Consider the reflection of parallelogram pqrs across the line of reflection, line w y. if rr' = 14, then rz = . if sx = 5, then = 5.

The line integral in both cases is  52/3

Given,

a) The line integral; L = ∫c xy dx + x² y³ dy

 Where C is counterclockwise around the triangle with vertices (0, 0),

(1, 0)  and (1, 4)

Our first line integral is

L₁ = ₁∫₍₀, ₀₎ ⁽¹ ⁰⁾ xy dx + x² y³ dy

The equation of this line is y = 0,  x varies from 0 to 1.

L₁ = 0

Our second line integral is

L₂ = ₁∫₍₁, ₀₎ ⁽¹ ⁴⁾ xy dx + x² y³ dy

The equation of this line is x = 0  and y varies from 1 to 4.

L₂ = 64/3

The third line integral is

L₃ = ∫₁⁰ xy dx + x² y³ dy

The equation of this line is y = 4x  and x varies from 0 to 1.

L₃ = -4

The value of the line integral is

L = L₁ + L₂ + L₃ = 0 + 64/3 + (-4) = 52/3

b) The second part requires the use of Green's Theorem to evaluate:

This is given by:

∫c Pdx + Qdy = ∫ ∫ R Qy - Px dA

∫c xy dx + x² y³ dy = ∫ ∫R 3x² y² - ydA

We choose our region of integration parallel to the y-axis.

∫c xy dx + x² y³ dy

= ∫¹₀ ∫⁴ˣ₀ 3x² y² - y dy dx

= ∫¹₀ x² y³ - 1/4 |y²|²ˣ₀ dx

=  ∫¹₀ 64x⁵ - 4x² dx = 52/3

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The 'base angles' are the angles that involve the base of an isosceles triangle.

What is the vertex angle of a isosceles triangle?

Vertex angle: The 'vertex angle' is the angle formed by two equal sides of an isosceles triangle. ∠BAC is a vertex angle of the isosceles triangle. 4. Base angles: The 'base angles' are the angles that involve the base of an isosceles triangle.

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Answer:

c. ( 5, 3)

Step-by-step explanation:

y = 6x - 27

y = 4x - 17

6x - 27 = 4x - 17

2x = 10

x = 5

y = 4x - 17

y = 4(5) - 17

y = 3

x = 5; y = 3

Answer: c. ( 5, 3)

The probability of picking a red and blue marble is 12/49.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

From the information, the bag contains 3 red marbles and 4 blue marbles a marble is taken at random and is replaced. The probability of picking a red and blue marble will be:

=P(red) × P(blue)

= 3/7 × 4/7

= 12/49

The probability is 12/49.

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Complete question

A bag contains 3 red marbles and 4 blue marbles a marble is taken at random and is replaced. What is the probability of picking a red and blue marble?

The angles in a circle are called inscribed angles, which can be formed by passing the line through the center.

What is a Central Angle?

The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.

An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.

When two chords intersect on a circle, an inscribed angle is an angle that is created inside the circle. It can alternatively be described as the angle formed at a particular point on a circle by two specified points.

Hence,

The angles in a circle are called inscribed angles, which can be formed by passing the line through the center.

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Answer:

D 50 minutes

Step-by-step explanation:

If the customer is the fifth car in line then x = 5, so

f(5) = 7(5) + 15

f(5) = 35 +15

f(5) = 50

Answer:

The sale price of the jacket is £55.65

Step-by-step explanation:

Because when you need to know how much is the discount so we take:
£79.50 x ( 30 ÷ 100 ) = £23.85 ( We take 30 ÷ 100 because it is 30% which means [tex]\frac{30}{100}[/tex] )
Then you need to minus the 30% to find the sale price when it's discount:
£79.50 - £23.85 = £55.65

So the Answer is: £55.65

Please mark me brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

0.10x < 12 + 0.02x  and  x < 150 are the answers.

What is an inequalioty?

A relationship between two expressions or values that are not equal to each other is called ‘inequality’ .

Plan A: 0.10x

Plan B: 12 + 0.02x

It  depends on how many texts they receive each month. If they send or receive only 50 text messages a month, plan A will be the plan to go with. They will pay $5.00 for plan A and they would pay $13 for plan B. If they send or receive 1000 text messages a month, plan B will be the plan to go with. They will pay $100.00 for plan A and they would pay $32 for plan B.

