how do you simplify the distributive property ?

There is no vertex in the graph and the transformations from are

By definition, a graph that has a vertex would have an obvious maximum or minimum point on it

In this case, there is no point that can be regarded as the minimum or the maximum in this graph

This means that the graph has no maximum or minimum; in other words, there is no vertex

The parent function of the above graph is a cubic function

A cubic function passes through the origin

However in this graph, we can see that the graph is 4 units to the left of the origin and 2 units below the origin

This means that the transformation is (x - 4, y - 2)

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Equation of the line for the given graph in slope-intercept form is given by  y = 5x -1.

As given in the question,

From the given graph,

Consider pair of two coordinates we have,

(x₁ , y₁) = (1, 4)

(x₂ , y₂) = (0,-1)

Equation of the line for the given graph in slope-intercept form is given by:

(y -y₁) / (x -x₁)= (y₂ -y₁) / (x₂ -x₁)

⇒ ( y - 4)/ (x -1) = (-1-4)/(0-1)

⇒(y-4)/(x-1) = 5

⇒y-4 = 5(x-1)

⇒y = 5x -5 +4

⇒ y= 5x -1

Therefore, equation of the line for the given graph in slope-intercept form is given by  y = 5x -1.

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Answer:

[tex] {x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4x + 1[/tex]

Step-by-step explanation:

as shown in photo attached :")

The expected number of customers that get back their own hat is 1.

Utilizing indicator random variables, we resolve this issue. For 1 ≤ i ≤ n,

Let .

Xi = I {Customer 'i' who gets his hat back itself}.

The number of clients that receive their own hats back should be the random variable X. We want to figure out E[X].

Clearly,

      n

X = ∑ Xi

    i=1

It is clear that 1/n represents the likelihood that customer 'I' will receive his own hat.

Due to the fundamental characteristics of indicator random variables, this means that E[Xi] = 1/n.

                   n

  E[X] = E [ ∑ Xi  ]

                  i=1

                   n

           =  ∑ 1/n

                  i=1

Put the limits.

  E[X] = 1

As a result, 1 consumer is anticipated to have their own hats back.

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The value a = 2 and b = 5 is makes the expression (5x²y²){-4xªy³) =−20xªyᵇ as true.

Expression:

An expression is set of numbers or variables combined using the operations +, -, * and /.

Given,

Here we have the expression (5x²y²){-4xªy³) =−20xªy°.

Now, we have to the value of a and b which make both equation as equal.

In order to get the value a and b, first, we have to solve the expression in the left hand side,

To solve this type of equation, the first step is to combine the like terms, then we get,

=> (5x²y²){-4xªy³)

=> (5 x -4) (x² xᵃ) (y² y³)

Now, we have to do the multiplication on it, then we get,

=> -20 xᵃ⁺² y²⁺³

=> -20xᵃ⁺²y⁵

Now, we have to equate both LHS and RHS, then we get,

=> -20xᵃ⁺²y⁵ = -20xᵃyᵇ

While we looking into the equation, we have identified that the value of a is 2 and the value of b is 5.

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The solution of the system of equation by substitution is x = 3 and y = -1.

System of equation can be solved using different techniques such as substitution method, elimination method and graphical method.

Let's solve the system of equation by substitution method

Therefore,

3x + 2y = 7

x = 3y + 6

Substitute equation(ii) in equation(i)

3(3y + 6) + 2y = 7

9y + 18 + 2y = 7

9y + 2y + 18 = 7

11y = 7 - 18

11y = -11

y = -11 / 11

y = -1

Hence, let's find x

x = 3(-1) + 6

x = -3 + 6

x = 3

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Function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.

How do you find the maximum and minimum value of the function?

Calculus can be used to find the critical point, or the x-value of the vertex, by taking the derivative of the function, or f'(x). To determine the critical point, we shall set the function's first derivative to zero and solve for x. This point's maximum or minimum value can be determined by taking the second derivative, or f"(x). The second derivative will have a minimal value if it is positive. The second derivative will be the highest value if it is negative.

Given function:

[tex]-3x^2+18x+3[/tex]

To find the maximum and minimum value of the function use second derivative test.

On differentiating the above function we get,

-6x + 18

Now, find critical point

-6x + 18 = 0

-6x = - 18

x = - 18/-6 = 3

x = 3

Here, x = 3 is the critical point. Now again differentiate the above function we get,

-6

As , [tex]f^{''}(x)[/tex] < 0 , therefore x = 3 will given a maximum value of function and maximum value is

f(3) = [tex]-3(3)^2+18x+3 = -3(9) + 18(3) + 3 = -27 + 54 + 3 = 27 + 3 = 30[/tex]

Hence , function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.

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The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

The quadratic function is

f(x) = [tex]-3x^2[/tex] + 18x + 3

The general form of the quadratic function is

y = [tex]ax^2[/tex] + bx + c

If a < 0, the quadratic function has maximum value

Here the value of a = -3

Therefore the function has maximum value.

