The rational numbers are closed under addition. The answer is True.
What is a rational number?Any number that can be represented as the ratio of two integers and where the denominator is not zero is referred to as rational.
Consider two rational numbers a/b and c/d.
The addition of the two numbers is:
a/b + c/d
= (ad + bc)/bd
Now, (ad +bc) and bd are again an integer, therefore, let p = (ad +bc) and q = bd, then
(ad + bc)/bd
= p/q, Which is again a rational number.
Hence, the rational numbers are closed under addition. The answer is True.
Learn more about rational numbers:
https://brainly.com/question/24398433
#SPJ1
the dow jones industrial average is: an equally weighted index of all stocks traded on the new york stock exchange. an index of the 500 largest corporate stocks in america. an index of 30 major stocks. the most representative of the stock market indexes.
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.
To know more about Dow Jones Industrial Average refer to the link brainly.com/question/28775371
#SPJ4
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.
Un corredor corrió una distancia de 1 ⅘ millas.
Si este corredor se paraba cada 1/5 millas.
cuántas paradas este corredor hizo ?
The number of stops that the runner would make is 9.
What is a fraction?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
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
how many different collections of 30 coins can be chosen if there are at least 30 of each kind of coin?
The required number of collection of coins of each kind are C(33 4).
How to get the number of collection of 30 coins?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.
According to given information: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.
To know more about Permutation visit:
brainly.com/question/1216161
#SPJ4
a wire is cut into two pieces, one of length and the other of length . the piece of length is bent to form an equilateral triangle, and the piece of length is bent to form a regular hexagon. the triangle and the hexagon have equal area. what is ?
The value of a/b is [tex]\sqrt{6}[/tex] / 2
What is called mensuration?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.
What is mensuration in real life?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
To know more about about mensuration follow the link:-
https://brainly.com/question/19241268
#SPJ4
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, , what is the fuel efficiency for a speed of 60 mph? 3.65 mpg 33.90 mpg 36.52 mpg 38.55 mpg
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
Learn more about regression here:
https://brainly.com/question/25987747
#SPJ4
Give three logically possible directions of causality, saying for each whether it is a reasonable direction in light of the variables involved. Select all that apply. A. It could be that higher test scores cause longer study times. This is not a reasonable direction of causality, as the tests would have been graded after study time. B. It could be that longer study times cause higher test scores. This is not a reasonable direction of causality, as many students do not study without scores to motivate them. C. It could be that both study time and grades influence course subject. This is not a reasonable direction of causality, as the test is about the subject material. D. It could be that course subject influences both study time and grades. This is a reasonable direction of causality, as students may focus more on subjects they prefer. E. It could be that higher test scores cause longer study times. This is a reasonable direction of causality, as higher test scores motivate students to study more. OF. It could be that longer study times cause higher test scores. This is a reasonable direction of causality, as students that study more likely retain more knowledge
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.
What is meant by data representation?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.
To learn more about data representation, visit:
https://brainly.com/question/28901244
#SPJ4
Jutine tarted her own landcaping buine. She charge $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. How much money did he earn in September?
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.
To know more about money earned here
https://brainly.com/question/11555549
#SPJ4
Evaluate the line integral by the two following methods.
Image for Evaluate the line integral by the two following methods. Integrate xy dx + x2y3 dy C is counterclockwise aroun
xy dx + x2y3 dy
C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 4)
(a) directly
(b) using Green's Theorem
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
Learn more about integrals here;
https://brainly.com/question/12961041
#SPJ4
interior point methods the affine scaling algorithm convergence of affine scaling the potential reduction algorithm the primal path following algorithm the primal-dual path following algorithm an overview exercises notes and sources
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.
Learn more about the interior points here:
https://brainly.com/question/28598514
#SPJ4
Given â–³abc ~ â–³xyz, what is the value of cos(z)? five-thirteenths five-twelfths twelve-thirteenths twelve-fifths
Using trigonometric functions, the value of cos(z) in the given triangle is (C) 12/13.