0.10x = 12 + 0.02x

-11.90x = 0.02x

x = 150

For you to want plan A, the inequality would be x < 150 and for you to want plan B, the inequality would be x > 150. In other words, you must send or receive less than 150 text messages to want plan A and you must send or receive over 150 text messages for you to want plan B.

For sending x texts, the cost of Plan A in dollars is

0.10x

For sending x texts, the cost of Plan B in dollars is

12 + 0.02x    where 12 is the monthly charge regardless of texts sent

We want the Plan A charge to be less than the Plan B charge, so the inequality is ...

 0.10x < 12 + 0.02x

b. Subtract 0.02x both sides ,we obtain:

0.08x < 12

Divide by 0.08 both sides,we get

x < 12/0.08

x < 150  the solution to the inequality

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A cell phone company offers two texting plans. 0.10x < 12 + 0.02x  and  x < 150 are the answers.

A relationship between two expressions or values that are not equal to each other is called ‘inequality’ .

Plan A: 0.10x

Plan B: 12 + 0.02x

It depends on how many texts they receive each month. If they send or receive only 50 text messages a month, plan A will be the plan to go with. They will pay $5.00 for plan A and they would pay $13 for plan B. If they send or receive 1000 text messages a month, plan B will be the plan to go with. They will pay $100.00 for plan A and they would pay $32 for plan B.

0.10x = 12 + 0.02x

-11.90x = 0.02x

x = 150

For you to want plan A, the inequality would be x < 150 and for you to want plan B, the inequality would be x > 150. In other words, you must send or receive less than 150 text messages to want plan A and you must send or receive over 150 text messages for you to want plan B.

For sending x texts, the cost of Plan A in dollars is 0.10x

For sending x texts, the cost of Plan B in dollars is 12 + 0.02x    

where 12 is the monthly charge regardless of texts sent

We want the Plan A charge to be less than the Plan B charge, so the inequality is ...

0.10x < 12 + 0.02x

b. Subtract 0.02x both sides ,we obtain:

0.08x < 12

Divide by 0.08 both sides, we get

x < 12/0.08

x < 150  the solution to the inequality

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a) List the next two terms of the sequence as 28,36

b) [tex]A_{n} =A_{n-1} +n, A_{0} =0, n\geq 1[/tex]

c) [tex]P_{n} =P_{n-1} +n, P_{0} =0, n\geq 1[/tex]

consider the given sequence,

0,1,3,6,10,15,21,.........

= (0), (0+1), (1+2), (3+3), (6+4), (10+5),(15+6), (21+7), (28+8),......

therefore,

a) next two terms =28, 36

b)

[tex]A_{1} =0, A_{2}=1, A_{3} =3, A_{4} =6, A_{5} =10, A_{6} =15\\A_{n+1} = A_{n} +n, A_{1} =0, n\geq 1[/tex]

c)

[tex]P_{0} =0, P_{1} =1, P_{2} =3, P_{3} =6, P_{4} =10, P_{5} =15, P_{5} =21\\P_{n} =P_{n-1} +n, P_{0} =0, n\geq 1[/tex]

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The equation of line that is perpendicular to given line is (y-y1) = m(x - x1)

A perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes. Coordinates and line equation is the pre-requisite to finding out the perpendicular line.

Consider the equation of the line is ax + by + c = 0 and coordinates are (x1, y1), the slope m1 = − a/b.

If one line is perpendicular to this line, the product of slopes should be -1. Let m1 and m2 be the slopes of two lines, and if they are perpendicular to each other, then their product will be -1.

So , the slope of line will be given that is m1

To find out the slope of perpendicular line ,

m1 . m2 = -1

=> m2 = -1 / m1

=> m2 = -b/a is slope of perpendicular line

So, the equation of perpendicular line is :

(y - y1 ) = m2 (x - x1)

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Using trigonometric functions, the value of cos(z) in the given triangle is (C) 12/13.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Sine, Cosine, and Tangent are the three fundamental trigonometrical operations.

So, the value of cos(z) is:

The matching angles are congruent since the triangles are comparable. As a result, cos C = cos Z and m C = m∠Z.

