a) The parabolic path is 15/4.
b) The straight-line path is 5.
c) The polygonal path (0,0),(0,1),(5,1) is 5.
d) The cubic path x=5[tex]y^3[/tex] is 9.
We can evaluate the given line integral by parameterizing the path c and then using the line integral form
∫cydx + xydy = ∫t=a..b f(x(t), y(t)) × (dx/dt) dt + g(x(t), y(t)) × (dy/dt) dt
where (x(t), y(t)) is the parameterization of the path c, f(x,y) = y, and g(x,y) = x.
a) For the parabolic path x + 5[tex]y^2[/tex], we can parameterize the path as (x(t), y(t)) = (5[tex]t^2[/tex], t) for t from 0 to 1. Then we have:
∫cydx + xydy = ∫t=0..1 t×(10[tex]t^2[/tex])dt + 5[tex]t^2[/tex]) ×dt
= ∫t= 0..1 (10[tex]t^2[/tex] + 5[tex]t^2[/tex])dt
= [5[tex]t^2[/tex] + (10/4)[tex]t^4[/tex]] from 0 to 1
= 15/4
b) For the straight-line path from (0,0) to (5,1), we can parameterize the path as (x(t), y(t)) = (5t, t) for t from 0 to 1. Then we have:
∫cydx + xydy = ∫t=0..1 t×(5dt) + (5t)×dt
= ∫t=0..1 10t dt
= 5
c) For the polygonal path from (0,0) to (0,1) to (5,1), we can split the path into two line segments and use the line integral formula for each segment:
∫cydx + xydy = ∫0..1 f(x(t), y(t)) × (dx/dt) dt + g(x(t), y(t)) × (dy/dt) dt
+ ∫1..2 f(x(t), y(t)) × (dx/dt) dt + g(x(t), y(t)) × (dy/dt) dt
For the first segment from (0,0) to (0,1), we have (x(t), y(t)) = (0, t) for t from 0 to 1:
∫0..1cydx + xydy = ∫0..1 t0dt + 0t×dt = 0
For the second segment from (0,1) to (5,1), we have (x(t), y(t)) = (5t, 1) for t from 0 to 1:
∫1..2cydx + xydy = ∫0..1 1×(5dt) + 5t×0dt = 5
Therefore, the total line integral is:
∫cydx + xydy = 0 + 5 = 5
d) For the cubic path x = 5[tex]t^3[/tex] , we can parameterize the path as (x(t), y(t)) = (5[tex]t^3[/tex], t) for t from 0 to 1. Then we have:
∫cydx + xydy = ∫t=0..1 t × (15[tex]t^2[/tex] )dt + (5[tex]t^4[/tex]) × dt
= ∫t = 0..1(15[tex]t^3[/tex] + 5[tex]t^4[/tex] )dt
= [15/4[tex]t^4[/tex]+ (5/5)[tex]t^5[/tex]] from 0 to 1
= 15/4 + 1
= 19
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a) Along the parabolic path x=5y^2, we can write y as a function of x as y = (1/√5)√x. Then, dx = 10ydy and the integral becomes:
∫cydx + xydy = ∫0^1 5y^2(10ydy) + (5y^2)(ydy)
= ∫0^1 55y^3dy
= 55/4
b) Along the straight-line path, we can write y as a function of x as y = (1/5)x. Then, dx = 5dy and the integral becomes:
∫cydx + xydy = ∫0^5 (x/5)(5dy) + x(dy)
= ∫0^5 xdy
= 25/2
c) Along the polygonal path (0,0),(0,1),(5,1), we can break the integral into two parts: from (0,0) to (0,1) and from (0,1) to (5,1).
