1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
stira [4]
3 years ago
10

The congruence theorem that can be used to prove ALON

Mathematics
1 answer:
Arisa [49]3 years ago
3 0

Answer:

SSS is the congruence theorem that can be used to prove Δ LON  is congruent to Δ LMN ⇒ 1st answer

Step-by-step explanation:

Let us revise the cases of congruence

  • SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
  • SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ
  • ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ
  • AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ
  • HL ⇒ hypotenuse leg of the 1st right Δ ≅ hypotenuse leg of the 2nd right Δ  

In triangles LON and LMN

∵ LO ≅ LM ⇒ given

∵ NO ≅ NM ⇒ given

∵ LN is a common side in the two triangles

- That means the 3 sides of Δ LON are congruent to the 3 sides

   of Δ LMN

∴ Δ LON ≅ LMN ⇒ by using SSS theorem of congruence

SSS is the congruence theorem that can be used to prove Δ LON  is congruent to Δ LMN

You might be interested in
PLS HELP ME I HAVE ONLY 10 MINS
anastassius [24]
Sorry habibti it’s okay tho f school
8 0
2 years ago
The answer to the problem
frez [133]

Could you take a better picture please?

6 0
3 years ago
There are eight different jobs in a printer queue. Each job has a distinct tag which is a string of three upper case letters. Th
Vikentia [17]

Answer:

a. 40320 ways

b. 10080 ways

c. 25200 ways

d. 10080 ways

e. 10080 ways

Step-by-step explanation:

There are 8 different jobs in a printer queue.

a. They can be arranged in the queue in 8! ways.

No. of ways to arrange the 8 jobs = 8!

                                                        = 8*7*6*5*4*3*2*1

No. of ways to arrange the 8 jobs = 40320 ways

b. USU comes immediately before CDP. This means that these two jobs must be one after the other. They can be arranged in 2! ways. Consider both of them as one unit. The remaining 6 together with both these jobs can be arranged in 7! ways. So,

No. of ways to arrange the 8 jobs if USU comes immediately before CDP

= 2! * 7!

= 2*1 * 7*6*5*4*3*2*1

= 10080 ways

c. First consider a gap of 1 space between the two jobs USU and CDP. One case can be that USU comes at the first place and CDP at the third place. The remaining 6 jobs can be arranged in 6! ways. Another case can be when USU comes at the second place and CDP at the fourth. This will go on until CDP is at the last place. So, we will have 5 such cases.

The no. of ways USU and CDP can be arranged with a gap of one space is:

6! * 6 = 4320

Then, with a gap of two spaces, USU can come at the first place and CDP at the fourth.  This will go on until CDP is at the last place and USU at the sixth. So there will be 5 cases. No. of ways the rest of the jobs can be arranged is 6! and the total no. of ways in which USU and CDP can be arranged with a space of two is: 5 * 6! = 3600

Then, with a gap of three spaces, USU will come at the first place and CDP at the fifth. We will have four such cases until CDP comes last. So, total no of ways to arrange the jobs with USU and CDP three spaces apart = 4 * 6!

Then, with a gap of four spaces, USU will come at the first place and CDP at the sixth. We will have three such cases until CDP comes last. So, total no of ways to arrange the jobs with USU and CDP three spaces apart = 3 * 6!

Then, with a gap of five spaces, USU will come at the first place and CDP at the seventh. We will have two such cases until CDP comes last. So, total no of ways to arrange the jobs with USU and CDP three spaces apart = 2 * 6!

Finally, with a gap of 6 spaces, USU at first place and CDP at the last, we can arrange the rest of the jobs in 6! ways.

So, total no. of different ways to arrange the jobs such that USU comes before CDP = 10080 + 6*6! + 5*6! + 4*6! + 3*6! + 2*6! + 1*6!

                    = 10080 + 4320 + 3600 + 2880 + 2160 + 1440 + 720

                    = 25200 ways

d. If QKJ comes last then, the remaining 7 jobs can be arranged in 7! ways. Similarly, if LPW comes last, the remaining 7 jobs can be arranged in 7! ways. so, total no. of different ways in which the eight jobs can be arranged is 7! + 7! = 10080 ways

e. If QKJ comes last then, the remaining 7 jobs can be arranged in 7! ways in the queue. Similarly, if QKJ comes second-to-last then also the jobs can be arranged in the queue in 7! ways. So, total no. of ways to arrange the jobs in the queue is 7! + 7! = 10080 ways

5 0
3 years ago
PAGE 6
Ann [662]

a) A mathematical equation that represents the total cost, t, for a adult tickets and c child tickets is t = $5a + $3c.

b)No, she cannot buy 2 adult tickets and 7 child tickets.

<h3>Define equation.</h3>

Mathematical equations are relationships between two expressions that are equal on both sides of the equal to sign. An equation is, for instance, 3y = 16.

Given,

Maymont Middle School is selling tickets for the winter musical. Adult tickets cost $5 each and child tickets cost $3 each.

a) Mathematical equation:

represents the total cost, t, for a adult tickets and c child tickets

t = $5a + $3c

A mathematical equation that represents the total cost, t, for a adult tickets and c child tickets is t = $5a + $3c.

b) Ciera has $28.

a = 2 c = 7

Equating values in equation,

= $5(2) + $3(7)

= $10 + $27

= $37

No, she cannot buy 2 adult tickets and 7 child tickets.

To learn more about equation, visit:

brainly.com/question/10413253

#SPJ1

4 0
1 year ago
Which term describes the set of all possible output values for a function?
Liula [17]
The correct answer is C. Domain
4 0
3 years ago
Read 2 more answers
Other questions:
  • Trevor’s total employment compensation is $33,500. If Trevor has no job expenses and his gross pay is $28,600, then his total em
    10·2 answers
  • PLLLEEEAAASSSEEEE IT IS URGENT I NEED ANSWERS TO NO 17 FAST !!!!! PLZ I WILL MARK BRAINLIEST​
    11·2 answers
  • ohn is interested in purchasing a multi-office building containing five offices. The current owner provides the following probab
    6·1 answer
  • What does (4v+16v^2) equal to ?
    14·1 answer
  • Need answer. pls help​
    8·1 answer
  • HELP MEH PLZ!!
    9·1 answer
  • A television at Walmart cost $1,538 and $1,923 at Target. With taxes, what would you actually pay at each store. Walmart sales t
    6·1 answer
  • Plz help<br> what is the greatest common factor 9xy-y<br> then divide it with the number.
    12·1 answer
  • Solve the following.<br> 2x^2-7x-4/6x^2+7x+2&lt;0<br> Can someone explain how to solve this.
    11·1 answer
  • Find the measure of a positive angle and a negative angle that are coterminal with 100° sketch of three angles labeling clearly
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!