Cosine has an adjacent/hypotenuse ratio.

Since the side with the number 12 is next to angle C and 13 is the hypotenuse of this triangle, cos C = 12/13.

Since C and Z will have the same angles and cosines, cos Z will also equal 12/13.

Therefore, the value of cos(z) in the given triangle is (C) 12/13.

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Correct question:
Given â–³abc ~ â–³xyz, what is the value of cos(z)?

a. five-thirteenths

b. five-twelfths

c. twelve-thirteenths

d. twelve-fifths

The money earned by Jutine in the month of September is $133.

According to the question,

We have the following information:

Jutine charges $6 an hour for mowing lawn and $11 for pulling weed. In September he mowed lawn for 13 hour and pulled weed for 5 hour.

Now, the amount earned by mowing the lawn can be found using multiplication:

6*13 = $78

Now, we have the amount earned by pulling weeds by using the same concept:

11*5 = $55

Now, the total money earned in September:

$(78+55)

$133

Hence, the money earned by Jutine in the month of September is $133.

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The required number of collection of coins of each kind are C(33 4).

Since there are no less than 30 coins of every sort of coin, there is plausible that we can pick each of the 30 of a similar kind.

So reiteration is permitted and request doesn't make any difference since every sort of coin is something very similar.

So we utilize the recipe C(k+n­1 k). There are four kinds of coin (k=4), and we pick 30 coins (n=30).

Then,

there are C(33 4) potential ways.

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According to the SSS test for triangle similarity, two triangles are considered similar if their third sides are proportionate to one another.

According to the statement, we have stated:

If two triangles ABC and DEF have the relationship

BC/EF = AC/DF = AB/DE, then

Triangle ABC therefore resembles triangle DEF.

This suggests that Angle A, Angle B, and Angle C are all equal to Angle D, Angle E, and Angle F.

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The dow jones industrial average is c) the index of 30 major stocks. the most representative of the stock market indexes.

The Dow Jones Industrial Average, in short DJIA, moreover known as the Dow 30, maybe a stock market index that tracks 30 huge, publicly-owned blue-chip companies exchanging on the New York Stock Exchange and Nasdaq. The Dow Jones is named after Charles Dow, who made the record in 1896 beside his trade accomplice Edward Jones. The DJIA was outlined to serve as an intermediary for the well-being of the broader U.S. economy. Often referred to basically as the Dow, the DJIA is one of the most-watched stock market lists in the world. Whereas the Dow incorporates a run of companies, all can be depicted as blue-chip companies with reliably steady profits.

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The dow jones industrial average is:

a) an equally weighted index of all stocks traded on the new york stock exchange.

b )an index of the 500 largest corporate stocks in america.

c) an index of 30 major stocks. the most representative of the stock market indexes.

2500 positive integers with 5 or less digits are even or divisible by 5 and do not contain any repeated digits

A number system is defined as a system of writing to express numbers.

The smallest 5 digit even integer is 10000. The largest is 99998.

The difference between these numbers is 89998. Half of these are even, or about 45000 numbers.

But, we want all of the digits to be even. So, the digits can only be 0, 2, 4, 6, or 8. 0 cannot be the first digit.

4×5×5×5×5=2500

Hence, 2500 positive integers with 5 or less digits are even or divisible by 5 and do not contain any repeated digits

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The number of stops that the runner would make is 9.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Since the runner runs 1 4/5 miles and stops every 1/5 mile. The number of stops will be:

= Total mile / Stop

= 1 4/5 ÷ 1/5

= 9/5 ÷ 1/5.

= 9/5 × 5/1

= 9

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It identifies possible future routes for advancement using interior-point approaches for linear programming.

The majority of interior-point techniques fall into one of three groups: affine-scaling techniques, potential reduction techniques, or central path techniques. Along with impractical interior approaches and homogeneous self-dual methods for linear programming, these techniques are examined. Some theoretical problems with interior-point techniques are also covered, such as the dependence of complexity bounds on non-standard metrics other than the problem's input length L. Finally, the study finishes with comments on how interior-point methods and the simplex approach compare in terms of how well they perform when tested against the NITLIB suite, a common set of test problems.

