100PT! Which method would you use to prove AEC ≅ BED?

SAS
AAS
SSS
ASA

Answer:

C ≈ 251.33

Step-by-step explanation:

The circumference of a circle is C = 2πr

Radius = r = 40 is given in the problem

C = 2* 3.14 * 40

C ≈ 251.33

Answer:

251.2

Step-by-step explanation:

Given,

Radius ( r ) = 40

To find : Circumference of a circle = ?

Formula : -

Circumference of a circle = 2πr

Note : -

The value of π is :

Solution : -

Circumference of a circle = 2πr

= 2 x 3.14 x 40

Circumference of a circle = 251.2

Therefore,

Circumference of a circle is 251.2

The Taylor series is \(ln(x) = x - x^2/2 + x^3/3 - x^4/4 + ...\) , The Fourier series is  \(f(t) = (1 - cos(t))/2 + 9/(2\pi) sin(t)\) , The transfer function is\(H(s) = (35s-140)/((5s+2)(s-5))\).

The Taylor series for the function\(f(x) = ln(x)\) about x = 0 can be found using the following steps:

Let \(f(x) = ln(x)\).

Let \(f(0) = ln(1) = 0\).

Let\(f'(x) = 1/x\).

Let\(f''(x) = -1/x^2\).

Continue differentiating f(x) to find higher-order derivatives.

Substitute x = 0 into the Taylor series formula to get the Taylor series for f(x) about x = 0.

The Taylor series for\(f(x) = ln(x)\) about x = 0 is:

\(ln(x) = x - x^2/2 + x^3/3 - x^4/4 + ...\)

The Fourier series of the function \(f(t) = {-1; -\pi \leq t \leq 0 0 < t < \pi 19 1}\)can be found using the following steps:

Let \(f(t) = {-1; -\pi \leq t \leq 0 0 < t < \pi 19 1}\).

Let \(a_0 = 1/2\).

Let\(a_1 = -1/(2\pi)\).

Let \(a_2 = 9/(2\pi^2).\)

Let\(b_0 = 0\).

Let\(b_1 = 1/(2\pi)\).

Let\(b_2 = 0.\)

The Fourier series for f(t) is:

\(f(t) = a_0 + a_1cos(t) + a_2cos(2t) + b_1sin(t) + b_2sin(2t)\)

\(= (1 - cos(t))/2 + 9/(2\pi) sin(t)\)

The transfer function\(H(s) = 7/(5s+2) + 3/(s-5)\)can be found using the following steps:

Let \(H(s) = 7/(5s+2) + 3/(s-5).\)

Find the partial fraction decomposition of H(s).

The transfer function is the ratio of the numerator polynomial to the denominator polynomial.

The partial fraction decomposition of \(H(s) = 7/(5s+2) + 3/(s-5)\) is:

\(H(s) = (7/(5(s-5))) + (3/(s-5))\\= (7/5) (1/(s-5)) + (3/5) (1/(s-5))\\= (2) (1/(s-5))\)

The transfer function is:

\(H(s) = (2)/(s-5)\)

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Therefore, as per the solution from the linear equation in one variable, the line segment PR is 9 units.

A linear equation in one variable is one that is written in the form ax + b = 0, where a, and b are real numbers and the coefficients of x and constant, i.e. a and b, are not equal to zero.

Given :

PR is a line.

Q is the midpoint of PR. So PQ = PR.

QR = x + 9

PR = 3x + 9

According to the question, verification is

PQ = PR

X + 9 = 3x + 9

3x – x = 9 - 9

2x = 0

x = 0

Therefore, as PQ = PR

x + 9 = 3x + 9

0 + 9 = 0(3) + 9

     9 = 9

  PR = 3(0) + 9

  PR = 0 +  9

  PR = 9

Therefore, as per the solution from the linear equation in one variable, The line segment PR is 9 units.

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Therefore, as per the solution from the linear equation in one variable, the line segment PR is 9 units.

A linear equation in one variable is one that is written in the form ax + b = 0, where a, and b are real numbers and the coefficients of x and constant, i.e. a and b, are not equal to zero.

Given :

PR is a line.

Q is the midpoint of PR. So PQ = PR.

QR = x + 9

PR = 3x + 9

According to the question, verification is

PQ = PR

X + 9 = 3x + 9

3x – x = 9 - 9

2x = 0

x = 0

Therefore, as PQ = PR

x + 9 = 3x + 9

0 + 9 = 0(3) + 9

    9 = 9

 PR = 3(0) + 9

 PR = 0 +  9

 PR = 9

Therefore, as per the solution from the linear equation in one variable, The line segment PR is 9 units.

