Definition of Relation:
Let A and B be sets. A relation R from A to B is a subset of Ax B
Definition of Function:
A function f from a set A (domain) to a set B (codomain) is a relation that satisfies the following properties:
1) Every element in A there is an element y in B such that (x,y) F
2) For all elements z in A there exist a unique element y in B.
The cartesian product of the sets A (a, b) and B (r,y) is
A x B {(a,z) (a,y).(b,),(b,s)}
Step 2
1. T ((a,x), (a,y))
Since T-((a,z), (a,y)) is a subset of (a, b) x (x,y).
so T is a relation from (a,b) to (x,y).
But for the element a in domain, there exist two different images x and y in co-domain.
This violates the definition of function.
Therefore, T_{1} = \{(a, x), (a, y)\} is a relation but not a function.
Step 3
2. T_{2} = \{(b, x), (b, y)\}
Since T_{2} - \{(b, x), (b, y)\} is a subset of \{a, b\}\{x, y\} .
so T_{1} is a relation from \{a, b\} to \{x, y\}
But for the element b in domain, there exist two different images x and y in co-domain
This violates the definition of function
Therefore, T_{2} = \{(b, x), (b, y)\} is a relation but not a function.
Step 4
,T 1 =\ (a,z)\
Since 7-((a,z)) is a subset of \{a, b\}\{x, y\}
so Ty is a relation from \{a, b\} * to (x,y\
But the element & in domain does not map with any element in co-domain
This violates the definition of function
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show that 2 1/4 - 6/7 = 11/28
blehh
Hence the required expression is Proved.
Given the expression is 2 1/4 ₋ 6/7 = 39/28
Consider L.H.S 2 1/4 ₋ 6/7
Convert improper fraction to proper fraction.
2 1/4 = 9/4
take LCM of the denominators.
The LCM is 28.
9×7/28 ₋ 6×4/28
63/28 ₋ 24/28
Now subtract.
63 ₋ 24/28
39/28
Hence proved.
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Your question is incomplete. Please find the missing content here.
Show that 2 1/4 ₋ 6/7 = 39/28
Please help me I will give 30 points and brainiest
What is the absolute value of 30?
(08.07 HC)
An expression is shown below:
f(x) = 2x² - x - 10
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)
Answer:
[tex]\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}[/tex]
[tex]\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)[/tex]
C) See attachment.
Step-by-step explanation:
Given function:
[tex]f(x)=2x^2-x-10[/tex]
Part ATo factor a quadratic in the form [tex]ax^2+bx+c[/tex] , find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex] :
[tex]\implies ac=2 \cdot -10=-20[/tex]
[tex]\implies b=-1[/tex]
Therefore, the two numbers are -5 and 4.
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies f(x)=2x^2-5x+4x-10[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies f(x)=x(2x-5)+2(2x-5)[/tex]
Factor out the common term (2x - 5):
[tex]\implies f(x)=(x+2)(2x-5)[/tex]
The x-intercepts are when the curve crosses the x-axis, so when y = 0:
[tex]\implies (x+2)(2x-5)=0[/tex]
Therefore:
[tex]\implies (x+2)=0 \implies x=-2[/tex]
[tex]\implies (2x-5)=0 \implies x=\dfrac{5}{2}[/tex]
So the x-intercepts are:
[tex]x=-2, \:\:x=\dfrac{5}{2}[/tex]
Part B
The x-value of the vertex is:
[tex]\implies x=\dfrac{-b}{2a}[/tex]
Therefore, the x-value of the vertex of the given function is:
[tex]\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}[/tex]
To find the y-value of the vertex, substitute the found value of x into the function:
[tex]\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}[/tex]
Therefore, the vertex of the function is:
[tex]\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)[/tex]
Part CPlot the x-intercepts found in Part A.
Plot the vertex found in Part B.
As the leading coefficient of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.
The axis of symmetry is the x-value of the vertex. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is symmetrical.
Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).
Is 168 divisible by 2,3,4,5,6,8,9 or 10 explain why please
Help ASAP
Answer:
2,3,4,6,8
Step-by-step explanation:
prime factorization: 2^3×3×7 which has: 2, 3, 4, 6, 8
Answer:
It is divisible by 1, 2, 3, 4, 6, 7, 8
Step-by-step explanation:
Everything is divisible by one, so this is obvious.
