The equivalence class of a is [a] = {x ∈ A: (a, x) ∈ R}. This includes all elements of A that are related to 'a'.
An equivalence class is the name we give to the subset S that includes all elements that are equivalent to each other. If there is an equivalence relation between any two elements, they are called equivalent.
Equivalence class properties : The relation ~ is an equivalence relation if and only if:
It is reflexive: any a∈ X , a ~ aIt is symmetric: Let a, b ∈ X . if a ~b ⇔ b ~ a.It is transitive: Let a, b, c ∈ X ; if a ~ b and b ~ c, it follows that a ~ c.When our relation ~ satisfies the above three properties, we can write the definition of an element equivalence class as follows [a] = { x ∈ X | and ~ x}. Consider an example, If X were the set of all polygons and the equivalence relation ~ was defined as "having the same number of sides", the set of all triangles, the set of all quadrilaterals, the set of all pentagons, etc., are represents the equivalence classes.
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Complete question:
What is equivalence class ?
How do you find the domain and range of a square root of a quadratic function?.
Domain and range of a square root of a quadratic function is as [ 0, ∞ ) , and [ 0 ,∞ ) respectively which is find by simplification.
Let us consider a square root quadratic function y = √x.
Domain of a square root quadratic function is :
All input values of x are domain of a function.
y = √x
⇒ x = y²
⇒ x ≥ 0
All the input values representing the domain are x > 0.
This implies domain is [0 , ∞ ).
And range of a square root quadratic function is:
All output values of y are range of a function.
y = √x
As we know x = y²
√y² = y > 0 .
Range is [ 0, ∞ ).
Therefore, domain and range of square root of a quadratic function is calculated by simplifying the function.
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Find the angle e between vectors u and v to the nearest tenth of a degree
u = <5, 2> and v = <4, -3>
The angle e between vectors u and v to the nearest tenth of a degree is
≈ 3.14°.
What is an angle?An angle in plane geometry is a shape created by two rays or lines that have a shared termination. The name "angle" originates from the Latin word "angulus," which means "corner. "The common terminus of two rays is known as the vertex, and the two rays are known as sides of an angle.
According to the given information:When u and v's two vectors are at an angle, if, then cosθ = (u·v) / [llull llvll]
u·v = (5)(4) + (2)(-3)
= 20 - 6
= 14
llull = √[(5)2 + (2)2]
= √29
llvll = √[(4)2+(-3)2]
= √25
So, cosθ = 14 / [√725]
= 0.51
θ = cosθ-(0.51) ≈ 3.14°
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What number would you multiply the second equation by in order to eliminate the x term when adding to the first equation?.
For the given system of equations 4x – 9y = 7 , –2x + 3y = 4 answer of the following question are:
a. To eliminate x-terms we need to multiply 2 to the second equation and add it to the first equation.
b. To eliminate y-terms we need to multiply 3 to the second equation and add it to the first equation.
As given in the question,
For the given system of equation,
4x – 9y = 7 ___(1)
–2x + 3y = 4 ___(2)
a. To eliminate x-terms multiply by 2 to the (2) equation and add it to (1)
4x – 9y = 7
–4x + 6y = 8
-3y = 15
⇒ y = -5
b. To eliminate y-terms multiply by 3 to the (2) equation and add it to (1):
4x – 9y = 7
–6x + 9y = 12
-2x = 19
⇒x = -19/2
Therefore, for the given system of equations 4x – 9y = 7 , –2x + 3y = 4 :
a. To eliminate x-terms we need to multiply 2 to the second equation and add it to the first equation.
b. To eliminate y-terms we need to multiply 3 to the second equation and add it to the first equation.
The above question is incomplete , the complete question is:
Use this system of equations to answer the questions that follow.
4x – 9y = 7 , –2x + 3y = 4
a. What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?
b. What number would you multiply the second equation by in order to eliminate the y-terms when adding to the first equation?
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If Jenna Owen 15% of the stock in a business that has 50,000 shares, how many shares does she own?
Answer:
7500
Step-by-step explanation:
15/100×50000
750000/100
=7500
Write the prime factorization of 21. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
The prime factorization of the number 21 is:
21 = 3*7
How to write the prime factorization?We want to write the prime factorization of 21.
