Answer: The image T(V) is defined as the set {k | k=T(v) for some v in V}. So x=T(y) where y is an element of T^-1(S). The preimage of S is the set {m | T(m) is in S}. Thus T(y) is in S, so since x=T(y), we have that x is in S.
Given a function f:A→B, and D⊆B, the preimage D of under f is defined as f−1(D)={x∈A∣f(x)∈D}. Hence, f−1(D) is the set of elements in the domain whose images are in C. The symbol f−1(D) is also pronounced as “f inverse of D.”
In geometry, figures in a plane can be transformed in a variety of ways, including shifts and scaling, to produce new shapes. The new (transformed) shapes are called images and the original, unaltered shapes are called preimages.
In geometry, figures in a plane can be transformed in a variety of ways, including shifts and scaling, to produce new shapes. The new (transformed) shapes are called images and the original, unaltered shapes are called preimages.
Step-by-step explanation:
What is the nature of roots of the quadratic equation x2 2 √ 3x 3 0?
The roots of the quadratic equation x² + 2√3 x + 3 = 0 have only one root and it is -√3
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 2√3 x + 3 = 0 be equation (1)
On factorizing the equation , we get
The roots of the quadratic equations are calculated by
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
Substituting the values in the equation , we get
x = [ -2√3 ± √ ( ( 2√3 )² - 4 ( 3 ) ) ] / 2
On simplifying the equation , we get
x = [ -2√3 ± √ ( 12 - 12 ) ] / 2
The discriminant is zero we get just one real solution
So ,
x = [ -2√3 ± √0 ] / 2
x = ( -2√3 ) / 2
x = -√3
Therefore , the value of x is -√3
Hence , the root of the quadratic equation is -√3
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two parallel lines are crossed by a transversal. What is the value of m? m=68 m=78 m=102 m=112 .
Answer:
m=102
Step-by-step explanation:
You forgot to attach an image of the lines, but I have it here, so no worries
We know that two parallel lines are crossed by a transversal. m are consecutive interior angles. We know that they add up to 180 degrees.
So, our equation is
78 + m = 180
m = 102
HELP I NEED HELP. ASAP. PLEASE!!!!!!!!!
In the last three years, Frederico's basketball team won 50 more games than they lost. If they won 130 games, what was the ratio of wins to losses? Write the ratio in all three forms.
Please! :(
The ratios of win to lose are 13 : 8, 13/8 and 1.625%
How to determine the ratio of win to lose?From the question, we have the following parameters that can be used in our computation:
Win = 50 more than lose
Win = 130
This means that
Win = 50 + Lose
So, we have
50 + Lose = 130
Evaluate
Lose = 80
The ratio is then represented as
Ratio = win to lose
This gives
Ratio = 130 : 80
So, we have
Ratio = 13 : 8
Express as fraction
Ratio = 13/8
Lastly, we have
Ratio = 1.625%
Hence, the ratio is 1.625%
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the equation for line w is y=3x-4.line d contains the point (2,-1) and is parallel to line with.write an equation that describes line d?
Please answer asap.thank you
Considering the definition of parallel line, the equation of the line d is y= 3x -7.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts.
Equation of parallel line in this caseIn this case, the line is y=3x-4
where:
The slope m is 3.The y-intercept is -4.Since two lines are parallel if they have the same slope, the parallel line has a slope of 3.
The line passes through the point (2, -1). Replacing in the expression for a line:
-1= 3× 2 + b
-1= 6 + b
-1 -6= b
- 7= b
Finally, the equation of parallel line is y= 3x -7.
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How do you find the mean of 4 numbers?
How do you find the mean of 4 numbers?
Finding the mean, refers to finding the average. To do this, add the four numbers together and then divide that number by 4.
What does 4 more than a number mean?
'4 more than a number' implies that there exists a number which is 4 units greater than the original number, using the concept of addition.
Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").
Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.
Now, let us understand the meaning.
Let the original number be x.
'4 more than a number' implies x + 4.
This means that the new number, x + 4, is greater than the original number, x, by 4 units. We also have to keep in mind, [tex]x + 4 > x[/tex].
Hence, the final meaning is 4 units greater than the original number.
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How can I solve from problems A-F
Answer:
B. 1 & 1
C. 5 & 3
D. 2 & 2
E. 4 & 0
Something interesting about these was me having to just use simple and smaller numbers to complete the equations.
