What is the first step in constructing a segment congruent to a given segment?

A firm has the short-run total cost function c(y) = 4y^2 + 100; its marginal cost is mc(y) = 8y. At the A: 5 quantity of output the short-run average cost is minimized.

AC=c/y,   where y is the output produced

AC= c/y= (4y^2 + 100)/y

            = 4y+100/y

To minimize AC, the first derivative of the AC function is determined

dAC/dy= 4 -100/y^2

4 -100/y^2=0

4 = 100/y^2

y^2 = 100 /4

y^2 = 25

y = 5

At y=5 we find the second derivative of the AC function to ascertain if AC is minimized.

d(dAC/dy)= -200/y^3

-200/(5)^3= 1.6,   revealing that AC is minimized at y=5.

You can learn more about total cost at

https://brainly.com/question/29367524

#SPJ4

The Riemann sum formula to find RN is RN = (5/n) × Σ(i=1 to n) [f(x_i) × (5/n)], and the area under the graph as a limit is 400.

The function f(x) = (5x)² is a polynomial function, and we can use the formula for the nth Riemann sum to find RN. The formula for the nth Riemann sum is:

RN = (5/n) × Σ(i=1 to n) [f(x_i) × (5/n)]

where x_i = -1 + (i-1)(5/n) and f(x_i) = (5x_i)²

Substituting these values into the formula, we get:

RN = (5/n) × Σ(i=1 to n) [(5x_i)² × (5/n)]

RN = (5/n) × Σ(i=1 to n) [(25x_i²) × (1/n)]

Therefore the formula for RN is (5/n) × Σ(i=1 to n) [(25x_i²) × (1/n)]

To find the area under the graph as a limit, we take the limit as n approaches infinity:

limN→[infinity] RN = limN→infinity × Σ(i=1 to n) [(25x_i²) × (1/n)]

The function is defined on the closed interval [-1,5], so the definite integral is the definite integral from -1 to 5 of (25x²) dx

limN→[infinity] RN = (25/3) × 5³ - (25/3) × (-1)³

limN→[infinity] RN = (25/3)×(125 -1)

limN→[infinity] RN = 400

Therefore, limN→[infinity] RN = 400

To learn more about Riemann sum visit: https://brainly.com/question/9043837

#SPJ4

The distance between the two cities is 1305 miles

From the question, we have the following parameters that can be used in our computation:

1 inch = 300 miles

Also, we have

Distance = 4.35 inches

Multiply both sides of the scale by 4.35

So, we have

4.35 inches = 300 * 4.35

Evaluate the product

4.35 inches = 1305 miles

Hence, the distance is 1305 miles

Read more about scale at

https://brainly.com/question/29229124

#SPJ1

The numerical length of BD is 16 units

as given in the question,

There is a line segment BD

and a point lies on the line segment BD which is point C

but we don't know the exact position where the point C lies on the line segment BD

from the details given

The distance between C and B is x

the distance between B and D is 2x

the distance between C and D is 8

let the point C be a arbitrary point in the line segment BD

now ,

BC + CD = BD

x + 8 = 2x

x = 8

now  BD is 2x that is 2( 8) is 16

The length of BD is 16.

To learn more about line segment :

https://brainly.com/question/17299505

#SPJ4

The numerical length of [tex]\overline{bd}[/tex] is 16 units.

Using the formula for the length of a line segment, we can calculate the length of segment BD. The formula is

Length = [tex]√((x2-x1)^2+(y2-y1)^2)[/tex]

We know that BD = 2x so x2 = 2x and x1 = 0. We also know that CD = 8 and BC = x so we can calculate y2 and y1. y2 = 8 - 2x and y1 = x - 0.

Therefore, plugging in these values we get:

Length =[tex]√((2x-0)^2+(8-2x)^2)[/tex]

Solving for the length of BD we get:

Length = [tex]√(4x^2 + 64)[/tex]

Substituting in the value of x = 8, we get:

Length = [tex]√(4*8^2 + 64)[/tex]

Length = [tex]√(256 + 64)[/tex]

Length = [tex]√320[/tex]

Length = 16 units.