To do so, we just need to divide the number by prime numbers.
The first prime number we can try is 2, if we divide by 2 we get:
21/2 = 10.5
This is not an integer, so 2 is not a factor.
The next one is 3:
21/3 = 7
Now we can rewrite:
21 = 3*7
Where 3 and 7 are prime numbers, so that is the prime factorization.
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Find AC
A. 36
B. 60
C. 48
D. 12
Answer:
48
Step-by-step explanation:
AB+CB=AC which is 18+30 which is 48
Answer:
C. 48
Step-by-step explanation:
This distance of AC is the same as the distance between BC plus the distance between AB. In other words: AB + BC = AC
AB = 18
BC = 30
30 + 18 = AC
AC = 48
please i need help. what is the answer???
ok
0 is the smallest value or X is the smallest value
the number of nickels exceeds the number of dimes by 7. the total value of the coins is $1.55. How many coins of each type are there?
Answer:
15 nickels and 8 dimes
Step-by-step explanation:
Let N = number of nickels and D = number of dimes
N - D = 7 (the number of nickels exceeds the number of dimes by 7.)
or
N = D + 7
Total value of N nickels = 5N
Total value of D nickels = 10D
Combined total value => 5N + 10D = 155
Substitute for N in terms of D
==> 5(D + 7) + 10D = 155
5D + 35 + 10D = 155
15D + 35 = 155
15D = 155 - 35
15D = 120
D = 120/15
D = 8
N = D + 7 = 8 + 7 = 15
15 nickels and 8 dimes
Which is the shortest side of the triangle?
What is the line y =- 7?.
A horizontal straight line at the -7 point.
A straight line can be formed between two points also but both ends extend to infinity.
A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point.
A straight line does not have any curve in it. It can be horizontal, vertical, or slanted. If we draw an angle between any two points on a straight line, we will always get a 180-degree.
With no other values other than -7, the only value possible must be -7. Thus, we get a straight line.
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How do you plot a point?.
An x-y (or bivariate) plot is any graph or plot with two axes. The "x-axis" is typically the horizontal axis, whereas the "y-axis" is typically the vertical axis.
Your plot's axes should be identified, and the scale should be chosen (if the graph is not already labeled). Plot the first two pairs of numbers first (the top row of numbers).
Finding the number a on the horizontal, or x-, axis and tracing up or down from there while maintaining a parallel path to the vertical, or y-, axis, will allow you to draw the point at (a, b) on the Cartesian plane.
The position of the point is this area (a, b). The intersection of the two axes defines the plane's center. It is referred to as the beginning or point (0,0).
Each axis is further subdivided into equal units starting at the origin: rising, positive numbers on the x-axis and up the y-axis; falling, negative numbers on the x-axis and down the y-axis.
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Can someone please help me with this math problem? I can't use letters, the square box where I type doesn't allow it. Only numbers and infinity symbols, etc...
The math problem is in the picture, Thanks!
Answer:
Step-by-step explanation:
-4,+ infinity symbol which I can’t find
A political adviser stood at the corner of 1st Avenue and Main Street and asked every 10th person who walked past if they intended to vote in the next election. Identify the sampling method used.
How do you solve linear and nonlinear systems?.
To see the steps of linear and non linear system of equation.
Now, According to the question:
Steps to solve non linear equation are:
Identify the graph of each equation. Sketch the possible options for intersection.Graph the first equation.Graph the second equation on the same rectangular coordinate system.Determine whether the graphs intersect.Identify the points of intersection.Check that each ordered pair is a solution to both original equations.To solve a system of linear equations using substitution:
Isolate one of the two variables in one of the equations.Substitute the expression that is equal to the isolated variable from Step 1 into the other equation. This should result in a linear equation with only one variable.Solve the linear equation for the remaining variable.Use the solution of Step 3 to calculate the value of the other variable in the system by using one of the original equations.Learn more about Linear and non linear Equation at:
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Margo can purchase tile at a store for $0.59 per tile and rent a tile saw for $18. At another store she can borrow the tile saw for free if she buys tiles there for $1.19 per tile. How many tiles must she buy for the cost to be the same at both stores?
