Answers
X is an inductive set, then {X [tex]\in[/tex] x is transitive} is also an inductive set. Consequently, every n [tex]\in[/tex] N is transitive.
To prove the statement, we need to demonstrate that if X is an inductive set, then the set {[tex]X \in x[/tex]is transitive} is also an inductive set.
Let's break down the proof into two parts:
If X is an inductive set, then {[tex]X \in x[/tex] is transitive} is a subset of X:
To show that {[tex]X \in x[/tex]is transitive} is a subset of X, we need to prove that every element in {[tex]X \in x[/tex] is transitive} is also an element of X.
If X is an inductive set, it means that X contains the empty set (∅) and for every element x in X, the successor of x (denoted as S(x)) is also in X. Now, consider an arbitrary element y in {[tex]X \in x[/tex] is transitive}. By definition, y is a transitive set.
Since X is inductive, it contains the empty set and for every element in X, its successor is also in X. Thus, y must also be in X, and {[tex]X \in x[/tex] is transitive} is a subset of X.
{[tex]X \in x[/tex] is transitive} is an inductive set:
To show that {[tex]X \in x[/tex] is transitive} is an inductive set, we need to demonstrate that it satisfies the properties of an inductive set.
First, we prove that the empty set (∅) is an element of {EX: x is transitive}. Since the empty set is transitive (it vacuously satisfies the definition of transitivity), it belongs to {[tex]X \in x[/tex] is transitive}.
Second, we prove that for every element y in {[tex]X \in x[/tex] is transitive}, its successor S(y) is also in {[tex]X \in x[/tex] is transitive}. Let y be an arbitrary element in {[tex]X \in x[/tex] is transitive}.
By definition, y is a transitive set. We need to show that S(y) is also a transitive set. Since X is inductive, it means that for every element x in X, its successor S(x) is also in X. Applying this property to y, we conclude that S(y) is in X. Since S(y) is in X, it is also in [tex]X \in x[/tex] is transitive}. Hence, {[tex]X \in x[/tex] is transitive} satisfies the property of an inductive set.
By proving both parts, we have shown that if X is an inductive set, then {[tex]X \in x[/tex] is transitive} is also an inductive set. Consequently, every [tex]n \in N[/tex] is transitive.
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Related Questions
What is total area of the shaded sections
Answers
Answer:
Step-by-step explanation:
The shaded region is triangle.
Base = 1.1 in
Height = 3.8 in
Area of triangle = [tex]\frac{1}{2}*base * height[/tex]
[tex]=\frac{1}{2}*1.1*3.8\\\\= 1.1 * 1.9\\\\= 2.09 in^{2}[/tex]
Area of shaded region = 2 * 2.09 = 4.18 square inches
Create an algebraic expression to solve the following problems.
a) Jeff’s cell phone plan charges him $10 per GB with no extra fees. How much will his bill be for 6 GB?
b) Marks cell phone charges him $8 per GB and a monthly fee of $15 how much will his bill be for 10 GB
c) Ricks cell phone plan charges him $5 per GB and a monthly for of $30. How much will his bill be for 2 GB?
PLEASE ANSWER PLEASE
Answers
Answer:
Step-by-step explanation:
x is the number of GB
f(x) is the cost in dollars
f(x) = 10x
Bill for 6 GB = f(6) = 60
:::::
f(x) = 8x+15
Bill for 8 GB = f(10) = 95
:::::
f(x) = 5x+30
Bill for 2 GB = f(2) = 40
Find the equation of the line that
is parallel to y = 4x + 1 and
contains the point (1, 1).
Answers
Answer:
4x-3
Step-by-step explanation:
Equation of the line that is parallel to y = 4x + 1 and contains the point (1, 1) is y = 4x - 3.
What are equation of a line that is parallel to that line?Two lines are said to be parallel if they always maintain the same distance apart. If two lines are drawn so that they could extend into infinity without ever meeting each other, these lines are called parallel. Parallel lines are also called Equidistant lines.
Given
Equation of line y = 4x + 1
Point = (1, 1)
Equation of the line that is parallel to y = 4x + 1 is y=kx + b
Here k =4
y = 4x + b and contains the point (1,1)
Substitute the point (1,1) in y= 4x + b
⇒ 1 = 4(1) + b
⇒ 1 - 4 = b
⇒ b = -3
y = 4x + b
⇒ y = 4x - 3
Equation of the line that is parallel to y = 4x + 1 and contains the point (1, 1) is y = 4x - 3.
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Which of the fractions is equivalent to 2/5?
Answers
Answer:
4/10, 6/15, 8/20, 10/25
Step-by-step explanation:
Carter invested $16,000 in an account paying an interest rate of 5.6% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $29,600?
Answers
Answer:
11 years.