Learn more about length here:

https://brainly.com/question/30100801

#SPJ4

4,067.2

Step-by-step explanation:

—4067.23

You rounded to the nearest tenths place. The 2 in the tenths place rounds down to 2, or stays the same, because the digit to the right in the hundredths place is 3.

4,067.2

When the digit to the right is less than 5 we round toward 0.

4067.23 was rounded down toward zero to 4,067.2

The two triangles that are congruent by by ASA congruency postulate are; ΔCBA ≅ ΔDBA

There are different triangle congruence postulates such as;

SAS which means Side - Angle - Side

SSS which means Side - Side - Side

ASA which means Angle - Side - Angle

AAS which means Angle - Angle - Side

HL which means Hypotenuse Leg Congruence Postulate

Now, we want to look for the triangles that are congruent by Angle - Side - Angle Congruence Postulate.

Looking at triangles ABC and AED, we can see that;

∠ACB ≅ ∠ADE

∠ABC ≅ ∠AED

BC ≅ ED

Thus, we have 2 congruent angles and the included side and as such ΔCBA ≅ ΔDBA by ASA congruency postulate.

Read more about Triangle Congruence Postulate at; https://brainly.com/question/29268713

#SPJ1

Graph of a sine function ,The sinusoidal graph, often known as the sine graph, is an up-down graph that repeats every 360 degrees, or at 2[tex]\pi[/tex]. Amplitude is 7

Graph of a sine function ,The sinusoidal graph, often known as the sine graph, is an up-down graph that repeats every 360 degrees, or at 2[tex]\pi[/tex].

Trigonometric functions include sine functions. Keep in mind the intercepts, maximum points, and minimum points throughout one period if you wish to sketch the graph of the fundamental sine function. As a result, the graph is  h(x) = 7 sin x depicted in the image below.

h(x) = 7 sin x

Those intercepts are

(0 0) , ([tex]\pi[/tex] ,0) ,  and (2[tex]\pi[/tex], 0)

A maximum of:

([tex]\pi[/tex]/2 , 7)

Minimum score:

(3[tex]\pi[/tex]/2 , -7)

Period:

2[tex]\pi[/tex]

Amplitude = 7

To learn more about Graph refer to:

https://brainly.com/question/12026158

#SPJ1

The integer that represents the exact opposite of the real-world situation; "a credit of $38" is; -$38 which represents a debit for the same amount.

As evident in the task content; the integer which correctly represents the opposite of the given real world problem is required to be determined.

Since the given real-world problem is; $38 which represents a credit.

The exact opposite of that which represents a debit for the same amount is; -$38.

On this note, the number line representation of both integers is as represented in the attached image.

The number, zero represents a point of neither credit nor debit in this situation.

Read more on number line;

https://brainly.com/question/12399107

#SPJ1

The loan amount that Ahmad needs to relay will be RM 901600

From the information, Ahmad obtained a car loan of RM 700000 from a bank with an interest rate of 3.2% per annum for 9 years.

The interest based on the information will be:

= Principal × Rate × Time

= 700000 × 3.2% × 9

= $201600

The loan amount that Ahmad needs to relay will be:

= 700000 + 201600

= 901600

Learn more about interest on:

brainly.com/question/25793394

#SPJ1

Answer:

72 m

93 m

Step-by-step explanation:

1)  A = length x width

6264 m² = (87 m)w

w = 6264 m²/87 m = 72 m

2)  P = 2l + 2w

342 m = 2l + 2(78 m)

342 m - 156 m = 186 m = 2l

l = 186 m/2 = 93 m

The standard form of the polynomial is given as follows:

x^6 + 53x^5 + 2x^4 - 2.

The degree of the polynomial is given as follows:

6.

The leading coefficient of the polynomial is given as follows:

1.

This is called a polynomial because it has more than three terms.

The first feature we want to obtain is the standard form notation of the polynomial, which means that the terms should appear in the order of the exponents, as follows:

x^6 + 53x^5 + 2x^4 - 2.

Then the degree of the polynomial is given by the highest exponent, which is of six.

