B. x +6 <-8 and x-1

PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. the length TP in cm is:

kolezko [41]

<h3><u>Given</u><u> </u><u>:</u><u>-</u></h3>

PQ = 8cm
Radius = 5cm
Two Tangents = P & Q.

<h3><u>Construction</u><u> </u><u>:</u><u>-</u></h3>

Join OT.

<h3><u>⟼</u><u> </u><u>Solution</u><u> </u><u>:</u><u>-</u></h3>

Here, ΔTPQ is isosceles and TO is the angle bisector of ∠PTO.

[∵ TP=TQ = Tangents from T upon the circle]

⠀⠀⠀⠀⠀⠀⠀⠀∴ OT⊥PQ

So, PR = RQ = 4cm.

⠀⠀⠀

___________________________________________

$\longmapsto{}$ By Applying Pythagoras Theorem in ∆OPR :

OR = √OP² - PR²

OR = √5² - 4²

OR = 3cm

__________________________________________

Now,

$\leadsto$ ∠TPR + ∠RPO = 90° (∵TPO=90°)

$\leadsto$ ∠TPR + ∠PTR (∵TRP=90°)

<u> $\leadsto$ </u><u>∴ ∠RPO = ∠PTR</u>

⠀⠀

<u>∴ Right triangle TRP is similar to the right </u><u>triangle</u><u> </u><u>PR</u><u>O</u><u>.</u> [By A-A Rule of similar triangles]

⟼ $\frac{TP}{PO} = \frac{RP}{RO}$

⟼ $\frac{TP}{5} = \frac{4}{3}$

⟼ $TP= \frac{20}{3}$

<h3>Hence you got your answer here. </h3>

⠀⠀⠀⠀⠀

<h2>-MissAbhi</h2>

6 0

2 years ago

What does m represent in the equation y = mx+b?

NNADVOKAT [17]

Answer:

In the equation y = mx + b for a straight line, the number m is called the slope of the line

Step-by-step explanation:

8 0

3 years ago

Which pair of angles are corresponding angles?<br><br> PLEASE HELP ME THIS IS DUE TMR

stiks02 [169]

Answer:

the answer is 3 and 7

Step-by-step explanation:

Angles formed when a transversal line cuts across two straight lines are known as corresponding angles. Corresponding angles are located in the same relative position, an intersection of transversal and two or more straight lines.

3 0

2 years ago

a carnival sold tickets for $1.50 for adults and $1.00 for students. there were 54 tickets sold for a total of $70.50. write a s

Likurg_2 [28]

Answer:

The number of adult tickets are 33 and the number of student tickets are 21 .

Step-by-step explanation:

As

The number of adult tickets x and the number of student tickets y.

As given

A carnival sold tickets for $1.50 for adults and $1.00 for students.

There were 54 tickets sold for a total of $70.50.

Equations becomes

x + y = 54

1.50x + 1.00y = 54 × 70.50

Simplify the above

$\frac{150x}{100} + \frac{100y}{100} = \frac{7050}{100}$

150x + 100y =7050

Two equations are

x + y = 54

150x + 100y =7050

Multiply x + y = 54 by 150 from 150x + 100y =7050

150x - 150x + 100y - 150y = 7050 - 8100

-50y = -1050

50y = 1050

$y = \frac{1050}{50}$

y = 21

Putting the value of y in the equation .

x + 21 = 54

x = 54 - 21

x = 33

Therefore the number of adult tickets are 33 and the number of student tickets are 21 .

8 0

4 years ago

It's due todayyyyyyy (;ŏ﹏ŏ)

Thepotemich [5.8K]

The correct answer are

Sue interest : 169.6061952

Bill interest: 189.9131472

B. Bill will get more interest then sue

Explain

Sue principal balance p= 2300

Interest for 3 years so t= 3

Interest is compounded yearly n= 1

R= 2.4%

A= 2300(1+2.4/100)^3 = 2300(1+0.024)^3 = 2300 x (1.024)^3 = 2469.6061952

Interest for 3 year is A-p= 2469.6061952 -2300

169.6061952

Bill principle p= 1800

Interest for 3 years t= 3

Interest compounded so n= 1

R= 3.4%

A= 1800(1+3.4/100)^3 = 1800 (1+0.034)^3 = 1800 (1.034)^3 = 1989.9131472

Interest in 3 yrs = 1989.9131472 - 1800 =

189.9131472

For B is below

Hopefully this help you :D

3 0

3 years ago

B. x +6 <-8 and x-1 > -1