What are trigonometric functions?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.
Know more about the trigonometric functions here:
https://brainly.com/question/1143565
#SPJ4
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
What is the measure of the vertex angle of an isosceles triangle?.
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.
learn more about of triangle here
https://brainly.com/question/2773823
#SPJ4
a cook has 10 red peppers and 5 green peppers. if the cook selects 6 peppers at random, what is the probability that he selects at least 4 green peppers? express your answer as a common fraction.
The probability that he selects at least 4 green peppers is 0.0024
A cook has 10 red peppers and 5 green peppers
If the cook selects 6 peppers at random, what is the probability that he selects at least 4 green peppers
Event of getting green peppers be X
We need to find the probability that he selects at least 4 green peppers. This can be when the cook selects either 4 green peppers or 5 green peppers.
This can be found by binomial probabilty distribution.
P(X ≥ 4) = P(X = 4) + P(X = 5)
6C4(5/15)⁴(10/15)¹¹ + 6C5(5/15)⁵(10/15)¹⁰
15 x (1/3) ⁴ x (2/3) ¹¹ + 6 (1/3⁵) (2/3)¹⁰
= 0.002 + 0.0004
= 0.0024
Therefore, the probability that the cook selects at least 4 green peppers out 6 peppers he picked from 10 pred peppers and 5 green peppers is is 0.0024
To learn more about probability refer here
https://brainly.com/question/24756209
#SPJ4
What are angles in a circle called?.
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.
To learn more about the central angle, visit:
brainly.com/question/23636799
#SPJ4
1. what is the equation of the ellipse whose center is at the origin, foci at (2,0) and (-2,0), and the length of the major axis is 10 units?
x²/21 + y²/25 = 1 is the equation of the ellipse
How to find the equation of an 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
Learn more about equation of ellipse on:
https://brainly.com/question/16904744
#SPJ1
A jacket normally costs £79.50.
In a sale there is 30% off the normal price.
What is the sale price of the jacket?
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
a 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 is 12/49.
What is probability?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.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
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 function f(x) = 7x + 15 models the time in minutes that a customer will wait to get an oil change if there are x cars in line.
How long will a customer wait if they are the fifth car in the line?
A) 28 minutes
B) 35 minutes
C 43 minutes
D) 50 minutes
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
how many 4-digit positive integers (that is, integers between 1000 and 9999, inclusive) having only even digits are divisible by 5?
There are 100, 4-digit positive integers that are divisible by 5 between 1000 and 9999.
Define the term divisibility by 5?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.
There are [0, 2, 4, 6, and 8] things in all.Only one digit should be present because it is the only one that makes the integer divisible by five.There still are 1 methods for filling a position, making a total of 1.A location can be filled in five different ways, hence there are five different methods to fill it.Since all of the numbers in the specified sets can be used to fill the hundreds position, all integers can be used there.There are five different approaches to fill this hundreds place as a result.A set number of even numbers can be used to fill thousands of spots with four different numbers.The very next step is to apply the idea of factorial to determine how many even integers that really are divisible by five may be combined to create a 4-digit number.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.
To know more about the divisibility by 5, here
https://brainly.com/question/169628
#SPJ4
How do you prove SSS similarity theorem?.
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.
Learn more about triangle here
https://brainly.com/question/2773823
#SPJ4
Some cats have bobtails, which are short, stumpy tails that result from an inherited, recessive genotype (tt). Normal length tails are dominant in cats (TT, Tt). When a cat with a bobtail is crossed with a cat that is heterozygous for normal tail length, what is the likelihood that the offspring will have a bobtail?
75%
50%
25%
0%
I will give brainliest
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! :)
Solve the system of equations. y = 6x - 27 y = 4x - 17 a. ( -5, 3) c. ( 5, 3) b. ( -3, -5) d. no solution
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)
Consider the following sequence. 0, 1, 3, 6, 10, 15, 21,...