From (0,0) to (0,1), x = 0 and dx = 0, so the integral becomes:
∫cydx + xydy = ∫0^1 0dy
= 0
From (0,1) to (5,1), y = 1 and dy = 0, so the integral becomes:
∫cydx + xydy = ∫0^5 x(0)dx
= 0
Therefore, the total integral along the polygonal path is 0.
d) Along the cubic path x=5y^3, we can write y as a function of x as y = (1/∛5)√x. Then, dx = 15y^2dy and the integral becomes:
∫cydx + xydy = ∫0^1 5y^3(15y^2dy) + (5y^6)(ydy)
= ∫0^1 80y^6dy
= 80/7
Thus, the value of the integral depends on the path chosen. Along the parabolic path and the cubic path, the value of the integral is non-zero, while along the straight-line path and the polygonal path, the value of the integral is zero.
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Work out the Highest Common Factor of 375 and 150
Answer: 75
Step-by-step explanation:
Inusah is x years old now if his age in 11 years time will be 3 times his age 7 years ago, how old is he now
===============================================
Work Shown:
x = his age now
x+11 = his age 11 years into the future
x-7 = his age 7 years ago
The equation to set up is
x+11 = 3(x-7)
since his age 11 years into the future is triple that of his age 7 years ago.
-------
Let's solve for x.
x+11 = 3(x-7)
x+11 = 3x-21
x-3x = -21-11
-2x = -32
x = -32/(-2)
x = 16
He is currently 16 years old.
11 years from now he'll be 16+11 = 27, and 7 years ago he was 16-7 = 9.
Note that 9*3 = 27 to help confirm the answer.
Answer:
16
Step-by-step explanation:
3(x-7)=x+11
Plug into equation and find value of x
Find the missing value so that the line passing through the points has the given slope.
(x,9) and (1,6); m=1
Answer:
m = [F(y2) - F(y1) ] / [[F(x2) - F(x1)] slope of a line
[9 - 6] / [x - 1] = 1 that an increase in x equals the increase in y
Obviously, x must equal 4 so 3 / 3 = 1 or when x increases by 3, y must also increase by 3 for m to equal 1
12x-3.7+2x+13.3+4.1y simplified just give me the answer i dont really need an explanation. Thanks
The simplified expression is
14x + 9.6 + 4.1y
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
12x -3.7 + 2x + 13.3 + 4.1y
Combining the like terms.
(12x + 2x) - 3.7 + 13.3 + 4.1y
14x + 9.6 + 4.1y
Thus,
The final expression is 14x + 9.6 + 4.1y.
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The product (x+5)(x - 1)(x+2) is equal to:
OA³+61²-13x-10
OB. ³+6x² +13x+10
Ox³+6x²-3x - 10
D. x³ +6x² + 3x - 10
E. x² +6x-3x+10
The product (x+5)(x - 1)(x+2) is equal to x³ +6x² + 3x - 10 (C)
What is the product rule in math?According to the Product Rule, the derivative of a product of two functions is equal to the product of the first function times the second function's derivative plus the second function times the first function's derivative.
What are the product and sum rules?The sum rule explains how many different methods there are to choose between two distinct groups of options. The product rule explains how many different methods there are to choose from each of two sets of options. Both laws apply to bigger sets families in general.
In the given question:-
=(x+5)(x - 1)(x+2)
=(x+5)(x^2+x-2)
=x^3+6x^2+3x-10
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How do you change a number to base 12?
To convert a number to base 12, you can use the process of repeated division and remainder.
Converting Number To Base 12To convert a number to base 12, you can use the process of repeated division and remainder with these:
1. Divide the number by 12, and keep track of the remainder.
2. Replace the original number with the quotient from step 1.
3. Repeat steps 1 and 2 until the quotient is 0.
4. The remainders from each step form the digits of the base-12 representation of the original number, with the last remainder being the least significant digit.
For example, to convert the number 35 to base 12:
35 / 12 = 2 remainder 11
2 / 12 = 0 remainder 2
So the base-12 representation of 35 is "23".
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How many leap years will there be between 2001 and 3001
leap years
Answer:
2004, 2008, 2012, 2016, 2020, 2024, 2028,
Write an expression in simplest form to represent the area of the shaded region 3X 2 2X 3X 4X 
Answer:
6[tex]x^{2}[/tex] + 8x
Step-by-step explanation:
4x(3x + 2) = 12[tex]x^{2}[/tex] + 8x is the area of the big rectangle
2x(3x) = 6[tex]x^{2}[/tex] is the area of the small rectangle.