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The three angle bisector of a triangle intersect at a single point that point of concurrency of the angle of bisectors is called the incenter.

Given:

the 3 angle bisectors of a triangle intersect.

when three angle bisector of a triangle intersect then that point of concurrency is called incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Incenter formula:

= (ax1+bx2+x3 / a+b+c  , ay1+by2+y3 / a+b+c).

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Answer:

Infinite solutions

Step-by-step explanation:

3h-8h+10=10-5h

-5h+5h=10-10

0=0

Infinite solutions

Answer:

This should be the correct answer.

The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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Answer:

9 square feet

Step-by-step explanation:

A = bh / 2

b = 3

h = 6

A = 6 * 3 / 2 = 9

Answer:

50 days

Step-by-step explanation:

40×300=1200

1200-700

500

so 1 day is 10 . 50 days is 500

The number of days he was absent from work will be 50 days

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a man gets Rs. 40 for every day he works, but is fined Rs. 10 for every day he is absent If he got Rs. 700 at the end of 30 days.

The number of days he was absent from work will be calculated as below:-

40×300 = 1200

             = 1200-700

             = 500

1 day is 10 then 50 days is 500. Therefore, the number of days he was absent from work will be 50 days

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Answer:

13 each

Step-by-step explanation:

40/3= 13.3

Answer:

5 ft

Step-by-step explanation:

a²+b²=c²

3×3=9

4×4=16

9+16=25

√25=5

AB = BC

Since B is the midpoint of AC , Both segments AB and BC are equal:

Replacing with the values given:

20 = 2x

Solving for x

20/2 = x

10=x

Since:

AC= AB+BC

AC = 20+2x

Replacing x=10

AC = 20+2(10)

AC=20+20

AC=40

Answer:

a) $1,298   b) $1,448

Step-by-step explanation:

a)  total of monthly payments:  11 x 118 = $1,298

b ) total cost of refrigerator:   deposit + sum of monthly payments

                                              = 150 + 1298

                                              = $1,448

Step-by-step explanation:

The scale factor is 2 because the original PQR triangle is of 1 by 2 while the image is of 2 by 4, which is multiplied by 2.

To ensure the preservation of the clinical specimen for viral isolation, it should be stored at a specific temperature. The recommended temperature for storing the specimen is generally between 2 to 8 degrees Celsius (36 to 46 degrees Fahrenheit).

Storing the clinical specimen in viral transport medium at a temperature range of 2 to 8 degrees Celsius (36 to 46 degrees Fahrenheit) is commonly advised for preserving the viability of the virus. This temperature range helps to slow down the viral activity and prevents the specimen from deteriorating while awaiting processing. It provides an environment that can maintain the integrity of the viral particles until laboratory procedures can be carried out the following week. It's important to follow the recommended storage temperature to ensure accurate results and successful viral isolation from the specimen.

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The dimensions of the corral that will minimize the cost of the fencing are x = 4 yards (width) and y = 325 yards (length).

To begin solving this problem, we need to use the given information to set up an equation that represents the cost of the fencing. Let's start by defining the dimensions of the rectangular corral. We can use x to represent the width and y to represent the length.

Since the area of the corral is 1300 square yards, we know that:

xy = 1300

Now, let's think about the fencing. We need to divide the corral in half with a fence down the middle, which means we have two equal sections with a width of x/2. The length of each section is still y.

To find the perimeter of each section, we add up all the sides. For the top and bottom, we have two lengths of y and two widths of x/2. For the sides, we have two lengths of x/2 and two widths of y. This gives us a perimeter of:

2y + x + 2x + 2y = 4y + 2x

Since we have two sections, the total perimeter is:

2(4y + 2x) = 8y + 4x

We can now set up an equation for the cost of the fencing:

Cost = (8y + 4x)($5) + (x)($3)

The first part of the equation represents the cost of the perimeter fence, while the second part represents the cost of the fence down the middle.

Now, we want to find the dimensions of the corral that will minimize the cost of the fencing. To do this, we can use calculus. We take the derivative of the cost equation with respect to x and set it equal to zero:

dCost/dx = 20y + 3 = 0

Solving for y, we get:

y = -3/20

Since we can't have a negative length, this solution is not valid. However, we can find the minimum cost by plugging in the value of y that makes the derivative equal to zero into the original equation for the cost of the fencing. This gives us:

Cost = (8y + 4x)($5) + (x)($3)
Cost = (8(-3/20) + 4x)($5) + (x)($3)
Cost = (-(12/5) + 4x)($5) + (x)($3)
Cost = -24x + 3x^2 + 3900

To minimize the cost, we take the derivative with respect to x and set it equal to zero:

dCost/dx = -24 + 6x = 0
x = 4

Plugging this value of x back into the equation for the cost of the fencing gives us:

Cost = -24(4) + 3(4^2) + 3900
Cost = $3892

Therefore, the dimensions of the corral that will minimize the cost of the fencing are x = 4 yards (width) and y = 325 yards (length).