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The trigonometric function sin2x = -0.49

Given that,

cos(x) = -1/4              tan(x) < 0

x = cos⁻¹(-1/4)

x = 104.47

We will solve the trigonometric function as;

To find sin2x,

Let,

sin2x = sin 2 * 104.47

         = sin208.95

         = -0.484

         ≅ -0.49

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Answer:

B. -√15 / 4

Step-by-step explanation:

I can feel it in my nuggets

The slope of the parallel line is the same slope as this line the slope is 4.

Coplanar lines that do not intersect are said to be parallel. Parallel lines have the same slope in two dimensions.

The formula to determine whether any two lines with the equations y=m1x+c1 and y=m2x+c2 are parallel is m1=m2, where m1 and m2 are the slopes of the two lines.

The slope in the following form is the coefficient of the x when the y value is a unit value.

y = mx + c where m is the slope and c is the crossing on the y-axis.

From

8x - 2y = 5

8x = 5 + 2y = 8x

2y = 8x - 5

y = 4x - 2.5

So the slope is 4. It is irrelevant that it is parallel as only the c value will be different in a parallel line.

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Answer:

50%

Step-by-step explanation:

took the test and got it right

Answer:

Im sorry my post was removed, darn mods. it is 50%!

Step-by-step explanation:

I took the test a while ago and searched the same question, when i finished the quiz it said i was right! :)

The value of a/b is  [tex]\sqrt{6}[/tex] / 2

The area of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.

Measurement of agricultural fields, floor areas required for purchase/selling transactions. Measurement of volumes required for packaging milk, liquids, solid edible food items. Measurements of surface areas required for estimation of painting houses, buildings, etc.

According to the question:-

Side of an equilateral triangle equals a/3.

Therefore, the equilateral triangle's area is equal to (1/2)(a/3)2 sqrt (3) / 2 = a2 [sqrt (3)/ 36].

Hexagonal side equals b / 6.

The area is thus 6 (1/2) (b/6)^2 sqrt (3) / 2 

= b^2 [ 3 sqrt (3) / 72] = b^2 [sqrt (3) / 24]

So

sqrt (3) / 36 a2 = sqrt (3) / 24 b2

So

A2 / B2 = [Sqrt(3)/24] / [Sqrt(3)/36]

a^2 / b^2 = [ 36 / 24 ]

a^2/ b^2 = 3/2

A/ B = Sqrt(3) / Sqrt(2)

=Sqrt(6) / 2

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D and E are the only reasonable directions of causality in light of the variables. In A and B, the causality is not reasonable because the test scores would have been determined when study time was recorded.

In order to store and transmit data effectively, it must be organised and formatted properly. This is referred to as data representation. Data may be portrayed in a variety of forms, including text, statistics, graphics, audio, and video. In the subject of computer science, data representation is essential because it enables computers to process, store, and send information.The main application of data drives the choice of a specific data format. As an illustration, text data may be represented using ASCII or Unicode character sets, whereas numerical data can be represented using binary or decimal notation.This is a reasonable direction of causality, as students may focus more on subjects they prefer.

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There are 100, 4-digit positive integers that are divisible by 5 between  1000 and 9999.

A integer is divisible by 5 if it ends with 0 or 5. 35, 790, and 55, for instance, are also all divisible by 5.

We then multiply all the computed ways to fill in the corresponding spaces (4 x 5 x 5 x 1 = 100).

Therefore, there are 100 potential 4-digit positive integers.

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The counterexample is a rectangle with length 19.99 and width 0.01, in which case the area is 0.1999 and the perimeter is still 40.

Given ,

The perimeter of the rectangle is 40 units.

According to the statement, if the area is at least one unit and the perimeter is 40.

A counterexample to disprove this statement is the rectangle with dimensions of 19.99 units in length and 0.1 units in width, which has an area of 0.1999 square units and a perimeter of 40 units.

As a result, it is shown by a counterexample that an area does not necessarily need to be at least one unit when the perimeter is 40 units.

Any departure from a generalization constitutes a counterexample. A counterexample refutes the generalization in logic, and it does so persuasively in the disciplines of math and philosophy.

By using counterexamples to show that specific conjectures are false, mathematicians can avoid going down dead ends. They can then learn to modify hypotheses in order to arrive at testable theorems. It has been stated that the development of mathematics is greatly influenced by the discovery of theorems and counterexamples.