Subtract the small rectangle from the large rectangle to find the area of the shaded region
12[tex]x^{2}[/tex] + 8x - 6[tex]x^{2}[/tex]
6[tex]x^{2}[/tex] + 8x
To assist faculty and students with
research, a school librarian must be
which of the following?
Professional librarians should be accessible to pupils, according to administrators
What are the main leadership roles performed by a school librarian?Professional librarians should be accessible to pupils, according to administrators. Although librarians wear many hats, their three primary responsibilities are to promote literacy, manage resources, and specialize in research. By identifying and acquiring library items based on the curriculum and student interests, school librarians, who are information specialists, build a resource base for the school. Additionally, they keep the library collection organised and up-to-date to encourage individual reading and lifelong learning. They could teach you the fundamentals of literature or perhaps do it for you. They can offer you facts or data that they have gleaned from years of experience.
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Solve the system of inequalities by graphing.
y≥2
y<4
Select a line to change it between solid and dotted. Select a region to shade it.
The Graph to the y≥2 and y<4 is attached below.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
The Inequalities are:
y≥2
y<4
Now, if plot these inequalities in the graph we get
The y≥2 will have the shaded on the upper part where y= 2, 3, 4, and so on.
Now, y < 4 will have the shaded on the lower part of graph where y= 3, 2, 1, 0, -1, -2 and so on.
Now, The shaded region shown the common point between both inequality which is y= 2, 3 4.
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How do you graph a 3 dimensional coordinate system?
To graph a 3 dimensional coordinate system, you must first identify the three axis, often labeled x, y, and z.
What is coordinate system?A coordinate system is a system used to describe the position or location of a point in space. Coordinate systems are used in mathematics, physics, engineering, and other sciences to describe the position of objects, lines, or points in a given space. Coordinate systems are based on a set of axes, which are defined by a set of numbers, letters, or symbols. Common coordinate systems include Cartesian, polar, and cylindrical. In each system, the axes are used to describe the position of an object relative to the origin point. Coordinate systems are used to accurately describe the location of objects in space and can help to simplify many different mathematical operations.
Then, you will plot points along each of the three axis. For example, if the point is at (2,3,4), then you will plot the point two units away from the origin on the x-axis, three units away from the origin on the y-axis, and four units away from the origin on the z-axis. Once you have plotted all the points, you will connect them with lines to form a graph.
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Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of xx that support your conclusion -x=1
Answer: The equation -x = 1 has only one solution, x = -1.
This can be shown by solving the equation for x:
-x = 1
x = -1
To show that this equation has only one solution, we can plug in -1 for x and check that the equation is true:
-(-1) = 1
1 = 1
So x = -1 is the solution.
No other values of x would work here and make the equation true.
Step-by-step explanation:
What do 2 straight lines mean in math?
In mathematics, two straight lines can mean a number of things depending on the context. In general, a straight line is a geometric object that has no curvature and extends infinitely in both directions.
When two straight lines are considered together, they can either be parallel, meaning they will never intersect, or they can be intersecting, meaning they will cross at exactly one point. If the two lines are parallel, they will have the same slope, and if they are intersecting, the lines will have different slopes.
The slope-intercept equations for the two straight lines in analytical geometry are written as y = mx + b, where m is the slope, x and y are the coordinates of a point on the line, and b is the y-intercept.
In conclusion, two straight lines can have different meanings in mathematics depending on the context, such as parallel or intersecting, which can be represented by their equations in slope-intercept form.
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Is the mathematical basis for insurance?
Yes, mathematics plays a crucial role in the insurance industry. Actuarial science, which uses mathematical and statistical methods to assess and manage risk, is the foundation of the insurance industry.
Actuaries use mathematical models to calculate the likelihood of future events, such as accidents, illnesses, or natural disasters, and use this information to price insurance policies and estimate the company's potential losses.
The insurance industry also uses mathematical models to assess and manage the risk of potential losses, set prices for their products, and make investment decisions. For example, insurance companies use simulations to estimate the likelihood of different scenarios and the potential impact on their financials.