168 is an even number, therefore being able to be divided by 2
1+6+8=15 which is in the 3 times tables (3x5=15)
If the last two digits are divisible by 4 (which 68 is) then you can divide it by 4.
168 doesn't end in 5 or 0 so it can't be divided by 5
This number can be divisible by 2 and 3 so it can be divided by 6
160 is divisible by 8 so if you add 8 it is divisible.
1+6+8=15 again which is not divisible by 9
It doesn't end in 0 meaning it cannot be divisible by 10
Hope this helped! <3
Suppose that dollars in principal is invested for years at the given interest rates with continuous compounding. determine the amount that the investment is worth at the end of the given time period. p=1$2000, t=10yr
Amount after 10 years at 3%, 4% and 5.5% interest with principal $20000 is $26878.32, $29604.88 & $34162.88 respectively.
Although a part of your question is missing, you might be referring to this full question: Suppose that P dollars in principal are invested for years at the given interest rates with continuous compounding. Determine the amount that the investment is worth at the end of the given time period. p=$20000, t=10yr
a. 3% interest
b. 4% interest
c. 5.5% interest
P = $2000
T = 10 years
Formula to be used:
A = P(1+r/100)^n
A = total amount after n years
P = principal amount invested
r = rate of interest
n = number of years the money is invested
Solving for part a:
A = 20000(1+3/100)^10
= 20000*1.34
A = 26878.32
Solving for part b:
A = 20000(1+4/100)^10
= 20000*1.48
A = 29604.88
Solving for part c:
A = 20000(1+5.5/100)^10
= 20000*1.70
A = 34162.88
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Find the volume of the solid.
The volume of the solid is
cubic centimeters.
Answer:
27
Step-by-step explanation:
4.5*3*2 = 27
hi,
You just have to multiply the three measures.
So :
2*3*4.5 = 27 cm³
Easy, is it not ?
A statistical tool used to synthesize the results of previous, separate studies is called a(n)?
A statistical tool used to synthesize the results of previous, separate studies is called a(n):Odds-ratio.
We know that, the odds ratio is one that is often calculated with the use of the number of case-patients who were or were not exposed to a factor (e.g. as a particular cream) and the number of controls that did or did not have the exposure.
Odds ratio is nothing but is a measure of association between exposure and an outcome.
It calculates the relationship between a variables and the likelihood of an event occurring.
Note that there are different kinds of statistical tool that are used for research purpose.
Therefore, A statistical tool used to synthesize the results of previous, separate studies is called a(n):Odds-ratio.
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What is the value of the "?" in the figure below
Answer:
I think it is none of the choices.
Step-by-step explanation:
Help asap I need to get this done asap and I’m struggling with it and I’d appreciate help and I’ll give you brainliest
Answer:
x = 10
Step-by-step explanation:
the angle is equally bisected from the middle so
3x - 3 = 4x - 13
13 - 3 = 4x - 3x
x = 10
<FGH = 3(10) - 3 = 27
< HGI = 4(10) - 13 = 27
<FGI = <FGH + <HGI = 27 + 27 = 54
The difference of a number p and 1 is greater than 6
Answer: p - 1 > 6, or p > 7
Step-by-step explanation:
We will write an expression from the sentence given.
difference of a number (p) and 1 ➜ p - 1
is greater than ➜ >
The difference of a number p and 1 is greater than 6 ➜ p - 1 > 6
To solve for the possible values of p, we will add 1 to both sides of the equation;
p > 7
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1
tion
What fraction represents the shaded part of the circle?
Select one:
O a. 12
O b. 5
4555/5
O d.
12
O c. 7
12
7
Answer:
c
Step-by-step explanation:
because 7 of the 12 sections are shaded in blue.
I would love these answer please
The relation 1 is not a function, while the relation 2 is a function
How to determine if each relation is a function or not?For a relation to be a function, the following must be true:
Each y value in the function must have a unique x value
i.e. Each y value must have exactly one x value
Using the above as a guide, we have
Relation 1: This relation is not a function, because the x value 5 has two y values 2 and 4
Relation 2: This relation is a function, because each y value must have exactly one x value
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Point B is on line segment AC. Given AB = 7 and BC = 11, determine the length
AC.
