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Marat540 [252]
3 years ago
5

Transversal cuts parallel lines and at points X and Y respectively. The point nearest to C is X, and the point nearest to D is Y

. Points P and R lie on one side of , while Q and S lie on the other side. According to the Alternate Exterior Angles Theorem, which angle is congruent to ∠CXP? A. ∠RYD B. ∠SYD C. ∠CXQ D. ∠XYS

Mathematics
1 answer:
hammer [34]3 years ago
5 0

Answer:  The answer is (B) ∠SYD.


Step-by-step explanation: As mentioned in the question, two parallel lines PQ and RS are drawn in the attached figure. The transversal CD cut the lines PQ and RS at the points X and Y respectively.

We are given four angles, out of which one should be chosen which is congruent to ∠CXP.

The angles lying on opposite sides of the transversal and outside the two parallel lines are called alternate exterior angles.

For example, in the figure attached, ∠CXP, ∠SYD and ∠CXQ, ∠RYD are pairs of alternate exterior angles.

Now, the theorem of alternate exterior angles states that if the two lines are parallel having a transversal, then alternate exterior angles are congruent to each other.

Thus, we have

∠CXP ≅ ∠SYD.

So, option (B) is correct.

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There were 460 people at a local football game. 3/5 of them were students how many people that attended the football game were s
Irina18 [472]

Answer:

240

Step-by-step explanation:

3 0
2 years ago
There are 3 cards lettered A, B, and C and a 6 sided die. If you draw a card and then rolled the die, what is the P(A3)?
nirvana33 [79]

Answer:

1/18.

Step-by-step explanation:

P(A) = 1/3    (as there are 3 cards with one marked A).

P(3 on the die) = 1/6 (as there are 6 sides on a die).

P(A then 3) = 1/3 * 1/6 = 1/18.

Note: the probabilities are multiplied because the 2 events are independent.

3 0
3 years ago
Dawn has 5\6 yard of lace. She uses 4\5 of it on a dress and the rest on a jewel box. How much does she use on the jewel box
mr_godi [17]

Answer:

Jewelry box:  1/6 yard

Step-by-step explanation:

4/5 (not 4\5) of her 5/6 yard goes into a dress:   (4/5)(5/6 yd) = 2/3 yard.

This is the same as 4/6 yard.  The amount of lace remaining, to be used on a jewelry box, is 5/6 - 4/6, or 1/6 yard.

3 0
4 years ago
A company that teaches self-improvement seminars is holding one of its seminars in Middletown. The company pays a flat fee of $1
Nutka1998 [239]

Answers:

To reach the breakeven point, how many attendees will that take?  <u>   117   </u>

What will be the company's total expenses and revenues?  <u>    $1755  for each   </u>

=============================================================

Explanation:

x = number of attendees

C(x) = cost function for the company

C(x) = 14x+117

This is because the company pays $14 per person, so x of them accounts for 14x dollars. Then we add on the flat fee of $117 to get 14x+117 dollars overall.

In contrast, the revenue is

R(x) = 15x

because each attendee brings in $15 for the company

The breakeven point is when the cost and revenue are the same. This produces a profit of $0.

R(x) = C(x)

15x = 14x+117

15x-14x = 117

x = 117

If 117 people attend the seminar, then the company breaks even.

To check this, we'll compute the cost and revenue

C(x) = 14x+117

C(117) = 14*117+117

C(117) = 1755

R(x) = 15x

R(117) = 15*117

R(117) =  1755

The cost and revenue is $1755 for each. Because we get the same value, this confirms the correct x value.

Since 117 people is the breakeven point, the company should aim for an attendee count above this, so they can get a positive profit. At some point, there is a max capacity so x can't go up forever.

7 0
2 years ago
Solve for y in the following system of equations: −x+y=0 −2x+y=−5 1. 5 2. 7 3. 6 4. 5
lord [1]

Answer:

y = 5

Step-by-step explanation:

−x+y=0   −2x+y=−5

Multiply the first equation by -2

-2(-x+y=0)

2x-2y =0

Add this to the second equation

 2x-2y =0

−2x+y=−5

-------------------

0x -y = -5

-y =-5

Multiply by -1

y = 5

8 0
3 years ago
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