Additionally, underwriters use mathematical models to assess the risk of insuring a particular individual or business, they take into account factors such as the individual's age, health, and occupation when determining the price of the policy.
Insurance companies also use statistical models and Machine learning algorithms to detect patterns of suspicious behavior that could indicate fraud.
In summary, the mathematical basis for insurance is the use of mathematical and statistical models and techniques, such as probability and statistics, to assess and manage risk and make financial decisions in the insurance industry.
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A banker loaned $5000 to one cutomer and $8000 to another. If the annual interet on the econd loan i %2 higher than the firt and the combined annual interet i $810, What i the interet rate for each loan?
The interest rate for first loan is 5% and for the second loan is 7%.
The amount of first loan = $5000
Let the rate of interest for first loan = r
The interest from first loan = ($5000 × r)/100
= 50 r
The amount of second loan = $5000
Let the rate of interest for second loan = r+2
The interest from first loan = ($8000 × (r+2))/100
= 80 r + 160
Total interest = 50 r + 80 r + 160
= 130 r + 160
As per the question statement combined annual interest = $810
810 = 130 r + 160
r = (810-160)/130
r = 5%
Rate of second loan = r+2 = 5+2
= 7%
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Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).
YOU WILL GET BRAINLIEST IF SOLVED WITH EXPLANATION!
The area of the shaded region would be 4π - 8 square units.
What is the area of a circle?
The area of a circle is given by the formula: A = πr^2, where A is the area, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. The radius is the distance from the center of the circle to its edge.
In the given figure we have to find the height of the triangle and that will be the radius of the triangle.
In the triangle LMO,
Angle opposite to 45 = 1/√2* hypotenuse
MO = 1/√2 * 4
MO =2√2
Radius of the circle= 2√2
Area of the triangle = 1/2* MO * LN
= 1/2 * 2√2*4√2
= 8
Area of semi-circle =1/2 * πr²
=1/2 * π(2√2)²
= 4π
Area of shaded region = 4π - 8
Hence, the area of the shaded region would be 4π - 8 square units.
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the length of a rectangle is 3in longer than its width. if the perimeter of the rectangle is 66in, find its length and width
Answer:
Length = 18inch
Width = 15inch
Step-by-step explanation:
(Process/Explanation Below)
⇒ 66 ÷ 2 = 33 (We divide by 2 because we need to find two measurements which are our length and width)
⇒ 33 - 3 = 30 (Since the width is 3inches smaller than the length we have to subtract by 3.)
⇒ 30 ÷ 2 = 15in width (This is our width because since a rectange has 2 sides we have to divide by 2.)
⇒ 5 + 3 = 18in length (This is our length because it says the length is 3inches longer than the width and the width is 15inches.)
can someone help mr solve this i dont understand it
Answer: THE ANSWER IS 12
Step-by-step explanation:
HOPE IT HELPS =D
You are standing 50 meters from a hot air balloon that is preparing to take off. The angle of evolution to the top of the balloon is 28. Find the height of the balloon.
Therefore ,As a result, the answer to the above equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).
Equation : what is it?An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.
Here,
At time zero, Kadeesha stepped outside and drove 3 minutes at a speed of 1 block per minute to the store.
after traveling six blocks at her normal speed of three blocks per minute
She spent 5 minutes stopping at the bank as a result. She then sped home at a rate of three blocks per minute.
She therefore begins at (19,8), travels 8 blocks back in 2 minutes, and ends at (21,0).
Therefore ,As a result, the answer to the above equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).
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On solving the provided question, we can say that by trigonometry angle of evolution = x = [tex]tan^{-1}(1.2)[/tex]
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
by trigonometry
B = 50m
P = 28m
Tan(x) = 50/281.7857142857 = 1.2
angle of evolution = x = [tex]tan^{-1}(1.2)[/tex]
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I need help with this question
Answer:
-16
Step-by-step explanation:
-3a+4b=15 and 5a-6b=12 please
Using the substitution method we will see that the solution is:
a = 69
b = 55.5
How to solve the system of equations?Here we want to solve the system of equations below:
-3a + 4b = 15
5a - 6b = 12
We can isolate one of the variables in one of the equations, I will isolate b on the first one.
