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3 years ago

In the figure, FQ is parallel to RS". The length of PT is 3 cm; the length of PQ

Mathematics

1 answer:

sasho [114]3 years ago

3 0

Answer:

The measure of length RT is 9 cm .

Step-by-step explanation:

Given figure as :

The Triangle TRS and Triangle TPQ are similar triangles

I.e Δ TRS ≈ Δ TPQ

And The measure of side PT = 3 cm

The measure of side PQ = 5 cm

The measure of side RS = 15 cm

Let The measure of side RT = x cm

So, From the property of similar triangles

$\dfrac{\textrm measure of side TR}{\textrm measure of side TP}$ = $\dfrac{\textrm measure of side RQ}{\textrm measure of side PQ}$

I.e $\dfrac{TR}{TP}$ = $\dfrac{RS}{PQ}$

Or, $\dfrac{x}{3}$ = $\dfrac{15}{5}$

Or, $\dfrac{x}{3}$ = 3

∴ x = 3 × 3

I.e x = 9 cm

Hence The measure of length RT is 9 cm . Answer

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?Write the phrase as a rate in simplest form. ?260 inches in 15 seconds ?

melomori [17]

Answer: 52:3

Step-by-step explanation:

260 divided by 5 = 52

15 divided by 5 = 3

260:15 = 52:3

6 0

3 years ago

A mouse is trapped in a maze. To

Svetradugi [14.3K]

Answer: Approximately 9.43 meters

The more accurate version is 9.4339811320566 but that's not exact.

This is exact magnitude is sqrt(89)

=======================================================

Explanation:

Let's draw an xy grid for this. Place the starting point at (0,0) which I'll call point A. Now let's say the mouse goes east 15 meters. That would move it to (15,0) which is marked as point B. Refer to the diagram below.

From point B, we move to C which is at (15,8). So the mouse has gone 8 meters north. It might help to turn the page so that the east direction is facing completely north, and then look to the left and you'll see "north". In other words, each 90 degree left turn is a 90 degree counterclockwise turn.

After doing another 90 degree counterclockwise turn, the mouse will move 10 meters westward. It moves from C(15,8) to D(5,8). Point D is the final position of the mouse.

-----------------------

A(0,0) was the initial position and D(5,8) is the final position

The vector v is

v = <5,8>

This is because we basically are saying "the mouse ultimately moved 5 meters east and 8 meters north" when going from start to finish. We're ignoring the intermediate stops along the way.

------------------------

Recall that for any vector of the form

v = <a,b>

the magnitude of that vector is

|v| = sqrt(a^2+b^2)

this is the length of the vector based on the pythagorean theorem.

Applying this formula gets us

|v| = sqrt(5^2+8^2)

|v| = sqrt(89)

|v| = 9.43398 approximate

This represents the straight line distance from start to finish, where we ignore any intermediate stops. So this isn't the distance the mouse travels (since it goes from A to B, to C to D). Instead, it's the distance it would travel if it wanted to take the shortest path from A to D.