What does AC equal?
Answer:
AC = 18
Step-by-step explanation:
AC = AB + BC = 7 + 11 = 18
2 mandy is playing a game. early in the game she had - 250 points. now
mandy has 350 points. what was the change in mandy's score?
The change of Mandy's score is 600 points.
Here,
Mandy is playing a game.
Early in the game she had - 250 points.
Now, Mandy has 350 points.
We have to find the change of Mandy's score.
What is difference of two number?
To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value.
Now,
Early in the game she had - 250 points.
And, now Mandy has 350 points.
So, The change of Mandy's score = 350 - (-250) = 350 + 250 = 600
Hence, The change of Mandy's score is 600 points.
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The endpoint of the line segment is (4,6) and (-6,2). Point G divides the segment into two equal parts?
What are the coordinates of point of G?
Answer:
G = (-1,4)
I drew it and work it out tho
What are the coordinates of the point on the directed line segment from (-4, 1)(−4,1) to (1, 6)(1,6) that partitions the segment into a ratio of 4 to 1?
Any tips for doing complicated order of operation problems. Algebra 2
Graph the inequality x<3.
To graph an inequality, select the correct type of ray and then select the correct endpoint on the number line.
Answer:
You would start at 3 and then go backwords till the end.
So you'd choose the 3 option. <-o
Only use the filled in o if the equation is <_ with the line underneath, if its like < then its o
Hope this helps! <3
Which list shows the numbers in order from least to greatest?
A)−3π,−9.4,−283,−95−−√
B)−95−−√,−3π,−9.4,−283,
C)−95−−√,−283,−9.4,−3π
D)−283,−9.4,−3π,−95−−√
Answer:
judging from the list of numbers i would pick a
Solve the system:
c+12d=-66
-4c+3d=-42
Answer: c=6, d=-6
Step-by-step explanation:
c+12d=-66
-4c+3d=-42
(-4c+3d=-42)*4
-16c+12d=-168 ==> subtract this
c+12d=-66 ==> by this
-17c=-168-(-66) ==> subtract the top two equations
-17c=-168+66
-17c=-102
c=6
c+12d=-66
6+12d=-66
12d=-72
d=-6
Triple a number decreased by 25 is equivalent to five less than half the same number.
The number is??
The unknown number is 8.
Let the unknown number be x.
According to the given question.
We have a phrase "Triple a number decreased by 25 is equivalent to five less than half the same number".
Therefore, the equation for the phrase "Triple a number decreased by 25 is equivalent to five less than half the same number" is given by
3x - 25 = x/2 - 5
To find the unknown number we have to solve the above equation for x.
Therefore,
3x - 25 = x - 10/2
⇒ 6x - 50 = x - 10
⇒ 6x - x = -10 + 50
⇒ 5x = 40
⇒ x = 40/5
⇒ x = 8
Hence, the unknown number is 8.
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What feature in excel allows you to begin with a 1 in a1 and a 2 in a2 and complete the sequence through the number 30 in a30 without having to type in the entire sequence?
Answer:
type 1 in a1 type 2 in a2, (or whatever ur preferred no.s are),then heighlight both cells, then go to the bottom right corner of a2 and drag down or double click
Step-by-step explanation:
Drag down or double-click the bottom right corner of a2 to begin with a 1 in a1 and a 2 in a2 and complete the sequence.
What is excel?Excel is a software in which we can process large amount of data and data handling easily and effectively, Excel can be used in Data analysis.
in a1 type 1 Type 2 in cell a2 (or whatever your chosen numbers are), highlight both cells, and then drag down or double-click the bottom right corner of a2.
Thus, drag down or double-click the bottom right corner of a2 to begin with a 1 in a1 and a 2 in a2 and complete the sequence.
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i need help in algebra gang i pay 30 a month help mee
Answer:
2c+2
The number that will go in the green box is 2.
Step-by-step explanation:
3c-1-c+3
Combine the like terms.
3c-1-c+3=2c+2
Hope this helps!