Answer:
answers is in attached picture.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the equation of y = 2° with the given transformations? vertical compression by a factor of 1 7, horizontal shift 8 units to the left, reflection across the x-axis
The transformation of the function is y = -1/7(2ˣ ⁺ ⁸)
How to determine the transformation of the function?From the question, we have the following parameters that can be used in our computation:
y = 2°
Rewrite properly
So, we have
y = 2ˣ
The given transformations are
vertical compression by a factor of 1/7Horizontal shift 8 units to the leftReflection across the x-axisThe riles of these transformations are
vertical compression by a factor of 1/7: 1/7f(x)Horizontal shift 8 units to the left: (x + 8, y)Reflection across the x-axis: (x, -y)When they applied, we have
y = 1/7(2ˣ)
Then, we have
y = 1/7(2ˣ ⁺ ⁸)
Lastly, we have
y = -1/7(2ˣ ⁺ ⁸)
Hence, the transformed equation is y = -1/7(2ˣ ⁺ ⁸)
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What transformation can verify congruence?
It isometric to rotate, reflect, and translate. This indicates that the character size is unaffected by these modifications. If a form's size and shape have not altered, it is congruent.
What is congruence?
A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.
If 3 sides are equal
then By SSS, its congruent
AB = DE = 12
BC = EF = 11
AC= DF = 10
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given that n is an integer greater than 1, explain why the largest prime factor of 2(7^n) - 2(7^(n-1)) + 7^(n+1) is 61.
When we put the value of 1 in place of n in the equation, the value obtained will be equal to the largest prime factor that is 61.
What is a Prime number?A prime number is any whole number that is greater than 1 and cannot be created by combining other whole numbers. Consequently, a prime number's only factors are 1 and the actual number.
As per the given expression in the question,
2(7ⁿ) - 2(7ⁿ⁻¹) + 7ⁿ⁺¹
Use exponent rule:
[tex]a^b.a^c=a^b^+^c[/tex]
Put the values accordingly,
2(7ⁿ) - 2(7ⁿ⁻¹) + 7ⁿ . 7¹
So,
[tex]\frac{a^b}{a^c}= a^b^-^c[/tex]
⇒ 2(7ⁿ) - 2(7ⁿ/7¹) + 7ⁿ . 7¹
Simplify the above equation,
2(7ⁿ) - 2/7(7ⁿ) + (7)7ⁿ
Take out 7ⁿ as common,
(2 - 2/7 + 7)7ⁿ
Therefore,
61/7(7ⁿ)
Put n = 1 to check for the largest prime number,
61/7(7¹)
= 61
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if there is $0.85 for 8 oz, how much would 1 oz cost?
The cost of 1 oz is $0.10625
How to determine the cost of 1 oz?From the question, we have the following parameters that can be used in our computation:
If there is $0.85 for 8 oz
This means that
The cost of 8 oz = $0.85
Assume there exist a proportional relationship between the cost and the size i.e. oz
The cost of 1 oz can be calculated using the following equation
The cost of 1 oz = $0.85/8
Evaluate the quotient
The cost of 1 oz = $0.10625
Hence, the cost of 1 oz is $0.10625
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What is the slope-intercept form of a line that passes through points (2, 11) and (4, 17)?y = negative 3 x minus 5y = 3 x minus 5y = negative 3 x + 5y = 3 x + 5.
Answer:
y = 3x + 5
Step-by-step explanation:
The slope-intercept form of a line is [tex]y = mx + b[/tex], where m is the slope, and b is the y-intercept.
To solve for m (the slope), use the formula: [tex]m = \frac{y__{2} - y__{1}}{x__{2} - x__{1}}[/tex], where [tex](x_{1} , y_{1} )[/tex] and [tex](x_{2}, y_{2})[/tex] are the points you are given.
. . . . . . . . m = (17 - 11) / (4-2)
. . . . . . . . m = 6/2
. . . . . . . ∴ m = 3
Substitute the slope, m, into the slope-intercept equation.
y = 3x + b
Now we have to solve for b, the y-intercept. To do so, substitute a point that was given to you into the equation.
I chose the point (4,17), but you can also do (2,11).
. . . . . . . . 17 = 3(4) + b
. . . . . . . . . . remember that the x-variable is being multiplied to the m
. . . . . . . . -12 + 17 = 12 + b - 12
. . . . . . . . ∴ 5 = b
Substitute the y-intercept, b, into the slope-intercept equation, and you're done!
[tex]y = 3x + 5[/tex]
What is y 3x 1 in standard form?
The standard form of the linear equation can be written as -3x + y = 1
What means standard form?Standard form defines the method of expressing any mathematical concept such as expression, terms, equation or numbers in a systematic form by following a certain rule.
What is standard form of an equation?The system of writing an equation that follows particular rules is termed as standard form of equation.
The standard form of a linear equation with two variables x and y can be written as Ax + By = C
where, A and B are coefficient of x and y respectively, C is the constant.
This form of equation is required to solve linear equation.