Step-by-step explanation:
Given that Carter invested $ 16,000 in an account paying an interest rate of 5.6% compounded monthly, to determine, assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $ 29,600, the following calculation must be performed:
16,000 x (1 + 0.056 / 12) ^ Yx12 = 29,600
Y = 11
16,000 x 1.4666 ^ 132 = X
29,581.70 = X
Thus, rounded to the nearest year, it would take 11 years for the account to reach $ 29,600.
Which of the following are remote interior angles of Z6? Check all that apply.
4
1
5
2.
2
6
3
O A. 24
B. 21
O C. 22
O D. 25
E. <3
A F. 26
Answers
Answer:
B. <1
E. <3
Step-by-step explanation:
Remote interior angles are interior angles inside a triangle that are opposite to an exterior angle of the triangle.
<6 is an exterior angle. The remote interior angles that are opposite to <6 are <1 and <3.
Therefore, <1 and <3 are remote Interior angles of <6
They are away from <6.
The remote interior angles of ∠6 are ∠1 and ∠3
Remote interior angles:Remote interior angles are those angles that don't share a vertex or corner of a triangle with the exterior angle.
The remote interior angles are usually opposite of the exterior angles.
The remote interior angles of ∠6 are those angles interior angles that does not share a vertex with the ∠6(exterior angle).
Therefore, the remote interior angles of ∠6 are ∠1 and ∠3
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Bart owns a neighborhood Kwik-E-Mart. At the end of the day on Wednesday, he counted total receipts in his store of $8,399.70. If the sales tax on food items is 2%, how much merchandise did Bart sell on Wednesday? How much sales tax did he collect?
Answers
PLEASE HELP I WILL MARK YOU BRAINIEST
Answers
Answer:
y < 4
Step-by-step explanation:
2(5y-2) < 36
Divide both sides by 2.
5y-2 < 18
Add 2 to both sides.
5y < 20
Divide both sides by 5 to isolate y.
y < 4
Which line on the graph represents the information in the table?
A. Line a
B. Line b
C. Line c
D. Line c
First one near with CORRECT answer gets brainless.
Answers
Answer:
i Believe is is line b
Step-by-step explanation:
when you put all the lines on the graph they are all near line b
help plss i'm lost i need help
Answers
+14 above zero
-100 feet below sea level
-17 u owe ur aunt
-10 candy bars left over
-9 people who didn’t get burgers
-8 years younger
+11 years older
Answer:
2) +20
4) +14
5) -100
6) -17
7) 10
8) -9
9) -8
10) +11
Step-by-step explanation:
look at the words and it will tell you whether it's positive or negative
ex. one hundred feet below sea level- it says below which means you would be going down
A. Scalene
B. Isosceles
C. Right
D. Obsute
Answers
Answer:
Isosceles
Step-by-step explanation:
Because an equilateral triangle is also isosceles, all triangles are either scalene or isosceles. But when people call a triangle isosceles, they're usually referring to a triangle with only two equal sides, because if the triangle had three equal sides, they'd call it equilateral.
WILL GIVE BRAINLIEST to whoever solves this entire problem (completes all the steps). I WILL REPORT if you just steal the points without giving an answer. I know this is really long but I really need help on this and am low on time. To whoever answers this, thank you so much, you are a life saver.
We created this inequality to represent how Amy can meet her revenue goals:
-100x2 + 15,750x + 212,500 ≥ 243,600
In this activity, you’ll solve this inequality to find the minimum ticket price Amy should charge to meet her minimum revenue goal.
Step 1: set the inequality greater than or equal to zero
Step 2: simplify the inequality by dividing by the GCP so the leading coefficient is positive
Step 3: factor the left side of the inequality by grouping
Step 4: solve the quadratic inequality. Remember to check any possible solutions for viability.
Step 5: what is the minimum number of $2 increases that Amy needs to apply to the ticket price to reach her desired revenue?
Step 6: What’s the minimum ticket price that Amy can charge and reach her goal? Recall that the ticket price is represented by 25 + 2x, where x represents the number of $2 increases.
Seriously thank you to anyone who does this. I am low on time and this helps a bunch.
Answers
Trust me these are the correct answers :)
Answer:
Part A: -100x2 + 15,750x − 31,100 ≥0
Part B: 2x2-315x+622 ≤0
Part C: (2x-311)(x-2) ≤0
Part D:2 ≤ x ≤ 155.5
Part E: We know x = number of $2 increases. So, from the compound inequality, 2 ≤ x ≤ 155.5, we can conclude that the minimum possible value of x is 2.
Part F: 29
A dressmaker buys flannel fabric by the yard. A purchase
of 5 yards of flannel costs $40. How many yards of flannel
would the dressmaker be able to buy for $36?
Answers
Answer:
4.5yards
Step-by-step explanation:
$40 =5yards
$36 =?