Answer:
30 tiles
Step-by-step explanation:
We know
First store
$0.59 per tile
Rent a tile saw for $18
Second store
1 tile = $1.19
We have the equation
0.59x + 18 = 1.19x
18 = 0.6x
x = 30 tiles
So, she must buy 30 tiles for the same cost at both stores.
Answer:
Margo must purchase 30 tiles for the cost to be the same at both stores.
Step-by-step explanation:
By analyzing the "real-world" problem, we can convert the words into two algebraic equations.
Step 1:Store 1:
"$0.59 per tile and rent a tile saw for $18."
y = 0.59x + 18
y = the price of the tiles bought
0.59 = price of one tile
x = number of tiles
18 = the fixed cost of a saw
Store 2:
"At another store, she can borrow the tile saw for free if she buys tiles there for $1.19 per tile."
In this case, the saw is free. Thus, we don't need to add a price to the equation.
y = 1.19x
y = the price of the tiles bought
1.19 = price of one tile
x = number of tiles
Step 2:Now that we have both equations, we can write down the equations that equate other. This formula will indicate that the equations would intersect at a certain point on the x and y values. Hence, this step will answer how many tiles are required for both stores to equal the same price.
[tex]0.59x+18=1.19x[/tex]
Now solve for x:
[tex]0.59x-0.59x+18=1.19x-0.59x\\\\18=0.6x\\\\\frac{18}{0.6} =\frac{0.6x}{0.6}\\\\30=x[/tex]
Margo can buy 30 tiles from both stores for the cost to be equal.
You might ask, "But what about the price?" This is where we solve for y; this variable will answer how much the tiles would cost at 30 tiles. So, we can take the answer for "x" and plug it into any of the two equations.
[tex]y=1.19x\\y=1.19(30)[/tex]
For this equation, all you have to do is multiply both numbers to get your answer.
[tex]y=35.7[/tex]
Bottom Line:Therefore, Margo can buy 30 tiles for the cost to be same at both stores at $35.70.
Which of the following is the quotient of the rational expressions shown below?
The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)
Which is rational expressions?The quotient of the rational expressions is
4(x+2) / 5(x-1) (x-1)
The quotient of the rational expressions shown below
Explanation in detail:
Two expressions are shown here.
Expression 1 : 2x/x-1
Expression II for 5x/2x+4.
The product of expressions I and II must be calculated.
(2x / x-1 ) ÷ (5x / 2x+4)
applying the upcoming regulation
a ÷ b = a× 1/b
(2x/x-1)×( 2x+4 / 5x)
(2x) (2x+4) / (x-1)(5x) (5x)
(2) (2) (x+2) / (x-1)(5) (5)
The solution to the previous question is 4(x+2) / 5(x-1).
The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)
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Last week, Russell bought 11 books and 12 movies for a total of
$245. Today, Russell bought 10 books and 26 movies for a total of $434. Assuming neither item has changed in price, what is the cost of a book in dollars?
The cost of a book bought by Russell is found in in dollars is $7.
What is meant by the term equation?The description of an equation in algebra is a statistical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.For the stated question-
Let the price of the each book be 'x'.
Let the price of movie be 'y'.
Then,
11x + 12y = 245 ...eq 1
10x + 26y = 434 ...eq 2
Solving both eq 1 and 2 using calculator.
x = 7 and y = 14
Thus, the cost of a book bought by Russell is found in in dollars is $7.
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Cindy is 6 years older than half her
mother's age. Cindy's mom is 70 years old.
How old is Cindy?
Answer:
cindy is 51
Step-by-step explanation:
70 divided by 2 is 45
45+ 6 is 51
Determine whether the next pair of triangles is similar. If the triangles are similar, give a reason: write AA, SSS, or SAS.
The two triangles in this problem are not similar, as they do not have congruent angle measures.
What are similar triangles?Similar triangles are triangle that share these following two features:
Congruent angle measures.Proportional side lengths.The angle measures for each triangle are given as follows:
25º, 75º and 180 - 100 = 80º.25, 70º and 180 - 95 = 85º.As the triangles have different angle measures, they are not similar.
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Question 6 of 25
f(x) = 5x + 3. Find the inverse of f(x).
