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3 years ago

Complete the following proof. Prove: In an isosceles triangle, two medians are equal.

Mathematics

1 answer:

Paraphin [41]3 years ago

8 0

Answer:

Midpoint of AB = (0 + 2a / 2 , 0 + 0 / 2) = (2a / 2 , 0 / 2) = (a,0)

x coordinate of point c = a

N = (0 + a / 2 , 0 + b / 2) = (a / 2 , b / 2)

M = ( 2a + a / 2 , 0 + b / 2) = (3a / 2 , b / 2)

MA = √(3a / 2 - 0)² + b / 2 - 0)²

= √(3a / 2 )² + (b / 2) = 9a² / 4 + b² / 4

NB = √(a / 2 - 2a)² + (b / 2 - 0 )²

= √( a / 2 - 4a / 2)² + (b / 2 - 0)²

= √(-3a / 2)² + (b / 2)² = √9a² / 4 + b² / 4

Step-by-step explanation:

I tried my best hope its correct :0

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Dovator [93]

15 minutes= 2 problems
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3 years ago

Read 2 more answers

Given sin b = .88 find angle b in radians

Rama09 [41]

$sin^{-1}0.88=61.642\ degrees$
There are pi radians in 180 degrees. Therefore to convert degrees to radians we need to divide by 180 and multiply by pi, as follows:
$\frac{61.642}{180}\times \pi=1.076\ radians$

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3 years ago

Mr. Montes is writing a short, three-question, true or false quiz for his Algebra 2 classes. He had planned on using a random an

belka [17]

Answer:

There are 4 questions to answer here and the answers are given below:

1. COMBINATION

2. SET 2

3. {S2, S3, S4, S5}

4. { } OR ∅

Step-by-step explanation:

The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.

The assignment has 5 questions in all. The options for each question are listed below and separated by commas:

1. True, False

2. True, False

3. A, B, C, D

4. A, B, C, D

5. A, B, C, D

Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.

QUESTION 1

If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?

ANSWER TO QUESTION 1

You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only two possible answers (also known as options) while questions 3, 4 and 5 have four possible answers/options to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.

QUESTION 2

Find "Set 1 ∩ Set 2" and explain the notation in the sentence.

ANSWER TO QUESTION 2

First list out relevant information:

- The correct answers to questions 3, 4 and 5 are respectively C, B, A

- The universal set consists of five students: S1, S2, S3, S4, S5 hence

Ц = {S1, S2, S3, S4, S5}

Next, enlist the elements of each defined set

Set 1: {S1, S2, S3, S4, S5} Set 2: {S2, S3, S4} Set 3: {S4, S5}

Note: Set 1 is equal to the universal set.

Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.

In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.

If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:

The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.

So the answer to question 2 is

Set 1 ∩ Set 2 = Set 2

QUESTION 3

Find "Set 2 ∪ Set 3" and explain the notation in the sentence.

ANSWER TO QUESTION 3

The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.

So, Set 2 union Set 3 = {S2, S3, S4, S5}

As earlier stated, Student 4 isn't appearing twice in the new set.

QUESTION 4

Find the ' of Set 1 and explain the notation in this sentence.

ANSWER TO QUESTION 4

The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.

Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!

Set 1 ' Ц = { } or ∅

where the empty bracket symbol and the slashed zero symbol represent null set.

Kudos!

3 0

3 years ago

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

gizmo_the_mogwai [7]

Answer:

The large sample n = 1713.96

Step-by-step explanation:

Explanation:-

given the population proportion was estimated to be 0.22

population proportion (P) = 0.22

The 95 % level of significance = 1.96≅ 2

The margin of error = 0.02

The formula of margin error

$\frac{2\sqrt{p(1-p)} }{\sqrt{n} } = 0.02$ … ( i )

Substitute 'p' values in equation (1)

$\frac{2\sqrt{0.22(1-0.22)} }{\sqrt{n} } = 0.02$

cross multiplication and simplification, we get

$2X0.414= 0.02 \sqrt{n}$

$\frac{2X0.414}{0.02} = \sqrt{n}$

$41.4 = \sqrt{n}$

squaring on both sides, we get

the large sample n = 1713.96

7 0

3 years ago

What is the input of a transformation?

Semmy [17]

Operations are processes that take in a set of input resources which are used to transform something, or are transformed themselves, into outputs of products and services.

6 0

3 years ago