4b = 15 + 3a
b = (15 + 3a)/4
Now we can replace this on the other equation:
5a - 6*(15 + 3a)/4 = 12
Now we can solve that equation for a.
5a - (6/4)*15 - (6/4)*3a = 12
5a - (3/2)*15 - (9/2)*a = 12
(1/2)*a = 12 + (3/2)*15
a = 2*(12 + (3/2)*15)
a = 24 + 45
a = 69
And the value of b is:
b = (15 + 3a)/4
b = (15 + 3*69)/4 = 55.5
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A relation is plotted as a linear function on the coordinate plane starting at point E at(0, 27)and ending at point F at (5, −8).
What is the rate of change for the linear function and what is its initial value?
Select from the drop-down menus to correctly complete the statements.
The rate of change for a linear function, also known as the slope, can be found by calculating the change in the y-coordinate (rise) divided by the change in the x-coordinate (run) between two points on the line. The slope of a line describes how steep the line is and whether it is increasing or decreasing.
In this case, the slope of the linear function can be found by using the coordinates of points E and F:
Slope = (y2 - y1) / (x2 - x1)
Slope = (-8 - 27) / (5 - 0)
Slope = -35/5
The slope of the linear function is -35/5 or -7.
The initial value of a linear function is the y-intercept, which is the point where the line crosses the y-axis. To find the y-intercept, we can use the slope and one point on the line (in this case point E (0,27)):
y = mx + b
27 = -7(0) + b
b = 27
The y-intercept of the linear function is 27.
So, the linear function starts at point E (0,27) with an initial value of 27, and has a rate of change or slope of -7.
• A cylindrical potato chip container has a diameter of 3.5 inches and a height of 12 inches. What is the volume of thi
chip container? Use 3.14 for pi. Round your answer to the nearest hundredth. (4 points)
57.73 in3
115.40 in3
• 350.65 in3
461.81 in3
Accordingly, the cylinder's volume would be 115.45 cubic inches given its parameters.
Calculate the cylinder's volume?By multiplying the base area and height of a cylinder, one may get its volume. The radius of the circular base equals half its diameter, and the area of the base is equal to the area of a circle, which is denoted by the formula A = r2. As a result, a cylinder's volume equals:
Cylinder volume equals (r2)
h = 12 inches, where r = D/2 = 3.5 inches, 2 inches, and 1 inch.
Cylinder volume equals (1.75")2. ( 12 in )
147/4 in3 or 115.45353 in3 is the volume of the cylinder.
Accordingly, the cylinder's volume would be 115.45 cubic inches given its parameters.
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Someone please help rn I’ll mark brainliest !!
The length of the side BD is; 8
The measure of the angle DAB is; ∠DAB = 53°
How to interpret Congruent Triangles?Two triangles are said to be congruent by any of the following postulates;
1) SSS (Side Side Side) Congruence Postulate.
2) SAS (Side Angle Side) Congruence Postulate.
3) ASA (Angle Side Angle) Congruence Postulate.
4) AAS (Angle Angle Side) Congruence Postulate.
5) HL (Hypotenuse Leg) Congruence Postulate
Now, for the given triangles that are congruent, we can say that;
∠ADC ≅ ∠ACB
∠DAB ≅ ∠CAB
BD ≅ BC
AC ≅ AD
Thus;
BD = 8
∠DAB 53°
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How do you find the area of a 60 30 90 triangle?
The area of a 60°-30°-90° triangle can be found by using the formula A = (1/2) × b × h.
In this triangle, b is the length of the side opposite the 60° angle, and h is the length of the side opposite the 30° angle. For example, if the side opposite the 60° angle has a length of 8 and the side opposite the 30° angle has a length of 7, the area of the triangle can be calculated as A = (1/2) × 8 × 7 = 28. Therefore, the area of the triangle is 28 units squared.
