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ziro4ka [17]
3 years ago
5

Please Identify the congruent triangles in the figure.

Mathematics
1 answer:
Tpy6a [65]3 years ago
5 0

The missing steps are each right angles and \angle R \cong \angle O.

Solution:

Step 1: Given data:

\overline {P Q} \cong \overline{M N}

\overline{Q R} \cong \overline{N O}

\overline{P R} \cong \overline{M O}

Step 2: In the two polygons,

\angle Q =90^\circ and \angle N =90^\circ

\angle Q \cong \angle N (Each right angle)

Step 3: Given

\angle P \cong \angle M

Step 4: By third angle theorem,

If two angles in one triangle are congruent to the two angles in the other triangle, then the third angles in the triangles also congruent.

\angle R \cong \angle O

Step 5: By the definition of congruent polygons,

If two same shape polygons have all the angles are congruent and all the corresponding sides are congruent then the polygons are congruent.

Hence \Delta P Q R \cong \Delta M N O.

Therefore the missing steps are each right angles and \angle R \cong \angle O.

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This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 681
aleksley [76]

Answer:

680 games

Step-by-step explanation:

Suppose that 681 tennis players want to play an elimination tournament.

1st round:

One of 681 players, chosen at random, sits out that round and 680 players play. There will be 340 winners plus one player which sits - 341 players for the next round and 340 games

2nd round:

There will be 170 winners plus one player which sits - 171 players for the next round and 170 games

3rd round:

There will be 85 winners plus one player which sits - 86 players for the next round and 85 games

4th round:

There will be 43 winners - 43 players for the next round and 43 games

5th round:

There will be 21 winners plus one player which sits - 22 players for the next round and 21 games

6th round:

There will be 11 winners  - 11 players for the next round and 11 games

7th round:

There will be 5 winners plus one player which sits - 6 players for the next round and 5 games

8th round:

There will be 3 winners  - 3 players for the next round and 3 games

9th round:

There will be 1 winner plus one player which sits - 2 players for the next round and 1 game

10th round - final:

1 champion and 1 game.

In total,

340 + 170 + 85 + 43 + 21 + 11 + 5 + 3 + 1 + 1 = 680 games

4 0
3 years ago
Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k.
rewona [7]
Step 1
Find the equation of f(x)
we have the points
(-10,-6) and (0,4)
Find the slope m

The function in slope intercept form is equal to

we have

-----> the point (0,4) is the y-intercept
substitute

step 2
Find the equation of g(x)
we have the points
(-2,-6) and (0,4)
Find the slope m

The function in slope intercept form is equal to

we have

-----> the point (0,4) is the y-intercept
substitute

step 3
Find the value of k
we have

-----> equation A
-----> equation B
----> equation C
substitute equation A and equation C in equation B and solve for k

3 0
3 years ago
30% of 60 is <br><br> 30%of ____ is 60
ololo11 [35]
You know that 3 times 2 is 6 so 30'times 20 equals 60
6 0
3 years ago
Read 2 more answers
Let P(A)=47 and P(B|A)=38. What is the probability of events A and B occurring? Enter your answer in the box as a fraction in si
ella [17]

The value of the probability is 3/14

<h3>How to solve the probability?</h3>

The given parameters are:

P(A) = 4/7

P(B | A) = 3/8

The probability of events A and B occurring is calculated using:

P(A and B) = P(B | A) * P(A)

So, we have:

P(A and B) = 3/8 * 4/7

Evaluate the product

P(A and B) = 3/14

Hence, the value of the probability is 3/14

Read more about probability at:

brainly.com/question/25870256

#SPJ1

7 0
2 years ago
Solving a word problem using a two-step med
stepladder [879]

Inequality is 6t  ≤ 44 and Jim can rent a boat for 7.33 hrs or less

<u> Solution:</u>

Given that  

Maximum amount Jim can spend to rent a boat = $34

Rental cost of boat for 1 hour = $6

Also Jim has a discount coupon for $8 off.

Need to determine possible number of hours Jim could rent a boat.

Let’s assume possible number of hours Jim could rent a boat be represented by variable "t"

Cost of renting boat for 1 hour = 6

So Cost of renting a boat for t hours = t x renting boat for 1 hour = t x 6 = 6t

Also Maximum amount Jim can spend to rent a boat = $34

As Jim has a discount coupon for $8 off, so Total amount Jim can spend to rent a boat = $ 34 + $ 8 = $ 44

So cost of renting a boat for t hours must be less that of equal to Total amount Jim can spend to rent a boat

=> 6t  ≤ 44

On solving above equality for "t" we get ,

\begin{array}{l}{t \leq \frac{44}{6}} \\\\ {=>\mathrm{t} \leq 7.3333 \mathrm{hrs}}\end{array}

Hence inequality is  6t  ≤ 44 and Jim can rent a boat for 7.33 hrs or less.

5 0
2 years ago
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