The leading coefficient of the polynomial is the term that multiplies the term of the highest exponent, which is of x^6, hence it is of one.

Finally, it is classified as polynomial as the expression is composed by four terms.

More can be learned about polynomials at https://brainly.com/question/29946479

#SPJ1

The distance between two points is D and E, E and F, C and D, A and B, B and C, when the points are arranged in increasing order.

Discover the distance formula, a Pythagorean theorem application, to determine the separation between two places. To get the separation between any two points, we can rewrite the Pythagorean theorem as [tex]d= \sqrt{x_{2} -x_{1} + y_{2} -y_{1} }[/tex]

In geometry, distances are always positive unless the points are exactly adjacent. The distance between A and B is equal to the distance between B and A. We consider two points A(a,b) and B to get the formula for the distance between two points in the plane (c,d).

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

The distance is provided in the following equation as

A and B are [tex]\sqrt{39}[/tex] miles apart.

B and C are [tex]\sqrt{41}[/tex] miles apart.

C and D are five miles apart.

D and E are four miles apart.

E and F are [tex]\sqrt{17}[/tex] miles apart.

To learn more about distance refer to :

https://brainly.com/question/27956440

#SPJ1

Answer:

Step-by-step explanation:

you have to count the distance between each point then list them from smallest to greatest. The other answers on here made it more convoluted than necessary.

Answer:

15 kg

Step-by-step explanation:

.625 x 4.8 = 3

It takes 3 kg of flour to make 1 loaf of bread.

3 x 5 = 15

The total amount the homeowner would pay for the damages would be $5,150.

In this situation, the homeowner would pay $5,000 for the deductible, plus the premium of $150. The remaining amount of $165,000 would be covered by the policy up to the limit of $300,000. Therefore, the total amount the homeowner would pay for the damages would be $5,150.

To calculate this, we can use the following formula:

Total Cost = Deductible + Premium + (Damages - Limit)

Total Cost =[tex]$5,000 + $150 + ($170,000 - $300,000)[/tex]

Total Cost =[tex]$5,000 + $150 + (-$130,000)[/tex]

Total Cost = [tex]$5,150[/tex]

The total amount the homeowner would pay for the damages would be 5,150.

Learn more about total amount here:

https://brainly.com/question/29066172

#SPJ4

The time taken by cook to make one sandwich is equals to forty-five seconds.

let "x" be the time (in seconds) to make 1 sandwhich and " y " be the time (in seconds) to make 1 salad. Now, it takes 3 min 45 sec to make 3 sandwiches and 3 salads.

time in seconds , 3 min 45 sec = 225 sec

so, 3x + 3y = 225

=> x + y = 75 --(1)

Also, it takes 8 min 30 sec to make 6 sandwiches and 8 salads, i.e ,8min 30sec = 510 sec

so, 6x + 8y = 510

=> 3x + 4y = 255--(2)

We have a system of linear equations consists equation (1) and (2). We solve this system of equations by using Substitution,

Substitute the value of x = 75 - y in equation (2),

3x + 4y = 255

=> 3(75- y) + 4 y = 255

=> 225 - 3y + 4y = 255

=> y = 255 - 225 = 30

from equation (1) , x = 75 - 30 = 45.

So, it takes 45 seconds to make one sandwich and 30 seconds for one salad .

To learn more about system of linear equations, refer:

https://brainly.com/question/14323743

#SPJ4

The equation of this parabola in vertex form is y = ( -1/2) x² - 0.5

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

We are given that Focus (0,-1), Directrix is the line y=0

so, we have a vertical parabola open downward

Remember that the distance from the vertex to the directrix must be the same that the distance from the vertex to the focus

This means that the vertex is the point (0,-0.5)

The midpoint between the focus and the directrix

Find out the value of p (focal distance)

p=0.5

The equation of the parabola is given by

y =( -1/2) x² - 0.5

The vertex is (0,-0.5)

The value of p=0.5

To  learn more about parabola  from the given link:

brainly.com/question/21685473

#SPJ1

The probability that Larry wins the game is [tex]$\tfrac{1}{2}$[/tex].