(a) List the next two terms of the sequence.
(b) Assuming the sequence is denoted by A 1, A 2, A 3 ,..., give an explicit formula for AN.
(c) Assuming the sequence is denoted by P0, P1, P2,..., give an explicit formula for PN.
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]
To learn more about the sequence click here
https://brainly.com/question/12246947
#SPJ4
What is a counterexample for the conjecture? if the perimeter of a rectangle is 40 units, the area must be at least 1 square unit.
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.
Learn more about Counterexample visit:
brainly.com/question/24881803
#SPJ4
Please explain why the first option is correct.
Answer:
The ratio (center to focus)/(semi-major axis) is the greatest
Step-by-step explanation:
Given various foci coordinates and major axis lengths, you are asked to identify the ellipse with the highest eccentricity.
Ellipse EccentricityThe eccentricity of an ellipse can be defined as the ratio of distance between foci to the length of the major axis. A high value of eccentricity corresponds to a longer, narrower ellipse.
The attached graph plots the locations of the given foci. They are color coded to correspond with the color of the resulting ellipse. (We have used the given r-value as the semi-major axis, not the major axis.)
The blue focal points (A, A') of the blue ellipse give the "flattest" of the bunch, so corresponds to the highest eccentricity. Its parameters are those of the first answer choice.
ValuesIf we assume the given r-value is the semi-major axis, the eccentricity represented by each of the answer choices is ...
(15√2)/22 ≈ 0.964 . . . . highest(10√2)/20 ≈ 0.707(5√13)/22 ≈ 0.819(5√2)/12 ≈ 0.589The numerator in each case is the distance from the center (0, 0) to one focus.
find the area of the shaded region in the kite below.
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
How many positive integers with 5 or less digits are even or divisible by 5 and do not contain any repeated digits? leading 0’s are also not allowed.
2500 positive integers with 5 or less digits are even or divisible by 5 and do not contain any repeated digits
What is Number system?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
To learn more on Number system click:
brainly.com/question/22046046
#SPJ1
How do you determine the equation of the line that is perpendicular to the given line?.
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)
To know more about Perpendicular line here
https://brainly.com/question/18271653
#SPJ4
When the distance is half the gravitational force is?.
The gravitational force increases four times when the space between the items is cut in half.
What exactly does gravity mean?
Any two things with mass are drawn together by the gravitational force. Because it consistently attempts to pull masses together rather than pushing them apart, the gravitational force is known as attractive. In actuality, every thing in the cosmos, including you, is pulling on every other object.Who made the discovery of gravity?
It is said that after observing an apple fall and wondering why it fell straight down rather than sideways or even upward, Isaac Newton developed the theory of gravitation in 1665 or 1666.
Learn more about gravitational force
brainly.com/question/12528243
#SPJ4
Question 14 (5 points)
Solvex² - 2x=15 by applying the quadratic formula.
Ox= 1 + √14i, x = 1 - √√14i
Ox = -5, x = 3
Ox = 5, x = -3
Ox= -1 + √14i, x = -1 - √√14i
The required solution of the given expression is given as x = 5 and x = -3.
Given that,
To solve x² - 2x=15,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
x² - 2x - 15 = 0
x² -5x + 3x - 15 = 0
x (x - 5) + 3 (x - 5) = 0
(x + 3)(x - 5) = 0
So,
x = -3 and x = 5
Thus, the required solution of the given expression is given as x = 5 and x = -3.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ1
A bag contains 7 coins, of which 6 are fair; the remaining coin has a head on both sides. If a coin is selected at random from the bag and tossed three times, what is the probability of each of the following outcomes? (Enter your probabilities as fractions.)
(a) Heads will occur exactly twice.
(b) Heads will occur at least twice.
(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.
What is Probability?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
Learn more about Probability here:
https://brainly.com/question/30034780
#SPJ2