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Answer:

14.375

Step-by-step explanation:

2.5 * 4.5 = 11.25

(2.5 * 2.5) /2 = 3.125

3.125 + 11.25 = 14.375

x²/21 + y²/25 = 1 is the equation of the ellipse

Given: the length of the major axis = 10 and foci = (0, ± 2)

Since the foci are on the y-axis, the major axis will be along the y-axis. Thus, the equation of the ellipse is:

x²/b² + y²/a² = 1

Since the length of the major axis = 2a. Thus:

2a = 10

a = 10/2 = 5

a² = 5² = 25

c = 2

c² = a² - b²

2² = 5² - b²

4 = 25 - b²

b² = 25 - 4 = 21

Substitute a² = 25 and b² = 21 into the equation:

x²/b² + y²/a² = 1

x²/21 + y²/25 = 1

Therefore,  the equation of the ellipse is x²/21 + y²/25 = 1

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The least-square regression line between data fuel efficiency and speed is  In(Fuel Efficiency) = 1.437 + 0.541 In(Speed).  The fuel efficiency when the speed 60 mph is 38.55 mpg

Least square regression is a representation of data in a linear equation:

y = ax + b

where x, y are data variables.

The least-squares regression line is obtained by minimizing  the distance from  regression line to each data points.

In the given problem, the given least-squares regression line is:

In(Fuel Efficiency) = 1.437 + 0.541 In(Speed)

In this case,

y =  In(Fuel Efficiency)

x = ln(Speed)

Where ln is the natural logarithmic operator.

When speed = 60 mph, then,

In(Fuel Efficiency) = 1.437 + 0.541 In(60)

In(Fuel Efficiency) = 1.437 + 2.215

In(Fuel Efficiency) = 3.65

Fuel efficiency = e^(3.65) = 38.55

Hence, the fuel efficiency when the speed 60 mph is 38.55 mpg

Your question is incomplete, but most probably your question was:

Data were recorded for a car's fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, In(Fuel Efficiency) = 1.437 + 0.541 In(Speed), what is the fuel efficiency for a speed of 60 mph? 3.65 mpg 33.90 mpg 36.52 mpg 38.55 mpg

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(a) Heads will occur exactly twice.

a) The probability Heads will occur exactly twice is 1/2.

b) The probability Heads will occur at least twice is 5/8.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have,

Total coins = 7

Fair coins =6

One coin had head on both side.

Outcome of tossing a coin three times

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

a) The probability Heads will occur exactly twice

= 4/8

= 1/2

b) The probability Heads will occur at least twice

= 5/8

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The 7 types of numbers are:-

1) Natural Numbers.

2) Whole Numbers.

3) Integers.

4) Rational Numbers.

5) Irrational Numbers.

6) Real numbers.

7) Complex numbers.

A mathematical value used to indicate the amount is called a number. A number is a mathematical notion that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers.

1) Natural Numbers: Positive integers from 1 to infinity are known as natural numbers, often referred to as counting numbers. The collection of natural numbers is referred to as "N," and its members are N = 1, 2, 3, 4, 5,.

2) Whole Numbers: Whole numbers do not include any fractional or decimal portions and are known as non-negative integers. It is represented by the symbol "W," and the set of whole numbers contains W = 0–1, 2–3, 4–5,..........

3) Integers: An integer is any whole number, but it also contains a collection of negative natural numbers. The set of numbers represented by "Z" is Z = -3, -2, -1, 0, 1, 2, 3

4) Real Numbers: Real numbers are all positive and negative integers, fractional, and decimal values that do not contain imaginary numbers. The letter "R" stands for it.

Any number that can be expressed as a ratio of one number to another is referred to be a rational number. This implies that every integer that may be expressed as p/q. The rational number is represented by the letter "Q."

5) Irrational Numbers: The sign "P" stands for an irrational number, which is a number that cannot be described as a ratio of one over another.

6) Complex Numbers (C): A complex number is one that can be expressed as a+bi, where a and b are real numbers and I is an imaginary number.

7) Imaginary Numbers: The complex numbers that may be expressed as the product of a real number and a fictitious unit are known as imaginary numbers.

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