Please mark as brainliest if correct!
luna wants to sell a Tshirt
In her shop making a profit of
25%
if the cost of the Tshirt
is 100$, in the same time
the customer will have a discut
of 30%, what shall she put
on a Sale Tag
Answer:
Price: $178.57
30% off: -$53.57
Sale Price: $125.00
Step-by-step explanation:
She buys each shirt for $100.
She wants to make a profit of 25%.
25% of $100 = 0.25 × $100 = $125
She must sell the shirt at $125.
She wants to mark the shirt at a higher price than $125, so that after the 30% discount, she will still sell it for $125.
Call the higher price x.
x - 30% of x = 125
x - 0.3x = 125
0.7x = 125
x = 125/0.7
x = 178.57
The sale tag can read:
Price: $178.57
30% off: -$53.57
Sale Price: $125.00
1.
Write the numbers of dots in the next three steps of
this pattern:
3
6
10
15
2. What i
Answ
Answer:
your answer is 21
Step-by-step explanation:
The gap between 3 and 6 is 3 the gap between 6 and 10 is 4 the gap between 10 and 15 is 5 so your answer will be 6 more than 15 which is 21
your welcome
help please
15 points
need by the end of today
9. Enrique would earn $7. 50 per hour. Option B
10. The number of girls that were at the assembly is 1390 . Option J
11. 40% of 60 is 24 . Option C
12. The simple interest is $72. 00 . Option F
13. The factory produces 1080 shoes on Tuesday. Option D
How to determine the value9. From the information given, we have;
He earns $420He works a total of 56 hoursHe would earn;
= 420/ 56
= $7. 50 per hour
10. We have that;
There are 1200 boys at the assemblyRatio of boys to girls is 20: 23The number of girls at the assembly would be;
= 23/ 20 × 1200
= 1. 15 × 1200
= 1380
11. Let the number be x
40% of x = 24
40/ 100x = 24
0. 4 x = 24
Make 'x' the subject
x = 24/ 0. 4
x = 60
12. The formula for simple interest is expressed as;
Simple interest = PRT / 100
Simple interest = 300 × 4 × 6/ 100
Simple interest = 7200/ 100
Simple interest = $72. 00
13. We have that;
Monday's production = 900 shoes
Tuesday's production = 900 + 900 × 20% = 900 × 20/ 100 = 18000/ 100 = $900 + 180
= $1080
Thus, the total amount Enrique earns per hour is $7. 50 .Option B
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What is the answer ?
Answer:
xy + z = 16
5(2) = 10 + 6 = 16
ARITHMATIC SEQUENCE
Grade 11 - one question
Answer:
a₁ = - 11 and d = 3
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
given S₄₀ = 1900 , then
S₄₀ = [tex]\frac{40}{2}[/tex] [ 2a₁ + 39d ] = 1900 , that is
20(2a₁ + 39d) = 1900 ( divide both sides by 20 )
2a₁ + 39d = 95 → (1)
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
given a₄₀ = 106 , then
a₁ + 39d = 106 → (2)
subtract (2) from (1) term by term to eliminate d
a₁ + 0 = - 11 , so
a₁ = - 11
substitute a₁ = - 11 into (2) and solve for d
- 11 + 39d = 106 ( add 11 to both sides )
39d = 117 ( divide both sides by 39 )
d = 3
distribution consists of 30 scores of 10 and 30 scores of 20. Find the ratio of the range to the standard deviation.
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. ages of children: 5, 6, 7, 8, and 9
There are four levels of measurements in statistics, namely nominal, ordinal, interval, ratio. These levels are important when it comes to analyzing data, since it helps us determine the technique that we can use to support or refute our study.
In the nominal level, we can categorize data but they cannot be ranked. An example would be hair color. In an ordinal data, the data can be both categorize and ranked, but doing mathematical calculation may not make sense. Also, the intervals between rankings doesn't necessarily dictate how close or far apart the data are.
A good example is level of education. In an interval level, the data can be categorized, ranked, and measured but they do not have a true zero. An example could be a range of values that does not include zero. Lastly, in the Ratio level the data can be categorized, rank, and measured, and it has a true zero.
So ratio level is most appropriate for ages of children. Note that ages can be categorized, rank, and measured .Moreover, an age equal to zero means that there is no age or the absence of age.
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