Maximum value will be at x = -b / 2a

= -18 / 2(-3)

= -18 / -6

= 3

The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a

Substitute the value in the equation

(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3

= (-36 - 324 / -12

= -360 / -12

= 30

Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

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The solution to these are in form of equation as follows.

What is equation?

In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

x= number of HD headphones           y= number of basic headphones

z = price of HD headphones.             w = price of basic headphones

a)

110 (70) + y*w = 10,000

7,700+ y*w = 10,000

y*w = 2,300

y = 2,300/w

b)

x*z+ 55(20) = 2000

x*z = 2000 -1100

x*z = 900

z = 900/x

c)

x*z+y*w = 800

x*z+8(80) = 800

x*z+640=800

X*z=160

Hence the values to the equation are as follows.

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The slope of line 1 and line 2 are equal. Then the lines are parallel to each other.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The slope of the parallel lines will be equal.

The equations are given below.

5x − 3y = 2             ...1

5x − 3y = 8            ...2

The slope of line 1 is given as,

5x − 3y = 2

y = (5/3)x − 2/3

The slope of line 1 is 5/3.

The slope of line 2 is given as,

5x − 3y = 8

y = (5/3)x − 8/3

The slope of line 2 is 5/3.

The slope of line 1 and line 2 are equal. Then the lines are parallel to each other.

The graph is given below.

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The mean of the distribution of sample means is 100.

Considering the values provided in the question,

Population mean = 100

We know that,

The sample mean is a reliable indicator of the population mean.

That is, E( sample mean)=Mean(sample mean)= population mean

Here population mean is 100, therefore mean of distribution of sample means is also 100.

The total of all the values in a sample is known as the Sample Mean. It is a statistical metric used to examine different variables throughout time. It is calculated by statisticians and researchers by dividing the total sum of all data fragment values by the total number of data sets.

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Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700

Use the simple interest formula

I = P r t

where I = simple interest

P = principal

r= rate of interest

t= number of years

5922=Px6.3%x20

5922=Px1.26

P=5922/1.26

P=4700

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Table C is the only table that represents a function

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Based on the definition of function as seen above. Let's check the tables:

Table A has two inputs with the same value (4)  but with different outputs. So  Table A is not a function

Table B also has two inputs with the same value (9)  but with different outputs. Thus, Table B does not represent a function

In Table C  each input has exactly one output. Table C represents a function

Table D also has two inputs with the same value (8)  but with different outputs. So Table D does not represent a function

Therefore, Table C represents a function

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Answer:

Paco, Tim, Jenny, Maria

Step-by-step explanation:

By using the properties of parallelogram, it can be calculated that

[tex]\angle CFE = 30^{\circ}[/tex]

[tex]\angle[/tex]DEF = 70°

[tex]\angle AED = 110^{\circ}[/tex]

What is a parallelogram?

Parallelogram is a four sided two dimensional figure whose each pair of opposite sides are parallel.

Here, ABCD is a parallelogram

[tex]\angle CFE = 30^{\circ}[/tex] [Alternate angle]

[tex]140 = \angle CEF + \angle CFE[/tex] [ Exterior angle of a triangle is equal to the sum of two opposite interior angle]

[tex]\\\angle CEF = 140 - 30\\\angle CEF = 110^{\circ}[/tex]

[tex]\angle[/tex]DEF = 180 -  110 [ Angle on a straight line]

         = 70°

[tex]\angle AED = 110^{\circ}[/tex] [Vertically opposite angle]

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The terms of the algebraic equation 3+6ab+c are (d) 3, 6ab  and c

The algebraic equation is given as

3 + 6ab + c

Consider an equation represented as

x + y

The terms of the equation are x and y

Also, for an equation represented as

x + y + z;

The terms are x, y and z

Using the above as a guide, the terms of 3 + 6ab + c are 3, 6ab  and c

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81 percentile of the given test is 482

The square root of the means of the squared deviations from the arithmetic mean is known as the standard deviation. Standard deviation is used in finance to quantify the risks associated with an investment instrument.

Given that the Marble Academy of Whoville conducts an annual test for all high school juniors one year, the scores on the test were approximately normally distributed with a mean of 420 and a standard deviation of 70

Here mean μ = 420 and Standard deviation σ = 70

We have find 81 percentile of this test = ?

The z score corresponding to the area 0.81 is

Z = 0.88  By standard normal table

X = μ + z σ

X = 420 + 0.88 x 70

= 420 + 62

= 482

Therefore 81 percentile of this test is 482

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The equation for the vertical line that goes through point M(−2, 6) is x = -2.

Answer:

The equation of a straight line is:

y = mx + b;

y, x are variables, m is the slope of the line and b is the y intercept.

