PLeasse Helpp its urgent pleassesssssA rectangular piece of metal is 5 inches longer than a number, x. The width is 3 inches less than x. Squares with sides 2-inches long are cut from each of the four corners and the flaps are folded upward to form an open box. If the volume of the box is 40 inches cubed, what does x equal? *

What is the original length of the rectangular piece of metal in inches? Answer with a number, no units. *

What is the original width of the rectangular piece of metal in inches? Answer with a number, no units.

Answers

Answer 1

Answer:

X=16

Step-by-step explanation:

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Let P be the relation defined on the set of all American citizens by xPy if and only if x and y are registered for the same political party. Not being registered or being registered as an independent also counts as a registration. Check all properties that P has.anti-symmetric

reflexive

transitive

symmetric

Answers

Answer:

This relation is symmetric, reflexive and transitive, but not anti-symmetric. Therefore it is an equivalence relation.

Step-by-step explanation:

Let's first prove that it is reflexive:

$\forall x : xRx \quad ?$

The explanation is as follows: let x be some american citizen, $xRx$ means that this person x is registered for the same political party as himself. This is obviously truth, because we are talking about the same person.

Next comes symmetry:

$xRy \iff yRx$

What does this statement mean? It means that if a is in the same party as b, then b is in the same party as a, and viceversa. This must be true, for the statement $xRy$ tells us that x is in the same party as y, which can also be stated as "x and y are both in the same party". This last statement also implies that y is in the same party as x, which is written as: $yRx$ . That proves that:

$xRy \implies yRx$

And the converse follows from the same reasoning.

Now for Transitivity:

$aRb \, \wedge bRc \implies aRc$

What this statement means in this context is that if a,b and c are american citizens, and we have that it is simultaneously true that both a and b are in the same party, and that also b and c are in the same party, then a and c must be also in the same party. This is true because parties are exclusive organisations, you cannot be both a democrat and a republican at the same time, or an independent and a republican. Therefore if a and b belong to the same party, and b and c also belong to the same party, it must be true that a belongs to the same party as b, and the same holds for c, therefore a and c belong to the same party (b's party). which we write as: $aRc$ . Thus it is true that R is a transitive relation.

Finally, Antisymmetry is NOT a property of this relation.

Let's see why, antisymmetry means:

$xRy \wedge x \neq y \implies \neg yRx$

That would mean that if x and y are two distinct american citizens $x\neq y$ , then if x is in the same party as y ( $xRy$ ), then it is not true that y is in the same party as x! ( $\neg yRx$ )

Clearly this isn't true, for example if x and y are two distinct democratic party members, we can say that $xRy$ that is, x and y are registered for the same party, and given that this relation is symmetric, as we have shown, we can also say $yRx$ , but this comes in conflict with the definition of antisymmetry. Thus we conclude that the relation R is not antisymmetric.

On a final note, it's interesting to point out that reflexivity, symmetry and transitivity are the requirements for a relation to be an equivalence relation, which is a very useful concept in maths.

Final answer:

The relation P defined on the set of all American citizens by xPy is reflexive and symmetric, but not transitive.

Explanation:

The relation P defined on the set of all American citizens by xPy if and only if x and y are registered for the same political party has the properties of reflexivity, symmetry, but not transitivity.

Reflexivity means that every element is related to itself. In this case, every American citizen is registered for the same political party as themselves, including those who are registered as independent or not registered at all.

Symmetry means that if x is related to y, then y is related to x. In this case, if two American citizens are registered for the same political party, they are related to each other.

However, the relation P does not have the property of transitivity. Transitivity means that if x is related to y and y is related to z, then x is related to z. In the case of the relation P, if two American citizens are registered for the same political party and another two American citizens are registered for the same political party, it is not necessarily true that the first two citizens are also registered for the same political party as the second two citizens.

Learn more about Relation properties here:

brainly.com/question/25558669

#SPJ3

What is the right option?

Answers

C. -x + 2y = 8

Hope this helped :)

Question 3 (1 point) If the following is a rhombus, find the missing measures. Find PQ. PQ=

Answers

Answer:

Step-by-step explanation:

PQ*PQ=PQ²=(5x+16)²=25x²+160x+256

Karly is choosing between two health clubs. Yoga Studio A charges a membership fee of $22.00 and $24.50 per month. Yoga Studio B charges a membership fee of $47.00 and $18.25 per month. At how many months will they cost the same? *

Answers

Answer:

4 months

Step-by-step explanation:

Given

Studio A

$Membership = \$22.00$

$Monthly = \$24.50$

Studio B

$Membership = \$47.00$

$Monthly = \$18.25$

Required

Determine when the cost will be the same

For both, we have the total cost to be:

$Cost = Membership + Monthly\ Cost * m$

Where m represents the number of month

For Studio A:

$Cost = 22 + 24.5 * m$

For Studio B:

$Cost = 47 + 18.25 * m$

Equate both expressions to get the required month

$47 + 18.25 * m = 22 + 24.5 * m$

$47 + 18.25 m = 22 + 24.5m$

Collect Like Terms

$47 - 22 = 24.5m - 18.25 m$

$25= 6.25m$

Reorder

$6.25m = 25$

Solve for m

$m = 25/6.25$

$m = 4$

Hence, it'll take 4 months

If line p is perpendicular to line m what is the relationship between line p and line l

Answers

9514 1404 393

Answer:

p is perpendicular to l

Step-by-step explanation:

The congruent corresponding angles at the unmarked transversal mean that lines l and m are parallel. Just as corresponding angles at that unmarked transversal are congruent, so the corresponding angles at transversal p are congruent.

All of the angles of intersection of lines l and m with p are right angles. l and p are perpendicular lines.

5*Please answer this correctly very urgent!

Answers

Answer:

1 3/15 - 5/15

Step-by-step explanation:

Hope this helps. PS the / sign is supposed to be for the fraction.

Step-by-step explanation:

1 1/5 - 1/3 = 0.86

Hope I helped. The only way I know how to dot this is in decimal form sorry.

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Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the early years but began to grow rapidly after 2005. But the iPod era is coming to a close. Smartphones with music and video Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the END OF THE IPOD ERA players are replacing the iPod, along with the category of device it helped to create. Sales of the iPod worldwide from 2007 through 2011 (in millions) were approximately N(0= -165t2 + 13.13t+ 39.9 (0 < t< 4) in year t, where t= 0 corresponds to 2007. Show that the worldwide sales of the iPod peaked sometime in 2009. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?

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