The above equation is written in the slope intercept form, and we get
By = -Ax+C
y = -A/Bx+C/B
where, -A/B is the slope of equation, C/B is the y intercept
Now we have a linear equation written in the slope intercept form
y-3x-1 = 0
y= 3x+1
3 is the slope, 1 is the y intercept
now, we can write it in a standard form and get,
-3x+y = 1
hence, standard form of equation is -3x + y = 1
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Exercice 1
Sarah, who is twenty years old, runs regularly. During her workouts, she monitors her heart rate.It thus determined its maximum recommended heart rate and obtained 193 beats per minute. When she is forty years old, her maximum heart rate will be 178 beats per minute.Is it true that over this twenty-year period his maximum heart rate will have decreased by about 8%?
It is true that Sarah's maximum heart rate over this twenty-year period will have decreased by approximately 8%.
How is the percentage decrease computed?The percentage decrease is determined by ascertaining the reduction or difference in heart rate at the beginning and at forty.
This difference becomes the numerator of the division operation by the heart rate at the beginning and then multiplied by 100.
Sarah's heart rate at twenty years = 193 beats per minute
Sarah's heart rate at forty years = 178 beats per minute
Difference (Decrease) in heart rate = 15 beats per minute (193 - 178)
Percentage decrease = 7.77% (15/193 x 100)
= 8%
Thus, we can conclude that Sarah's heart rate has decreased by about 8%.
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what is the answer of this?
Answer:
x = 43.25
Step-by-step explanation:
(x + 2 )+ (x + 2) + (2x + 3) = 180(total angles in a triangle)
x + 2 + x + 2 + 2x + 3 = 180
x + x + 2x + 2 + 2 + 3 = 180
4x + 7= 180
4x = 180 – 7
4x = 173
divide both sides by (4)
[tex] \frac{4x}{4} = \frac{173}{4} [/tex]
x = 43.25
i hope this helps
Use proportional reasoning skills to figure out the unit rate of bananas if it costs $1.50 for 2/3 pound of bananas.
The unit rate of bananas is $2.25 per pound.
What is the meaning of unit rate?
Unit Rate = Ratio between two separate quantities with different units. = a:b. = a/b. This formula can be used to determine the rate of any two given quantities, such as a and b.
Given that the cost of 2/3 pound of bananas is $1.50.
If the number of pound of bananas increase then the cost of bananas will be increase.
So the relation between amount of banana is directly proportion with the cost.
Therefore,
Amount of bananas/ cost of bananas = Amount of bananas/ cost of bananas
(2/3)/1.50 = 1/x
2/4.50 = 1/x
x = 4.50/2
x = 2.25
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What are the properties of equilateral triangles?
Properties of equilateral triangles are:
All three sides of an equilateral triangles are equal and let be a units.All three angles are equal to 60 degreesEquilateral triangles is a regular polygon of 3 side.Equilateral triangles have the same point as its ortho-centre as well as its centroid . The median, angle bisector, and altitude of an equilateral triangle are all equal and the same straight line.An equilateral triangle's area is = [tex]\frac{\sqrt{3} }{4} *a^2[/tex].perimeter of an equilateral triangle is 3a.The length of perpendicular form a vertex to the side opposite to that vetex measure[tex]\frac{\sqrt{3} }{2} *a[/tex].To know more about equilateral triangles click on below link:
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How do you solve x squared minus 16?
All the options that result in (x + 4 ) (x 4 ) = 0 being true are the ultimate answer and x = − 4 , 4.
What is algebra?The broad field of mathematics includes algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics.Since many applications of mathematics include the manipulation of variables, which are frequently represented by Roman letters, elementary algebra is a prerequisite. For the most part in education, the study of algebraic structures like groups, rings, and fields is referred to as abstract algebra (the term is no more in common use outside educational context). Modern presentations of geometry are done using linear algebra, which deals with linear equations and linear translations. It also has a lot of practical uses (in weather forecasting, for example).Here, x²-16=0
rewrite 16 as 4²
then, (x+4)(x-4)
Any factor on the left side of the equation that is equal to 0 will make the entire expression equal to 0.
x+4=0 and find x
Then x=-4
x-4=0 and find x
x=4.
Hence, All the options that result in (x + 4 ) (x 4 ) = 0 being true are the ultimate answer and x = − 4 , 4.
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[tex] \sqrt{484} [/tex]
some one tell me answer with method.
Answer:
22
Step-by-step explanation:
I factor out the radicand and get 22
Let's test if my answer is correct!
22 times 22 = 484
So, my answer is correct!
What is the arithmetic mean of the data set 4 5 10 8 and 3?
Arithmetic mean of the data set 4,5,0,10,8and 3 is '5'
What Is the Arithmetic Mean?