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How do you reflect a line over Y =- 2?
To reflect a line over the line y = -2, we can first graph the line and then apply a transformation. A reflection in the y = -2 line can be thought of as a reflection in the x-axis, followed by a translation 2 units upward.
The transformation for a reflection over the line y = -2 is given by (x, y) → (x, -y - 4). To reflect a point (x, y) over the line y = -2, we substitute the coordinates of the point into the transformation and solve for the reflected point.
For example, to reflect the point (3, 4) over the line y = -2, we would substitute the coordinates into the transformation to get (3, -4 - 4) = (3, -8).
To reflect a line, we can reflect each point of the line over the line y=-2 and plot the reflected points.
In conclusion reflecting a line over y=-2 is done by applying a transformation (x, y) -> (x, -y - 4) to each point of the line, this can also be thought of as reflecting the line over x-axis and then translating 2 units upward.
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Write the relation as a set of ordered pairs. On a coordinate plane, points are at ( -2, 1), (0, -1), (2, -3).
a. ordered pairs: {(1, -2), (0, –1), (–3, 2)}
b. ordered pairs: {(1, –2), (–1, 0), (–3, 2)}
c. ordered pairs: {(–2, 1), (–1, 0), (2, –3)}
d. ordered pairs: {(–2, 1), (0, –1), (2, –3)}
The right answer is option c, which displays the relation as a set of ordered pairs in the coordinate plane, with points at (-2, 1), (0, -1), and (2, 3). (2, -3).
what is coordinates ?When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.
given
We have the ordered pair provided by the pair that complies with a set of requirements given that the points are on a coordinate plane.
The most appropriate set of coordinates that make up an ordered pair in the question are (-2, -1), (0, 1), and (2, 3).
The points are colinear because the slope between (-2, -1) and (0, 1) is the same as the slope between (-2, -1) and (y), and each x-coordinate term is less than the y-coordinate term by 1. (2, 3).
The right answer is option c, which displays the relation as a set of ordered pairs in the coordinate plane, with points at (-2, 1), (0, -1), and (2, 3). (2, -3).
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Lines a and b are parallel. What is the measure of angle m? Enter your answer in the box. m=
Answer:
m=55
Step-by-step explanation:
Since one line equals 180 degrees, 180-125=55
Find the SP
Radio : cp =2,720, profit = 5 % sp
Cost is equal to Selling price plus Loss ( when selling price and loss is given )Therefore, the cost price (C.P.) is 350.
Find the C.P ?Cost is the same as the selling price plus the loss ( when selling price and loss is given ).
The Profit and Loss Percentage Formula
Profitability (P%) is calculated as (Profit /Cost Price) / 100.
Loss percentage (L%) Equals 100 divided by (Loss / Cost price).
S.P. = {(100 + P%)/100}
if SP > CP, then CP
If SP > CP, S.P. = (100 - L%)/100 CP
C.P. = {100/(100 + P%)}
if SP > CP, then SP
C.P. = SP (if SP > CP)/100/(100 - L%)
Loss percent = 10%
To find:
The C.P.
Solution:
Let x be the C.P.
We have,
S.P. = 315
Loss percent = 10%
S.P = C.P - 10% 0f C.P
315 = X- 0.1X
315 = 0.9 X
Divide both sides by 0.9.
315/0.9 =X
350 = x
Therefore, the cost price (C.P.) is 350.
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What are the 4 properties of solution?
The 4 properties of solutions are:
1) Consistency
2) Validity
3) Feasibility
4) Stability
PROPERTIES OF SOLUTIONSIn mathematics, a solution to an equation or system of equations is a set of values that can be substituted into the equation(s) to make the statement(s) true. The four properties of a solution are:
1) Consistency: A solution exists and is unique, or multiple solutions exist.
2) Validity: The solution(s) must satisfy the equation(s) and any constraints or boundary conditions.
3) Feasibility: The solution(s) must be within the domain of the equation(s) and any constraints or boundary conditions.
4) Stability: The solution(s) should be insensitive to small changes in the equation(s) or initial conditions.
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