36*5=180÷40
=4.5yards
The dressmaker would be able to buy 4.5 yards of flannel for $36.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE have been given that dressmaker buys flannel fabric by the yard. A purchase of 5 yards of flannel cost $40 then we need to find yards of flannel would the dressmaker be able to buy for $36.
Given ; $40 =5yards
$36 =?
Therefore, we get
36*5 = 180÷40
= 4.5yards
Hence, the dressmaker would be able to buy 4.5 yards of flannel for $36.
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Solve for x....................................
Answers
Answer:
x = 4.5 is the answer to the question
What is the area of polygon LMN?
A. 50
B. 60
C. 65
D. 70
E.80
Answers
Answer:
c:65
Step-by-step explanation:
The area of a triangle can be found almost the same way as a sqaure L*W (Length times width). Except the area of a triangle is one half that of a square, so it is [tex]\frac{1}{2}[/tex]L*W. The length is 13 and the width is 10, so 13*10=130, than 1/2 that is 65.
Better be 65 I think not sure
Help me out I’ll give a stars real answers only.
Answers
Answer:
Step-by-step explanation:
Draw the graph of the equation: 1.6x=4.8
Answers
Answer:
Here...
Step-by-step explanation:
x | y
3 | 0
3 | 1
The picture is the graph ( I'm not sure why I wrote that you probably already knew... but, I'm not sure if this helps but here.. :D )
We write "3.4 cm + 4.3 cm = 7.7 cm," but the sum could be as small as --------- cm
Answers
Answer:
the smallest value of the sum is 7.65 cm.
Step-by-step explanation:
Given;
3.4 cm + 4.3 cm = 7.7 cm
To obtain the least value of the given result, we will apply the rounding-off method;
In the rounding-off method, digits between 0 to 4 will be rounded down to zero while digits between 5 and 9 will be rounded up to 1.
The smallest value of 7.7 cm = 7.65 cm (5 will be rounded up to 1 making 7.65 cm approximately 7.7 cm)
Also, other possible values of 7.7 cm include;
7.66 cm, 7.67 cm, 7.68 cm, 7.69 cm
Note :7.64 cm cannot be rounded up to 7.7 cm because 4 will be rounded down to zero making 7.64 cm approximately 7.6 cm.
Therefore, the smallest value of the sum is 7.65 cm.
What us this cab someone help? 1 1-18 = 4
Answers
Answer:
Y= -72
Step-by-step explanation:
I dont know if that was the answer needed
SUPER EASY QUESTION WILL GIVE BRAINLEST!!!!!!!!!!!!!!!!!!!!!
what is 11683.94 rounded to the nearest tenth.
Answers
Answer: It's 11683.9
Step-by-step explanation:
help pls, math due tonight :(
Answers
9514 1404 393
Answer:
40 ftt = 1 secondStep-by-step explanation:
A graphing calculator answers these questions easily.
The ball achieves a maximum height of 40 ft, 1 second after it is thrown.
__
The equation is usefully put into vertex form, as the vertex is the answer to the questions asked.
h(t) = -16(t^2 -2t) +24
h(t) = -16(t^2 -2t +1) +24 +16 . . . . . . complete the square
h(t) = -16(t -1)^2 +40 . . . . . . . . . vertex form
Compare this to the vertex form:
f(x) = a(x -h)^2 +k . . . . . . vertex (h, k); vertical stretch factor 'a'
We see the vertex of our height equation is ...
(h, k) = (1, 40)
The ball reaches a maximum height of 40 feet at t = 1 second after it is thrown.
Alright I’m not smart please help
Answers
Answer:
98 sq. in.
Step-by-step explanation:
Area of Triangle formula : 1/2 x Base x Height
1/2 x 14 x 14 =98
Help plsssssss i'm lost il give brainiest
Answers
Answer:
A 16°
B -8°
C 6°
D -16°
E -4°
Step-by-step explanation:
Look at 0° and 10°. There are 5 lines from one to the other, so each line represents 2°.
A
3 lines above 10° = 10° + 3 * 2° = 10° + 6° = 16°
B
1 lines above -10° = -10° + 2° = -8°
C
3 lines above 0° = 0° + 3 * 2° = 0° + 6° = 6°
D
2 lines above -20° = -20° + 2 * 2° = -20° + 4° = -16°
E
3 lines above -10° = -10° + 3 * 2° = -10° + 6° = -4°
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answers
Answer: all of dem except for 6
Step-by-step explanation:
Math 1 Sem 1 1 2.1.5 Quiz: Naming Functions Question 4 of 6 When you read S(h) aloud, you can shorten it to "S of h." O A. True O B. False
Answers
Answer: True!
Step-by-step explanation: When you pronounce the function you say it as is. :) Please rate and like thank you.