The easiest and most popular way to calculate a mean or average is with simple mathematics. It simply entails adding up a collection of numbers, dividing that total by the number of numbers in the series, and adding the result together.
given data set is -
4 , 5 , 0 , 10 , 8 and 3
number of observations in given data set are '6'
arithmetic mean ( AM ) formula is
AM = (sum of all observations in given data set) / (total number of observations)
sum of all observations in given data set = 4 + 5 + 0 + 10 + 8 + 3
= 30
AM = 30 / 6 = 5
arithmetic mean of the data set 4,5,0,10,8and 3 is '5'
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What are the 4 steps in constructing a line segment?
Line Segment has 2 end points.
How to construct a line segment?Building a line segment of a specified length involves the following stages.
First, draw a line.
Step 2: Pick any point on the line where point A is.
Step 3: Keep one end of the compass on the 0 cm mark at the specified length of the rule to extend it.
Step 4: Draw an arc on the line while maintaining the compass' pointed end on point A.
Make B the arc point.
In this way we can construct any line segment of given length using compass and scale.
Line Segment has 2 end points.
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The procedure and the answer, Pleaseeeee
Answer:
looooookkkkkk at the picture
72 minutes for 27 songs = 8 minutes for how many songs
Answer:
8 minutes = 3 songs
Step-by-step explanation:
Time taken for 1 song is,
→ 72/27
→ 2.6667
→ ≈ 2.7 minutes
Then songs played in 8 minutes,
→ Total time ÷ Time for 1 song
→ 8 ÷ 2.7
→ 2.96296
→ ≈ 3 songs
Hence, the answer is 3 songs.
How do I add a number to an existing cell in Excel?
On the Formula tab, click AutoSum > Sum. Excel will automatically sense the range to be summed.
Now, According to the question:
How do I add value to an existing cell in Excel?
One quick and easy way to add values in Excel is to use AutoSum. Just select an empty cell directly below a column of data. Then on the Formula tab, click AutoSum > Sum. Excel will automatically sense the range to be summed.
How do I add a digit to an existing number in Excel?
Say you have 50 in the cell in question, and want to add 30 to it. Then the clever part: Right-click on the cell with 50 in it, and select Paste Special. In the box that comes up, select 'Add'.
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Find the solution of the system of equations.
-5x - 5у = -30
10x+3y = -3
Jim invests $5,000 in an account that pays 2.5% annual interest, compounded semi-annually. What is his balance, to the nearest cent, at the end of 5 years?
The balance after 5 years would be near around 5661 dollars.
What is compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
According to the given question:
First, convert R as a percent to r as a decimal
r = R/100
r = 2.5/100
r = 0.025 rate per year,
Then solve the equation for A
A = P(1 + r/n)ⁿˣ
A = 5000(1 + 0.025/2)²ˣ⁵
A = 5661.35
Hence the balance after 5 years would be near around 5661 dollars.
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the two lines graphed below are not parallel. how many solutions are there to the system of equations
The number of solutions that are to the system of equations is (a) one
How to determine the number of solutions on the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (3, 1)
Hence, the solution is (3, 1) ie. one solution
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Answer: bro this ez 1.5 for the first one second should be 22 correct me if im wrong.
Step-by-step explanation:
Answer each of the following questions and show your reasoning. How many cubes with an edge length of 1 3 3 1 inch are needed to build a cube with an edge length of 1 inch? What is the volume, in cubic inches, of one cube with an edge length of 1 3 3 1 inch?
The number of cubes of edge length 1/3 is 27 and the volume of the cube is 1 cubic inches
How to determine the number of cubesFrom the question, we have the following parameters that can be used in our computation:
Edge length of cube 1 = 1/3 inchEdge length of cube 2 = 1 inchThe volume of a cube is the cube of its edge length
This means that the volumes are
Volume = Edge length³
So, we have
Volume of cube 1 = (1/3 inch)³ = 1/27 cubic inches
Volume of cube 2 = (1 inch)³ = 1 cubic inch
The number of cubes is then calculated as
Number of cubes = Volume of cube 2/Volume of cube 1
This gives
Number of cubes = 1/(1/27)
Number of cubes = 27
The volume of the cubesHere, we have
Edge length of cube = 1 inch
The volume of a cube is the cube of its edge length
This means that the volumes are
Volume = Edge length³
So, we have
Volume of cube = (1 inch)³ = 1 cubic inch
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What are the example of exponential equation?
Exponential equation has tow major types
exponential decay
f(x) = a(1.16)^xexponential growth
f(x) = a(0.84)^xWhat are exponential equation?Exponent-based equations in which the exponent or a portion of the exponent is a variable are known as exponential equations.
This is a type of function that are of 3 main parts
the starting or initial value
base function
the exponents
Atypical example includes: f(x) = 300(1.16)^x
the starting = 300
the base = 1.16
the exponents = x
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.
The base is what determines exponential growth or decay
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