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3 years ago

In ∆ABC, the median AM (M ∈ BC ) is perpendicular to the angle bisector BK (K ∈ AC ). Find AB, if BC = 12 in. Show with work

Mathematics

1 answer:

otez555 [7]3 years ago

3 0

Call the point where BK intersects AM point X. BX is the altitude of ∆ABM, and it is also the angle bisector of angle ∠ABM. Hence ∆ABM is isosceles, and AB ≅ MB.

M is the midpoint of BC, which is 12 inches long. Hence MB is half that length, or 6 inches.

Since AB is the same length as MB, which is 6 inches, ...

... AB is 6 inches.

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A number cube with faces labeled 1 to 6 is rolled once.

Zepler [3.9K]

Answer:

a) A ∪ B = {2, 4, 5, 6}

b) A ∩ B = {6}

c) $\sf B^c$ = {1, 3, 5}

Step-by-step explanation:

Set notation is used in math to list numbers, objects or outcomes.

It uses curly brackets called "braces". Objects placed within the braces are the elements of the set.

The listing method of set notation simply lists the numbers in the set.

The three dots "..." means it is infinite (goes on forever).

Given:

A number cube with faces labeled 1 to 6.

Therefore the set of all possible outcomes is {1, 2, 3, 4, 5, 6}.

Event A

The number rolled is greater than 4.

Therefore, the set of outcomes for event A is {5, 6}.

Event B

The number rolled is even.

Therefore, the set of outcomes for event B is {2, 4, 6}.

Part (a)
Event "A or B" means the outcomes in A or B or both.

⇒ A ∪ B = {2, 4, 5, 6}

Part (b)

Event "A and B" means the outcomes in both A and B.

⇒ A ∩ B = {6}

Part (c)

The complement of event B means everything that is not in B.

$\sf \implies B^c =$ {1, 3, 5}

Learn more about set notation here:

brainly.com/question/27913822

4 0

1 year ago

Could you help me with this. Express in simplest radical form. 162

Ivanshal [37]

Answer:

The square root of 162 in its simplest form means to get the number 162 inside the radical √ as low as possible.

Here is how to do that! First we write the square root of 162 like this:

√162

The largest perfect square of the factors of 162 is 81. We can therefore convert √162 like this:

√81 × 2

Next, we separate the numbers inside the √ as such:

√81 × √2

√81 is a perfect square that equals 9. We can therefore put 9 outside the radical and get the final answer to square root of 162 in simplest radical form as follows:

9√2

Step-by-step explanation:

7 0

3 years ago

What is the cost of a $19,500 plus a 6% sales tax?

vova2212 [387]

1% of 19,500= 195

6% = 1%x6 = 195x6 = 1170

19500+1170=20670

3 0

3 years ago

Replace the ? in each of these statements with the symbol >, <, or =.

saveliy_v [14]

39>38