O A. f-¹(x)=3-5x
OB. f-¹(x) = x-5/3
OC. f-¹(x) = 5x - 3
OD. f-¹ (x) = x-3/5
It is option D (f-¹ (x) = x-3/5
How will the area of the circle change if it i dilated by a cale factor of One-half?
A circle with radiu 8 centimeter. The area will be 2 time greater than the original. The area will be 4 time greater than the original. The area will be One-fourth the original. The area will be One-half the original
The area will be 1/4 of the original.
The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.
The area of all shapes is determined by their dimensions and attributes. Different shapes have various areas. The perimeter of a shape is defined as the total distance around the shape.
Given that,
[scale factor]=1/2
[dilated area of circle]=[original area of circle]*[scale factor]²
so
[dilated area of circle]=[original area of circle]*[1/2]²
[dilated area of circle]=[original area of circle]*[1/4]
Thus, The area will be 1/4 of the original.
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A store owner typically sells hats for $34. 99. During a sale he prices them at $29. 99. What is the approximate percent discount on a hat?.
Based on the price of the hats and the new price after the discount, the percent discount is 15%.
What is the Percentage discount?
Discount refers to the condition of the price of a bond that is lower than the face value. The discount equals the difference between the price paid for and its par value.
Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.
To find the discount, use the formula:
= (Difference between price before discount and price after discount) / Initial price of hat x 100%
According to the given values,
Solving gives:
= (34.99 - 29.99) / 34.99 x 100%
= 15%
In conclusion, the approximate percent discount is 15%.
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For a ride on a rental scooter, Boris paid a $8 fee to start the scooter plus $6 cents per minute of the ride. The total bill for Boris's ride was $19.58 . For how many minutes did Boris ride the scooter?
Answer:
193 minutes
Step-by-step explanation:
We know
Boris paid an $8 fee to start the scooter plus 6 cents per minute of the ride.
Let y represent the total cost and x represent the number of minutes we have the equation
y = 0.06x + 8
Now, put $19.58 in for y and solve
19.58 = 0.06x + 8
11.58 = 0.06x
x = 193 minutes
So, Boris rides the scooter for 193 minutes.
What is the solution of the equations 8x +3y 5 and 3x 2y 5?.
The solution of the given linear equations is (x,y) = (1,-1).
The given linear equations are
8x + 3y = 5 - - - ( 1 )
3x - 2y = 5 - - - ( 2 )
As the RHS of both equations is equal, equating the LHS of both equations, we get,
8x + 3y = 3x - 2y
⇒ 8x - 3x = - 2y - 3y
⇒ 5x = - 5y
⇒ x = - 5y ÷ 5
⇒ x = - y
By substituting x = - y in equation ( 1 ), we get,
8x + 3y = 5 - - - ( 1 )
⇒ 8 ( - y ) + 3y = 5
⇒ - 8y + 3y = 5
⇒ - 5y = 5
⇒ y = - 5 ÷ 5
⇒ y = - 1
Now,
x = - y
⇒ x = - ( - 1 )
⇒ x = 1
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What is the range is called?.
The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.
For e.g. the range of the function F is {1983, 1987, 1992, 1996}.
On the other hand, the whole set B is known as the codomain of the function.
It is the set that contains all the outputs of the function.
So, the set of real numbers is a codomain for every real-valued function. The codomain of the function F is set B.
How to Find the Range of a Function
Consider a function y = f(x).
The spread of all the y values from minimum to maximum is the range of the function.
In the given expression of y, substitute all the values of x to check whether it is positive, negative or equal to other values.
Find the minimum and maximum values for y.
Then draw a graph for the same.
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Lance and Alberto cycled along the same 75 km route.
It took Lance 3 hours to cycle the 75 km.
Alberto started to cycle 4 minutes after Lance started to cycle.
Alberto caught up with Lance when they had both cycled 10 km.
Lance and Alberto both cycled at constant speeds.
Work out Alberto's speed.
Lance and Alberto cycled along the same 75 km route. Speed of Alberto is 30 km/ hr
Calculating the problem:Since, Lance takes 3 hours to complete 75km, his speed will be
v= [tex]\frac{75}{3}[/tex]
v= 25 km/hr
The amount of time taken by Lance to complete 10 km is
t= 10/25
t =0.4 hr
t= 0,4×60 min
t=24 min.