The probability that Larry knocks the bottle off the ledge on his first throw is

[tex]$\tfrac{1}{2}$.[/tex]

The probability that Larry knocks the bottle off the ledge on his second throw, given that he did not knock it off on his first throw, is

[tex]$\tfrac{1}{2}$[/tex]

Therefore, the probability that Larry wins the game is

[tex]$\tfrac{1}{2} \times \tfrac{1}{2} = \tfrac{1}{2}$.[/tex]

By the law of total probability, we have:

[tex]$P(W) = P(W|F)P(F) + P(W|F^c)P(F^c)$[/tex]

[tex]$P(W) = 1 \times \tfrac{1}{2} + \tfrac{1}{2} \times \tfrac{1}{2}$[/tex]

[tex]$P(W) = \tfrac{1}{2}$[/tex]

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

The possible values of k for the equation of circle are -4 and 7.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

The equation of a circle is (x - 1)² + (y - k)² = 50

The equation of the circle passes through the point (2, 3) = (x, y).

Now,

(2 - 1)² + (3 - k)² = 50

1 + (3 - k)² = 50

(3 - k)² = 50 - 1

3 - k = √49

3 - k = ±7

Now,

3 - k = 7

3 - 7 = k

k = -4

3 - k = -7

3 + 7 = k

k = 10

Thus,

The possible values of k are -4 and 10.

Learn more about circle here:

https://brainly.com/question/11833983

#SPJ1

An expression for the electric field at points on the x-axis is [tex]$\frac{q}{4 \pi \epsilon_0}\left(\frac{4 d}{X^3}\right)$[/tex]

The electric field at a point P on the x-axis for which X is much larger than the distance between the charges​.

Let us consider two charge -q and +q separated by small distance 2d.

P is a point along the axial line of the dipole at a distance X from the midpoint O of the electric dipole.

The electric field at the point P due to +q placed at B

[tex]E_1=\frac{1}{4 \pi \epsilon_0} \frac{q}{(X-d)^2}[/tex]...(I)

The electric field at the point P due to -q placed at A

[tex]E_2=-\frac{1}{4 \pi \epsilon_0} \frac{-q}{(X+d)^2}[/tex]...(II)

We need to calculate the magnitude of resultant of electric field

Using formula of electric field

[tex]E=E_1+\left(-E_2\right)[/tex]

Put the value into the formula

[tex]& E=\frac{1}{4 \pi \epsilon_0} \frac{q}{(X-d)^2}-\frac{1}{4 \pi \epsilon_0} \frac{q}{(X+d)^2} \\[/tex]

[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{1}{(X-d)^2}-\frac{1}{(X+d)^2}\right) \\[/tex]

[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{4 X d}{\left(X^2-d^2\right)^2}\right)[/tex]

If the point P is far away from the charges, and X is much larger than the distance between the charges

The electric field will be

[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{4 X d}{X^4}\right) \\[/tex]

[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{4 d}{X^3}\right)[/tex]

Hence, the electric field will be [tex]$\frac{q}{4 \pi \epsilon_0}\left(\frac{4 d}{X^3}\right)$[/tex]

For more questions on electric field

https://brainly.com/question/8971780

#SPJ4

Derive an expression for the electric field at a point P on the x-axis for which X is much larger than the distance between the charges​.

The value of |(a x a) u a)| = 16, when a is a set with a = { 2, 5, 7, 11 }.

|(a x a) u a)| is the cardinality of the set obtained by the union of the cartesian product of a with itself, and a.

The cartesian product of a with itself is the set of all possible ordered pairs (x,y) where x and y are elements of a. Therefore, a x a = { (2,2), (2,5), (2,7), (2,11), (5,2), (5,5), (5,7), (5,11), (7,2), (7,5), (7,7), (7,11), (11,2), (11,5), (11,7), (11,11) }

The union of a x a and a is the set of all unique elements that belong to both sets. Since all elements of a are also in a x a, the union will have the same elements as a x a plus the elements of a. Therefore, (a x a) u a = { (2,2), (2,5), (2,7), (2,11), (5,2), (5,5), (5,7), (5,11), (7,2), (7,5), (7,7), (7,11), (11,2), (11,5), (11,7), (11,11), 2, 5, 7, 11 }

The cardinality of a set is the number of distinct elements it contains. The set (a x a) u a contains 16 distinct elements, therefore |(a x a) u a)| = 16.