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The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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Answer:

The sum of the series Σ (5an + 86m) from n = 1 to 12 is 7086.

Step-by-step explanation:

To find the sum of the series, we need to calculate the sum of each term in the series and add them up.

The series is given as Σ (5an + 86m) from n = 1 to 12.

Let's substitute the given values of a, b, and r into the series:

Σ (5an + 86m) = 5(a(1) + a(2) + ... + a(12)) + 86(1 + 2 + ... + 12)

Since a = 1 and b = -4, we have:

Σ (5an + 86m) = 5((1)(1) + (1)(2) + ... + (1)(12)) + 86(1 + 2 + ... + 12)

Simplifying further:

Σ (5an + 86m) = 5(1 + 2 + ... + 12) + 86(1 + 2 + ... + 12)

Now, we can use the formula for the sum of an arithmetic series to simplify the expression:

The sum of an arithmetic series Sn = (n/2)(a1 + an), where n is the number of terms and a1 is the first term.

Using this formula, the sum of the series becomes:

Σ (5an + 86m) = 5(12/2)(1 + 12) + 86(12/2)(1 + 12)

Σ (5an + 86m) = 5(6)(13) + 86(6)(13)

Σ (5an + 86m) = 390 + 6696

Σ (5an + 86m) = 7086

Therefore, the sum of the series Σ (5an + 86m) from n = 1 to 12 is 7086.

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Answer:

Commutative property of multiplcation.

Step-by-step explanation:

An identifier for the property of multiplcation is by multiplying it by 1. Therefore the answer remains the same.

The probability of selecting a pen from the first box is 1/8 (since there is only 1 pen out of 8 items in the box). The probability of selecting a crayon from the second box is 3/6 (since there are 3 crayons out of 6 items in the box).

To find the probability of both events happening together, we multiply the probabilities:

P(pen and crayon) = P(pen) x P(crayon)

P(pen and crayon) = (1/8) x (3/6)

Simplifying the fraction 3/6 to 1/2:

P(pen and crayon) = (1/8) x (1/2)

Multiplying the numerators and denominators:

P(pen and crayon) = 1/16

Therefore, the probability of selecting a pen from the first box and a crayon from the second box is 1/16.

The correct option is (B) put forth an idea or claim.

As used in line 35, "postulate" most nearly means to put forth an idea or claim.

The male mite begins life as an unfertilized egg, just like honey bees do. The female mite lays an egg that develops into a haploid male after about 72 hours within the cell. A person who is haploid only has one set of parental chromosomes. Approximately one egg is still laid daily by the female mite.

The authors contend that certain bees may be harmed by beekeepers' usage of insecticides to eradicate mite infestations in lines 31–35. The authors go on to speculate that it could be best to leave the bees to determine the proper dosage needed to prevent mite infestation (lines 35-37). The authors "postulate," or advance, that bees may more effectively naturally reduce mite infestations than insecticides in this situation.

So, the author used in line 35, "postulate" most nearly means to put forth an idea or claim.

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Answer:

$8.2225

Step-by-step explanation:

100% - 45% = 55%

then divide 55 by 100 to get .55

lastly multiply .55 to 14.95 to get 8.2225

In Utah, if not directly involved in diving activity, motorized vessels and personal watercraft (PWCs) must remain 150 feet from the diver down flags.

The diver down flag is a banner that is used by vessels to indicate that divers are in the water. It is typically a red flag with a white diagonal stripe that is used to indicate the presence of divers in the water. The flag must be at least 12 x 12 inches in size and must be clearly visible from all directions. When the flag is raised, boaters are expected to keep a safe distance from the divers and to take extra precautions to ensure that they do not pose a hazard to the divers.The diver down flag should be used whenever there are divers in the water. This includes scuba divers, free divers, and anyone else who is swimming or diving underwater. The flag should be raised before the divers enter the water and should be lowered when they exit the water. In addition to the flag, divers are required to use other means of indicating their presence in the water, such as lights and audible signals, to ensure that boaters can see and hear them. Motorized vessels and personal watercraft (PWCs) must remain at least 150 feet from the diver-down flag. This means that they must keep a safe distance from the divers and take extra precautions to ensure that they do not pose a hazard to the divers. If a motorized vessel or PWC is directly involved in the diving activity, such as transporting divers to and from the dive site, they may operate closer to the flag, but they must still maintain a safe distance from the divers at all times.

