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Rufina [12.5K]
4 years ago
15

How do you determine if polygons are similar?

Mathematics
1 answer:
Vikentia [17]4 years ago
8 0

Answer:

  a) corresponding angles of similar polygons are congruent

  b) corresponding sides of similar polygons are proportional

  c) a triangle is a polygon

Step-by-step explanation:

By <em>definition</em>, similar polygons have congruent corresponding angles and proportional corresponding sides.

A triangle is a polygon, so two triangles will be similar if they have congruent corresponding angles and proportional corresponding sides.

___

For an n-sided polygon, one only needs to show the conditions are met for n-1 angles and sides. Those will determine the measures of the final angle/side.

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Please help me i don’t understand
kotykmax [81]

537Answer:

Step-by-step explanation:73853ndnxhxnkxgsjdd

8 0
3 years ago
Suppose the names of the months of the year are placed in a hat and a name is drawn at random. (a) list the sample space for thi
ollegr [7]

(a)

The sample space is a set whose elements are all the possible outcomes for the experiment. Since we will extract one of the months of the years, the sample space is the set composed by all the 12 months:

\Omega = \{ \text{January},\ \text{February},\ldots,\text{December}\}

(b)

An event is a subset of the sample space. Events are often defined by their properties. In this example, the event E is the subset of the sample space defined as

E = \{ x \in \Omega: x \text{ starts with the letter J}\}

So, we have

E = \{\text{January},\ \text{June},\ \text{July}\}

(c)

If all outcomes have equal probability, then the probability of an event is the ratio bewteen its cardinality, and the cardinality of the whole sample space:

P(E) = \dfrac{n(E)}{n(\Omega)} = \dfrac{3}{12} = \dfrac{1}{4}

In words, since there are three months beginning with J out of 12 months, we have a probability of 3 over 12 to pick a month starting with J, which simplifies to 1 over 4.

3 0
3 years ago
Four different digits from 1 to 9 are required to open a safe.
masha68 [24]

Answer:  5942

<u>Step-by-step explanation:</u>

Clue 4 states exactly two of the digits = 1, 4, or 9

Clue 1 leaves us with the following combinations:

1, 9, 2, 8

1, 9, 3, 7    eliminate by clue 5

4, 9, 2, 5

1, 4, 7, 8

Clue 5 directs us to the following order for 1,9,2,8

2 __ __ 1     --> 2981 or 2891   eliminate by clue 2

9 __ __ 8    --> 9128 or 9218   eliminate by clue 6

9 __ __ 2    --> 9182 or 9812   eliminate by clue 6

Clue 5 directs us to the following order for 4,9,2,5

5 __ __ 2     --> 5492 or 5942   eliminate 5492 by clue 2

9 __ __ 2    --> 9452 or 9542   eliminate by clue 3

Clue 5 directs us to the following order for 1,4,7,8

4 __ __ 1    --> 4781 or 4871    eliminate by clue 2

The only combination not eliminated is 5-9-4-2, which satisfies all six clues.

1) 5 + 9 + 4 + 2 = 20

2) 5 > 4

3) 9 - 2 > 5

4) 4 & 9 but not 1 are included

5) 5 + 2 = 7, which is a prime number

6) 2 <  5, 9, 4

5 0
3 years ago
Round 76070.7376413 to 2 decimal places
lakkis [162]
<h3>Answer:</h3><h2>76,070.74</h2><h3>Step-by-step explanation:</h3>

When you round decimals, your looking at the place value, then your looking at the place value next to it.

<u>If you see a number that is 0 - 4 behind the place value your rounding to, you do nothing to the place value.</u>

<u>If you see a number that is 5 - 9 behind the place value your rounding to, you add one to the place value.</u>

<h3><u>Example 1:</u></h3>

Round the Number 71.25 to the <u>Tenths place.</u>

<u>When we go to the place value, Tenths, we go behind the Tenths place value:</u>

71.<em>2</em><u>5</u>

<u>2 is the Tenths place value, 5 is the place value behind the Tenths place value.</u>

<u>Since 5 is able to be rounded up, you add one to the tenths place.</u>

<u>It should be rounded to 71.3. There cannot be numbers where you've rounded, just zeroes.</u>

<h3><u>Example 2:</u></h3>

Round the Number <u>3,345.8493</u> to the <u>Thousands place.</u>

3 is the Thousands place, 3 is the place value behind the Thousands place value.

3 is not in between 5 - 9. So, the rounded answer is 3,000.

When numbers behind the Place Value cannot round the Thousands place value, it turns into zeroes too.

Answer:

Round  76070.7376413 to the Hundredths place value.

The 3 is the Hundredths place value, the 7 is the place value behind the Hundredths place value.

7 qualifies for the numbers 5 - 9.

Therefore, you add 1 to the hundredths place value.

Your final answer is (76,070.74)

Best of Luck to you.

If you have any questions, feel free to comment below.

Merry Christmas!

8 0
3 years ago
Solve for x.<br><br> 2(4x− 9) = 5(x − 4)
cluponka [151]

Answer:

2(4x− 9) = 5(x − 4)

=>8x- 18= 5x-20

=>8x-5x= -20+18

=>3x = -2

=>x= -2/3

8 0
3 years ago
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