the width of the rectangle.

Now, let us look at the area of a rectangle;

=> l × b

So, we get an equation from the above condition;

=> l = 2b - 4

Now, the area of the rectangle is given that is 286 square​ meters;

=> A = 286 sq. m.

Using the above-mentioned formula for the area of the rectangle we get;

=> A = l × b

=> 286 = (2b - 4) × b

=> 286 = 2b² - 4b

=> 2b² - 4b - 286 = 0

After solving it further we get;

=> 2b² - 4b - 286 = 0

=> b² - 2b - 143 = 0

=> b² - 13b + 11b - 143 = 0

=> (b - 13) + (b + 11) = 0

Now, after equating both the sides we get;

=> (b - 13) = 0

=> b = 13

and

=> (b + 11) = 0

=> b = -11

But, b = -11 is not possible so, the width of the rectangle is 13 meters.

And the length of the rectangle would be,

=> l = 2b - 4

=> l = 2 × 13 - 4

=> l = 22

Therefore, the dimensions of the rectangle are length = 22 meters and width = 13 meters.

To know more about the topic, click here:

https://brainly.com/question/6613994

#SPJ9

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

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).

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°

learn more on angles here: https://brainly.com/question/25950519

#SPJ1

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.

To learn more about inverse function refer to:

brainly.com/question/10687170

#SPJ4

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

Read more about logarithm equations at

https://brainly.com/question/21101829

#SPJ1

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.

Learn more about slope of a line on:

https://brainly.com/question/3493733

#SPJ1

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:

-18k

Step-by-step explanation:

-> -8k+ 10k

-> minus and plus is = minus

-> 8k+10k

-> -18k(ans)

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.

Know more about equations here:

https://brainly.com/question/2972832

#SPJ4

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%

To know more about the composite discount refer to the link given below:

https://brainly.com/question/1538797

#SPJ4

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

To learn more about quadratic function visit:

brainly.com/question/12723502

#SPJ1

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:

your question is empty please give right questions to get answers

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.

To learn more about equations, refer to the link: brainly.com/question/2972832

#SPJ4