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3 years ago

Given the incomplete proof below, what is the missing reason for the statement in step 4?

Mathematics

1 answer:

LuckyWell [14K]3 years ago

8 0

Answer:

ASA Congruence Theorem

Step-by-step explanation:

Already,it has been stated and proved that two angles (<ABC and <CAB) and an included side (AB) in ∆ABC are congruent to corresponding two angles (<ABD and <DAB) and an included side (AB) in ∆ABD.

Therefore, based on the ASA Congruence Theorem, ∆ABC is congruent to ∆ABD.

The missing reason is "ASA Congruence Theorem"

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On a certain hot summer's day, 581 people used the public swimming pool. The daily prices are $1.50 for children and $2.50 for

Tanya [424]

Answer:

A = 219

C = 362

Step-by-step explanation:

Given,

581 = C + A

and

$1090.50 = 1.5C + 2.5A

solve 1st for A

A =581 - C

substute into 2nd

1090.50 = 1.5C + 2.5(581 - C)

solve for C

1090.50 = 1.5C + 1452.50 - 2.5C

1090.50 = -C + 1452.50

1090.50 - 1452.50 = -C

-362 = -C

C = 362

then

581 = C + A

581 = 362 + A

219 = A

A = 219

8 0

3 years ago

Of the cars sold during the month of July, 89 had air conditioning, 99 had an automatic transmission, and 74 had power steering.

DedPeter [7]

Answer:

There are a total of 23 cars with air conditioning and automatic transmission but not power steering

Step-by-step explanation:

Let A be the cars that have Air conditioning, B the cars that have Automatic transmission and C the cars that have pwoer Steering. Lets denote |D| the cardinality of a set D.

Remember that for 2 sets E and F, we have that

$|E \cup F| = |E| + |F| - |E \cap F|$

Also,

|E| = |E ∩F| + |E∩F^c|

We now alredy the following:

|A| = 89

|B| = 99

|C| = 74

$|A \cap B \cap C| = 5$

|(A \cup B \cup C)^c| = 24

|A \ (B U C)| = 24 (This is A minus B and C, in other words, cars that only have Air conditioning).

|B \ (AUC)| = 65

|C \ (AUB)| = 26

$|B \cap C| = 11$

We want to know |(A∩B) \ C|. Lets calculate it by taking the information given and deducting more things

For example:

99 = |B| = |B ∩ C| + |B∩C^c| = 11 + |B∩C^c|

Therefore, |B∩C^c| = 99-11 = 88

And |A ∩ B ∩ C^c| = |B∩C^c| - |B∩C^c∩A^c| = |B∩C^c| - |B \ (AUC)| = 88-65 = 23.

This means that the amount of cars that have both transmission and air conditioning but now power steering is 23.

3 0

3 years ago

If 2tanA=3tanB,then prove that tan(A-B)=sin2B/(5-cos2B) ...?

andreev551 [17]

Tan ( A - B ) = ( tan A - tan B ) / ( 1 + tan A tan B )
tan A = 3 tan B/2
tan ( A - B ) = ((3 tan B/ 2)-tan B) / ( 1 + 3 tan² B/2)=
= (tan B/2) / ( 2 + 3 sin²B/cos²B )=
= (sin B / cos B) / (( 2cos² B+3sin²B)/cos²B)=
=( sin B cos B ) / ( 2 cos²B + 3 ( 1 - cos² B ) ) =
= (sin B cos B ) / ( 2 cos² B + 3 - 3 cos² B ) =
= ( sin 2 B ) / 2 ( 3 - cos² B ) =
= ( sin 2 B ) / ( 6 - cos² B )=
= ( sin 2 B ) / ( 5 + 1 - 2 cos² B )=
= ( sin 2 B ) / ( 5 + sin² B + cos ² B - 2 cos² B ) =
= ( sin 2 B ) / ( 5 - ( cos² B - sin² B ) ) =
= ( sin 2 B ) / ( 5 - cos 2 B ) - correct

8 0

3 years ago

Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the

djverab [1.8K]

I believe the correct answer is 3×13^4+2×15^4=total area

4 0

3 years ago

-y varies inversely with x. If y = 8 and k (the constant of variation) = 19, what is x?

Dimas [21]

Answer:

Part 1) $x=2.375$