Please help with this math equation
Answers
Select the correct answer. Given: is a rectangle with vertices , , , and , where . Prove: is a square. Statements Reasons 1. is a rectangle with vertices , , , and . 1. given 2. units 2. ? 3. units 3. distance formula 4. 4. ? 5. is a square. 5. ? What is the correct order of reasons that complete the proof?
Answers
The correct order of reasons that complete the proof is:
Given
AB = 6 units
BC = 4 units
AC = 4 units
Diagonals are congruent
AC = BD = 4 units
ABCD is a rhombus
ABCD is a square.
Based on the given statements and reasons, let's determine the correct order of reasons to complete the proof that ABCD is a square.
Given: ABCD is a rectangle with vertices A, B, C, and D.
Reason: Given.
AB = 6 units.
Reason: The length of AB is given as 6 units.
BC = 4 units.
Reason: The length of BC is given as 4 units.
AC = 4 units.
Reason: Since ABCD is a rectangle, opposite sides are equal. Therefore, AB = CD = 6 units and BC = AD = 4 units.
Diagonals are congruent.
Reason: In a rectangle, the diagonals are congruent. Therefore, AC = BD.
AC = BD = 4 units.
Reason: From reason 4, we know that AC = 4 units. From reason 5, we know that AC = BD.
ABCD is a rhombus.
Reason: In a rhombus, all sides are equal, and opposite angles are congruent. Since AC = BD = 4 units (reason 6), ABCD satisfies the properties of a rhombus.
ABCD is a square.
Reason: In a square, all sides are equal, and all angles are right angles. Since ABCD is a rectangle (reason 1) and a rhombus (reason 7), it must also be a square.
Therefore, the correct order of reasons that complete the proof is:
Given
AB = 6 units
BC = 4 units
AC = 4 units
Diagonals are congruent
AC = BD = 4 units
ABCD is a rhombus
ABCD is a square.
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If x = 1 does x² - x = 0?
Answers
Answer:
Yes it does
Step-by-step explanation:
we would like to Prove the following for x=1:
[tex] \displaystyle {x}^{2} - x = 0[/tex]
since x=1 substitute:
[tex] \displaystyle {1}^{2} - 1 \stackrel {?}{=}0[/tex]
to simplify it we can consider the order of PEMDAS which is a abbreviation of
ParenthesesExponentMultiplication orDivision Addition orSubstractionsince exponent come first
simplify exponent:
[tex] \displaystyle {1}^{} - 1 \stackrel {?}{ = }0[/tex]
simplify substraction:
[tex]\displaystyle 0 \stackrel { \checkmark}{ = }0[/tex]
since left hand side equal to right hand side
hence, Proven
Alternate way:use a²-b²=(a+b)(a-b) to rewrite:
[tex] \displaystyle (x + \sqrt{x} )(x - \sqrt{x} ) = 0[/tex]
since x=1 substitute:
[tex] \displaystyle (1 + \sqrt{1} )( 1- \sqrt{1} ) \stackrel {?}{=} 0[/tex]
simplify square root:
[tex] \displaystyle (1 + 1)( 1- 1 ) \stackrel {?}{=} 0[/tex]
simplify parentheses:
[tex] \displaystyle (2)( 0) \stackrel {?}{=} 0[/tex]
Multiplying any number by 0 results 0 thus
[tex] \displaystyle 0 \stackrel { \checkmark}{=} 0[/tex]
since left hand side equal to right hand side
hence, Proven
Given,
x = 1
We need to find if x² - x = 0 is true or false.
If x = 1, then x² will be equal to 1² = 1 (1 multiplied by 1 is one / 1 square is equal to 1)
So,
=》x² - x = 0
By substituting ...
=》1² - 1 = 0
Now calculate...
=》1 - 1 = 0
=》0 = 0
•°• The given statement is true.
_____
RainbowSalt2222 ☔
ANSWER THE QUESTION IN THE PIC BELOW PLEASE
sorry if the pic is blurry if u can't tell what it says beside the line it says 4 in and at the bottom it says 8 in
Answers
Will give brainliest
Find the area of the shaded region.
800
5 cm
A = [?] cm2
Enter a decimal rounded to the nearest tenth.
Answers
The area of the shaded region is 73.4 cm².
What is Area ?
An object's area is the space that its boundary encloses. A closed figure's area is determined by how many unit squares are present on its surface.
Given : Radius of circle = 5 cm
The area of circle = πr²
= 25π = 78.57 cm²
Now, the area of segment can be found by using the formula :
= 1/2 × r² × [ πФ/180 - sinФ]
So, area of segment = 1/2 × 25 × [ π×80/180 - Sin 80 ]
= 25/2 × [4π/9 - 0.9848 ]
= 25/2 × [1.3968 - 0.9848]
= 5.15 cm² approx.
So, Th area of shaded region = area of circle - area of segment
= 78.57 - 5.15
= 73.4 cm²
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