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3 years ago

UV and RV are secant segments that intersect at point V.

Mathematics

2 answers:

Nonamiya [84]3 years ago

8 0

Answer:

a=3

Step-by-step explanation:

<u>Intersecting Secants Theorem</u>

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Applying the theorem of Intersecting Secants in the diagram

$TV\cdot UV=SV\cdot RV$

$a*12=4X9\\12a=36\\a=36\div12\\a=3$

Therefore, the value of a=3

dusya [7]3 years ago

4 0

Answer:

The answer to this question is 3

Step-by-step explanation:

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Rose spent 124 on 10 cars & 4 cats what is the cost for 1 car & 1 cat.

Rudiy27

Answer:

$6 per cat, $10 per car

Step-by-step explanation:

I guess and checked my work.

4 0

3 years ago

Determine whether the statements in (a) and (b) are logically equivalent.

Andru [333]

Answer:

The two statements are logically equivalent.

Step-by-step explanation:

Let X be the statement that Bob is a double math and computer science major.

Y be the statement that Ann is a maths major.

Z be the statement that Ann is a double maths and computer science major.

The two statements written in terms of X, Y and Z now

a. Bob is a double math and computer science major and Ann is a math major, but Ann is not a double math and computer science major.

(x and y) and not z

b. It is not the case that both Bob and Ann are double math and computer science majors, but it is the case that Ann is a math major and Bob is a double math and computer science major.

not (x and z) and (x and y)

Noting that for logical statements,

Negation is represented by ~

And is represented by conjunction sign Λ

Or is represented by disjunction sign V

(x and y) and not z

(x Λ y) Λ (~z)

not (x and z) and (x and y)

~(x Λ z) Λ (x Λ y)

We can then simplify the second statement to obtain the first statement and prove the equivalence of both sides

~(x Λ z) Λ (x Λ y)

Using DE MORGAN'S theory, ~(x Λ z) = (~x) V (~z)

~(x Λ z) Λ (x Λ y) = ((~x) V (~z)) Λ (x Λ y)

Then applying the distributive law to the expression, we can open the bracket up

((~x) V (~z)) Λ (x Λ y)

= ((~x) Λ (x Λ y)) V ((~z) Λ (x Λ y))

Opening the first bracket up further

((~x) Λ (x Λ y)) V ((~z) Λ (x Λ y))

= ((~x) Λ x) Λ y) V ((~z) Λ (x Λ y))

The NEGATION law shows that (~x Λ x) = c (where c is a negation law parameter for when two opposite statements are combined in this manner, it works like a 0 in operation)

((~x) Λ x) Λ y) V ((~z) Λ (x Λ y))

= (c Λ y) V ((~z) Λ (x Λ y))

But (c Λ y) = (y Λ c) = c (according to the UNIVERSALLY BOUND law, see how c works like a 0 now?)

(c Λ y) V ((~z) Λ (x Λ y))

= c V ((~z) Λ (x Λ y))

= ((~z) Λ (x Λ y)) V c (commutative)

And one of the foremost IDENTITY laws is that (any statement) V c = c

((~z) Λ (x Λ y)) V c

= ((~z) Λ (x Λ y))

= (x Λ y) Λ (~z)

Which is the same as the first statement!

PROVED!!!

Hope this Helps!!!

5 0

3 years ago

Read 2 more answers

What if 30% of volcanoes were in california?

EleoNora [17]

Then 70% of volcanos wouldn't be in California.

7 0

3 years ago

A sheet of paper has a perimeter of 39 in. If the width of the paper is 8.5 in. What is the length of the sheet of paper?

natta225 [31]

Perimeter of a rectangle = 2L + 2W

Perimeter = 39
W = 8.5

we plug those into the perimeter equation and get
2L + 2(8.5) = 39

simplify
2L + 17 = 39

subtract 17 from both sides
2L = 22

divide both sides by 2
L = 11

therefore the length of the sheet of paper is 11 in.

7 0

3 years ago

Read 2 more answers

You created a new playlist in 100 of your friends listened to it and shared if they likedThe new playlist or not nadhi said the

Nostrana [21]

Given

You created a new playlist in 100 of your friends listened to it and shared if they liked

The new playlist said the ratio Of people who liked the playlist to those who did not like the playlist is 75:25.

Dylan said that for every three people who like to playlist one person did not

Find out Do Nadhii and Dylan Agree or not.

To proof

As given in the question

created a new playlist in 100 of your friends listened to it and shared if they liked

new playlist said the ratio Of people who liked the playlist to those who did not like the playlist is 75:25.

Simply the ratio of people who liked the playlist to those who did not like the playlist

$= \frac{75}{25}$

$= \frac{3}{1}$

Thus

$\frac{People \ like \ the \ playlist}{People \ didnot \ like \ the\ playlist}=\frac{3}{1}$

also

Dylan said that for every three people who like to playlist one person did not

In the form of ratio written as

$\frac{People \ like \ the \ playlist}{People \ didnot \ like \ the\ playlist}=\frac{3}{1}$

the value of both new playlist and Dylan said about the ratio of people who liked the playlist to those who did not like the playlist is 3:1.

The value both of their ratio are equivalent .

Thus Nadhii and Dylan Agree

Hence proved

7 0

3 years ago