Learn more about cardinality here:

https://brainly.com/question/23976339

#SPJ4

The regular price of the soda is $1.59

From the question, we have the following parameters that can be used in our computation:

Number of bottles = 5

Total cost = 5.20

Coupon = 0.55

Using the above as a guide, we have the following:

Total cost = Number of bottles * (Regular price - Coupon)

Substitute the known values in the above equation, so, we have the following representation

5 * (Regular price - 0.55) = 5.20

So, we have

Regular price - 0.55 = 1.04

Add 0.55 to both sides

Regular price = 1.59

Hence, the regular price is 1.59

Read more about coupon at

https://brainly.com/question/28383863

#SPJ1

48$ dollars would be the correct anwser

Answer: {1024/3 r^3

Step-by-step explanation:

Similar Question

There is a 0.5 probability that the first toss and the last toss yield different outputs.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The sample space for a coin tossed three times is:

P = {HHH, HTH, HHT, HTT, TTT, THH, THT, TTH}

Now, out of this, we have to find the probability that the first and last toss are different results, i.e., if first toss is heads then last toss should be tails, and vice-versa.

The sample space for this is:

P = {HHT, HTT, THH, TTH}

The probability is:

[tex]P = \frac{4}{8} = \frac{1}{2}[/tex]

Therefore, there is a 0.5 probability that the first toss and the last toss yield different outputs.

To learn more about probability, visit the link:

brainly.com/question/30034780

#SPJ4

There is a 0.5 probability that the first toss and the last toss yield different outputs.

Now, According to the question:

Let's know:

What is probability and example?

It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.

The sample space for a coin tossed three times is:

P = {HHH, HTH, HHT, HTT, TTT, THH, THT, TTH}

Now, out of this, we have to find the probability that the first and last toss are different results, i.e., if first toss is heads then last toss should be tails, and vice-versa.

The sample space for this is:

P = {HHT, HTT, THH, TTH}

Probability = Number of Favorable Outcomes / Total Number of Outcomes.

P = 4/8 = 1/2
Therefore, there is a 0.5 probability that the first toss and the last toss yield different outputs.

Learn more about Probability at;

https://brainly.com/question/11234923

#SPJ4

Answer:

To find the area of a triangle, you use the following formula:
[tex]\frac{1}{2}[/tex] x base x height

= [tex]\frac{1}{2}[/tex] x 13 x 4

= 6.5 x 4

= 26

Answer:The answer is -18

Step-by-step explanation: Add -13+5 and you will get the correct answer.

Answer:

x = 6.5

Step-by-step explanation:

For the two expressions to be equal, we'll set them equal to each other and solve.

7x - 5 = 5x + 8

Subtract 5x from both sides.

2x - 5 = 8

Add 5 to both sides.

2x = 13

Divide both sides by 2.

x = 13/2

Divide to find the decimal answer.

x = 6.5

The coefficient of y in the expression -2x² * y² * z is 0

From the question, we have the following parameters that can be used in our computation:

An algebraic expression

The algebraic expression is given as

- 2x ^ 2 * y ^ 2 * z

Express the exponents as proper subscripts

So, we have the following representation

-2x² * y² * z

There is no term in the expression with the variable y

Instead, the term has a y² as its variable

This means that the coefficient of y is 0

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

The height of the rocket  is directly proportional to the time and the graph is attached.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that A toy rocket launch can be represented by a parabolic function.

The science fair can be modeled by the function y = -4(x - 5)² + 125 where y is the height of the rocket and

x is the number of seconds since launch.

We will graph this function by taking the values as below

x     0       1        2     3

y     25     61     89   109

By taking this values we  plotted the graph.

From the graph we can tell that the height of the rocket  is directly proportional to the time.

Hence,  the height of the rocket  is directly proportional to the time and the graph is attached.

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ1

Answer:

6

Step-by-step explanation: