Which statement best describes the relationship shown in the table?

Which is a correct two-column proof? Given: r || s Prove: ∠b and ∠h are supplementary. Picture 1, Picture 2, Picture 3 or none o

aliina [53]

Answer: The second proof table is the the proper proof table.

We always start out with what we are given, which in this case is r || s saying that r is parallel to s. Also, we always end up with what we want to prove which is angles b and h are supplementary. So this is the last line of the proof.

So far, this eliminates the first proof table because in this table, the last line says "angle c and angle h are supplementary" which is not what we want to end up with. We want the last line to say "angle b and angle h are supplementary".

We can also eliminate the third proof table because of the statement "angle d and angle h are supplementary". They are only supplementary if they are both right angles. Also, the reasoning of "alternate interior angles" is false as they are corresponding angles.

The only thing left is the second proof table which is correctly argued from start to finish.

1. r || s ........................ given

2. angle b = angle c ................ vertical angles

3. c and e are supplementary angles ....... same side interior

4. angle e = angle h ................. vertical angles

5. b and h are supplementary ...... substitution

Note: in line 5, we start with line 3's statement. Then we replace 'c' with 'b', at the same we replace 'e' with 'h'.

8 0

3 years ago

Read 2 more answers

Your friend comes from a large family. This list shows the ages of all of the children in her family. What is the median age of

Vilka [71]

The median would be 12!

3 0

3 years ago

Read 2 more answers

The point-slope form of a line is y - y1 = m(x-x1), where m is the slope and (x1,

Vlada [557]

Answer

False

FalseThe correct point slope form passing through points (x1,y1) is (y-y1)=m (x-x1)(y−y1)=m(x−x1)

4 0

2 years ago

Naval intelligence reports that 4 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 9 vessels are randomly targete

icang [17]

Answer:

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Step-by-step explanation:

The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

Fleet of 17 means that $N = 17$

4 are carrying nucleas weapons, which means that $k = 4$

9 are destroyed, which means that $n = 9$

What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?

This is:

$P(X > 1) = 1 - P(X \leq 1)$

In which

$P(X \leq 1) = P(X = 0) + P(X = 1)$

So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294$

$P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118$

Then

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412$

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588$

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

8 0

2 years ago

The distance between itahari and Damak is

Ludmilka [50]

Answer:

8 km by motorbike.

Step-by-step explanation:

The distance between itahari and Damak is 42 km.

Mr. Dhamala travelled 18.325 km by a bus / 15.675 km by a taxi and the remaining distance by a motorbike.

Let he covered x distance by motorbike. So,

Remaining distance = Total distance -(distance covered by bus + distance by taxi)

= 42 -(18.325 +15.675 )

= 42-34

= 8 km

So, he travelled 8 km by motorbike.

8 0

2 years ago