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AnnZ [28]
2 years ago
11

TU = 3, RS = 15, TW = 4, TR = 9; Assume that the sides of triangle TUW are proportional to the sides of triangle TRS. What is th

e length of WS? 8 12 15 24

Mathematics
2 answers:
sertanlavr [38]2 years ago
5 0
The answer is 8. Hope it helped!
VMariaS [17]2 years ago
3 0

Answer:

  WS=8\ units

Step-by-step explanation:

we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal and the corresponding angles are also equal

In this problem

\frac{TU}{TR}=\frac{UW}{RS}=\frac{TW}{TS}

we have

TU=3\ units, RS=15\ units, TW=4\ units,TR=9\ units

Find the value of TS

\frac{TU}{TR}=\frac{TW}{TS}

substitute

\frac{3}{9}=\frac{4}{TS}

TS=36/3=12\ units

WS=TS-TW

WS=12-4=8\ units

see the attached figure to better understand the problem

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. A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1 ft/sec, and the bottom of the l
Vlada [557]

Answer:

0.75 feet per second.

Step-by-step explanation:

Please find the attachment.

We have been given that a 25-ft ladder is leaning against a wall. We can see from the attachment that ladder forms a right triangle with respect to wall and ground.

So we can set a Pythagoras theorem as:

x^2+y^2=25^2

x^2+y^2=625

Now, we need to find the derivative of above equation with respect to time.

2x\cdot \frac{dx}{dt}+2y\cdot \frac{dy}{dt}=0

Since the adder is moving toward the wall at a rate of 1 ft/sec for 5 sec, so x after 5 seconds would be: 20-1(5)=20-5=15

Let us solve for y using Pythagoras theorem.

y^2+15^2=25^2

y^2+225=625

y^2=625-225

y^2=400

Take positive square root:

\sqrt{y^2}=\sqrt{400}

y=20

Upon substituting our given values in derivative equation, we will get:

2x\cdot \frac{dx}{dt}+2y\cdot \frac{dy}{dt}=0

2(15)\cdot(-1)+2(20)\cdot \frac{dy}{dt}=0

-30+40\cdot \frac{dy}{dt}=0

40\cdot \frac{dy}{dt}=30

\frac{dy}{dt}=\frac{30}{40}

\frac{dy}{dt}=0.75

Therefore, the ladder is moving up at a rate of 0.75 feet per second.

3 0
2 years ago
In circle S,diameter PN is drawn .If measurement arc MN=110 degrees and PS=10 then find the length of MN to the nearest tenth.Sh
Goryan [66]

Answer:

MN=16.4\ units

Step-by-step explanation:

step 1

Find PN

we know that

PN is a diameter

PS is a radius

PS=10\ units

so

PN=2*PS=2*10=20\ units

step 2

Find the measure of arc MP

arc\ MN+arc\ MP=180\°

arc\ MN=110\°

arc\ MP=180\°-110\°=70\°

step 3

Find the measure of angle MNP

we know that

The inscribed angle measures half that of the arc comprising

substitute the value

step 4

Find the measure of angle MPN

we know that

The inscribed angle measures half that of the arc comprising

substitute the value

step 5

Find the measure of angle NMP

The sum of the internal angles of a triangle must be equal to 180 degrees

therefore

The triangle MNP is a right triangle

step 6

Find the length MN

In the right triangle MNP

sin(

substitute the values

sin(55\°)=\frac{MN}{20}

MN=(20)sin(55\°)=16.4\ units

7 0
2 years ago
Ivan used coordinate geometry to prove that quadrilateral EFGH is a square.
Thepotemich [5.8K]

Answer:

this is geometry?

Step-by-step explanation:

5 0
2 years ago
Bill is bisecting an angle with technology. Which of the following describes his next step?
mojhsa [17]

Answer:

the first step is correct

Step-by-step explanation:

the first step is correct

then draw 2 circles with the same radius with centre  D and E ( the point BC intersect the first circle )

Where the 2 circles are intersecting is the point F

Then BF is the bisector

7 0
2 years ago
Square ABCD is shown below with line EF passing through the center: If Square ABCD is dilated by a scale factor of two about the
dlinn [17]
Line E'F' would also double.


3 0
2 years ago
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