Since Alberto started 4 min late and time taken by Alberto to complete 10 km is
t= 24-4
t=20 min.
Hence, speed of Alberto is v=10/0.33
v=30 km/hr.
In math, what is speed?A measure of how quickly something is moving is speed. The distance an object travels in a single time unit is its speed. The speed formula is: Distance times speed. Meters per second (m/s), kilometres per hour (km/h), and miles per hour (mph) are the most common units of speed.
What is distance and speed of time?Speed is calculated by dividing distance by time. You must be familiar with the distance and time units in order to determine the units of speed. The units will be measured in meters per second (m/s) because distance is measured in meters (m) and time is measured in seconds (s).
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PLEASE HURRY, LIMITED TIME EARLY!!!
Question-The center of circle A with equation (x – 7)2 + (y – 1)2 = 16 is mapped to the center of circle B with equation (x + 8)2 + (y – 2)2 = 16. Determine the translation needed for this mapping.
Answers-
A. (x, y) ⟶ (x - 15, y + 1)
B. (x, y) ⟶ (x - 12, y + 9)
C. (x, y) ⟶ (x - 8, y + 2)
D. (x, y) ⟶ (x + 15, y - 1)
The solution is Option A.
The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
Given data ,
Let the equation for the circle A be represented as
( x - 7 )² + ( y - 1 )² = 16
Now , the equation is of the form ( x - h )² + ( y - k )² = r²
So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )
Let the equation for the circle A be represented as
( x + 8 )² + ( y - 2 )² = 16
Now , the equation is of the form ( x - h )² + ( y - k )² = r²
So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )
So , the translation of circle A to B is given by
( 7 , 1 ) to ( -8 , 2 )
So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up
Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )
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Tiana hare a granola bar with her brother. They each get one piece of the bar. What fraction name one part?
A fraction share that Tiana share with her brother called half part. This because the part is split into two where the first part is called first half and other called as second half.
How to name a piece that split into several part?To name a piece of an object that split into several you have to:
Determine how many part that the object splitDetermine the name the total part that created such as half for two, one third for three, quarter for four, etc. The name always following by the order of the split like the first part of quarter part called the first quarter.Learn more about fraction of a set here
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Where is the vertex of the parabola y X² 2x 3?.
The vertex of the equation y = x² + 2x -3 is (-1, -4).
The term vertex in math is known as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.
Here we have the expression y = x² + 2x -3
As we all know that the given equation of parabola is written as,
=> y = ax² + bx + c
As we all know that the vertex of the parabola is given by (h, k).
Here we have calculated the value of the x coordinate of vertex as ,
=> h = -b/2a
And the value of y coordinate of vertex k by using the formula,
=> k = y(h)
Through the given equation we have identified the value of a = 1, b = 2 and c = -3
Then the value of x coordinate is calculated as,
=> h = -2/(2 × 1)
Therefore, the value of h is -1
Then the value of y coordinate is calculated as,
=> k = y (-1)
Here we have to substitute -1 in the equation, then we get
=> k = (-1)2 + 2(-1) - 3
=> k = 1 - 5 = -4
Hence the coordinate of the vertex is (-1, -4).
Complete Question:
Where is the vertex of the parabola of the equation y = x² + 2x -3?
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What is linear inequality in two variables and linear equation in two variables?.
A linear inequality in two variables is an inequality that can be written in the form "ax + by < c" or "ax + by > c" or "ax + by = c", where a, b, and c are constants and x and y are variables. This inequality represents a boundary line and all the solutions of the inequality make up a region of the xy-plane.
For example, the inequality "2x + 3y < 6" represents the region of the xy-plane that is on one side of line 2x + 3y = 6. To graph this inequality, one can find the boundary line by setting the inequality equal to zero and then shading in the region that satisfies the inequality.
A linear equation in two variables is an equation that can be written in the form "ax + by = c", where a, b, and c are constants and x and y are variables. This equation represents a straight line in the xy-plane and all the solutions of the equation are the coordinates of the points on that line.
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