The slope of a vertical is undefined. Since the line passes through the point M(−2, 6), hence the equation of the vertical line is:

x = -2

Using a system of equations, it is found that:

Leah takes 3 minutes to run a lap and 6 minutes to walk a lap.

The variables of the system of equations are presented as follows:

She requires 84 minutes to do 8 laps running and 10 laps walking, hence the first equation is:

8x + 10y = 84.

She requires 66 minutes to do 2 laps running and 10 laps walking, hence the second equation is:

2x + 10y = 66.

Simplifying by 2, we have that:

x + 5y = 33.

x = 33 - 5y.

Replacing in the first equation, we can find the time it takes to walk a lap, as follows:

8(33 - 5y) + 10y = 84.

264 - 40y + 10y = 84

30y = 180

y = 180/30

y = 6 minutes.

Then the time it takes to run a lap is obtained as follows:

x = 33 - 5y = 33 - 5(6) = 33 - 30 = 3 minutes.

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The inequality that can be used to solve for x, the number of minutes it will take Amy to finish typing her paper is D. 38x + 1,450 > 4,000.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since Amy types at an average speed of 38 words per minute and has already typed 1,450 words of her final paper, which will be more than 4,000 words.

Let the number of minutes be x.

This will be:

1450 + 38(x) > 400

1450 + 38x > 4000

In conclusion, the correct option is D.

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By using the diagram and the given angle measure we get that:

if, m∠1 = 143°

then, m∠2 = 37°

         m∠3 = 143°

         m∠4 = 37°

What is angles?

An angle is formed when two straight lines or rays meet at a common endpoint.

What is Properties of Congruence?

       For all angles A ,

        ∠A≅∠A .

       An angle is congruent to itself.

        For any angles A  and  B ,

        if ∠A≅∠B , then ∠B≅∠A .

         Order of congruence does not matter.

        For any angles A,B,  and  C ,

        if ∠A≅∠B and ∠B≅∠C , then ∠A≅∠C .

        If two angles are both congruent to a third angle, then the first two        angles are also congruent.

I assume that, this refers to two intersecting lines which form four angles.

         ∠1 + ∠2 = 180°

          143° + ∠2 = 180°

          ∠2 = 180° - 143°

          ∠2 = 37°.

         It means that,  ∠1 = ∠3 =143° (properties of congruency)

         and ∠2 = ∠4 =37° (properties of congruency).

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The dimensions of the rectangle that will allow for the most economical fence to be built is 50 feet and 25 feet in length and width respectively.

Given in the question,

Area = 1250 ft²

The three sides cost $3 per foot, and the fourth side costs $9 per foot.

Let x and y be the length and width of the rectangle.

Because the area is 1250 ft², therefore

xy = 1250, or

y = 1250/x            

Case 1: Three sides are (x,y,x) and the 4-th side is y.

The cost is

C = 3(2x +y) + 9y

  = 6x + 12y

  = 6x + 12(1250/x)

  = 6x + 15000/x

For C to be minimum, C' = 0. That is

6 - 15000/x² = 0

x² = 15000/6

x =  50 ft, y = 1250/50 = 25 ft

C = 6(50) + 15000/(50²) = $600

Case 2: Three sides are (y,x,y) and the 4-th side is x.

The cost is

C = 3(x + 2y) + 9x

   = 12x + 6y

   = 12x + 6(1250/x)

   = 12x + 7500/x

For C to be minimum, C' = 0.

12 - 7500/x² = 0

x² = 7500/12 = 625

x = 25 ft, y = 50ft

C = 12(25) + 7500/25 = $600

Thus, the Dimensions will be 25 feet and 50 feet.

Question:

A fence is to be built to enclose a rectangular area of 1250 square feet. the fence along three sides is to be made of material that costs ​$3 per foot. the material for the fourth side costs ​$9 per foot. find the dimensions of the rectangle that will allow for the most economical fence to be built.

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Answer:

-2

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

distribute

-7x-14-x=2

-8x-14=2

    +14. +14

-8x=16

/-8. /-8

x=-2

Hopes this helps please mark brainliest

Answer:

5

Step-by-step explanation:

21/8 must be added to the terms to give the result as 6. The answer will be in a fraction.

What is a fraction?

In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. In ordinary English, a fraction refers to the number of parts of a specific size.

Main Body:

Let the term to be added be x.

3+3/8+x =6

on solving this we will get the value of  x= 21/8

Hence the answer of this question is 21/8.

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When the divisor is missing, you divide the dividend (3.472) by the quotient (0.112)

So, we will do 3.472 divided by 0.112

3.472/0.112 = 31

Another method is multiplication. Multiplication is the opposite of division. We'd multiply 0.112 by 31.

0.112 x 31 = 3.472

In conclusion,

3.472/31 = 0.122

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Answer: 3.472/31 = 0.122

Step-by-step explanation: I hope this helps:)