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(a) The rate of change of the total cost when the level of production is 4 units is 330.

(b) The revenue function R is R(q) = 60q^2 - 180q. The marginal revenue function R'(q) = 120q - 180. R'(4) = 300, indicating the marginal revenue at a production level of 4 units.

(c) The profit function P is P(q) = 15q^2 - 150q - 595. The marginal profit function P'(q) = 30q - 150. P'(4) = -30, P'(5) = 0, P'(6) = 30. P'(4) < 0 indicates a decrease in profit, P'(5) = 0 indicates no change, and P'(6) > 0 indicates an increase in profit.

(a) To find the rate of change of the total cost when the level of production is 4 units, we need to calculate the derivative of the total cost function C(q) with respect to q and evaluate it at q = 4.

C(q) = 45q^2 - 30q + 595

Taking the derivative of C(q) with respect to q:

C'(q) = 90q - 30

Substituting q = 4 into the derivative:

C'(4) = 90(4) - 30 = 360 - 30 = 330

(b) The unit price p and quantity demanded q are related by p = 60q - 180. To find the revenue function R, we multiply the unit price by the quantity demanded:

R(q) = p(q) * q = (60q - 180) * q = 60q^2 - 180q

The marginal revenue function R'(q) represents the rate of change of revenue with respect to the quantity demanded. To find R'(4), we take the derivative of the revenue function:

R'(q) = 120q - 180

Substituting q = 4 into the derivative:

R'(4) = 120(4) - 180 = 480 - 180 = 300

From this result, we can deduce that when the level of production is 4 units, the marginal revenue is 300.

(c) The profit function P is calculated by subtracting the total cost function from the revenue function:

P(q) = R(q) - C(q) = (60q^2 - 180q) - (45q^2 - 30q + 595) = 15q^2 - 150q - 595

The marginal profit function P'(q) represents the rate of change of profit with respect to the quantity demanded.

To find P'(4), we take the derivative of the profit function:

P'(q) = 30q - 150

Substituting q = 4 into the derivative:

P'(4) = 30(4) - 150 = 120 - 150 = -30

To find P'(5):

P'(5) = 30(5) - 150 = 150 - 150 = 0

To find P'(6):

P'(6) = 30(6) - 150 = 180 - 150 = 30

From these results, we can deduce that at a level of production of 4 units, the marginal profit is -30, indicating a decrease in profit. At a level of production of 5 units, the marginal profit is 0, indicating no change in profit. At a level of production of 6 units, the marginal profit is 30, indicating an increase in profit.

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Question

2. A certain company produces a product with daily total cost C(q)=45q 2−30q+595, where 3<q≤15 is measured in units of hundreds of items; C is expressed in thousands of dollars. (a) What is the rate of change of the total cost when the level of production is 4 units? (b) Suppose the unit price p and the quantity demanded q of the product are related by p=60q−180. Determine the revenue function R and the marginal revenue function. Find R (4), what can you deduce from your result? (c) Determine the profit function P and the marginal profit function. Compute P ′ (4),P ′ (5) and P ' (6). What can you deduce from your result?

The positive root of the quadratic equation x² - 5x = 14 is 7.

A quadratic equation in its standard form is expressed as;

ax² + bx + c = 0

Where x is the unknown

To solve for x, we use the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

Given the equation in the question.

x² - 5x = 14

Rearrange in standard form
x² - 5x - 14 = 0

Plug the values of a, b and c into the quadratic formula and solve for x.

x = (-b±√(b² - 4ac)) / (2a)

x = ( -(-5) ±√( (-5)² - ( 4 × 1 × -14) )) / (2 × 1)

x = ( 5 ±√( 25 - ( -56 ) )) / 2

x = ( 5 ±√( 25 + 56 )) / 2

x = ( 5 ±√( 81 )) / 2

x = ( 5 ± 9 )/2

x = ( 5 - 9 )/2, x = ( 5 + 9 )/2

x = (-4)/2, x = (14)/2

x = -2, x = 7

Therefore, the solutions are x = -2 and x = 7.

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However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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Answer:

–2x – 4?

Step-by-step explanation:

make sure its the one with the question mark. plus i got it right

1st. since we are adding whats in the ( ), ignore them. If we were multiplying or dividing it would not be that easy, but we arent. 2nd, add your like terms.... so (4-2x)+(3x-2) would become 4 - 2x + 3x - 2..... which by adding like terms we can simplify that by adding (-2x) + (3x) which gives us 1x or just x. then 4 - 2 is just 2... sooooo,.... x -2 is your answer.

Credit to: sma51664 for getting the right answer

Answer:

1true 2tre3false tenciu

Answer:

x = 4

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.