circle o is inscribed in triangle rst such that it is tangent at points m,n, and p. if rp is 7, rt is 17 and sm is 5, then what is the length of side st?


Answer 1


The length of side st is 15.

Step-by-step explanation:

A tangent is a straigth line that touches a circle externally at a point on the circumference. Considering one of its properties that tangents from the same point to a fixed point outside a circle are equal.


     /rn/ = /rp/

    /tm/ = /tn/

   /sm/ = /sp/

But, /rp/ = 7, /rt/ = 17 and /sm/ = 5.


 /rt/ = /rn/ + /tn/

17 = 7 + /tn/ (∵ /rp/ = /rn/ = 7)

⇒ /tn/ = 10

Since /nt/ = 10, then /tm/ = 10 (/tm/ = /nt/)

So that,

 /st/ = /sm/ + /tm/

     = 5 +10

 /st/ = 15

The length of side st is 15.

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The cube of a number is less than five times the square of the number. For what set of numbers is this true?(–ꝏ, 5)
(5, ꝏ)
(–ꝏ, 0) U (0, 5)
(–ꝏ, 5) U (5, ꝏ)



  (–ꝏ, 0) U (0, 5)

Step-by-step explanation:

The relation can be written as ...

  x³ < 5x²

  x³ -5x² < 0

  x²(x -5) < 0

This is not true for x = 0. It is true for x < 5, otherwise. Then the solution set is ...

  x ∈ {(–ꝏ, 0) U (0, 5)}

The cube of any number from the set (-∞, 0) ∪ (0, 5) is less than five times the square of the number. So, the third option is correct.

Mathematically, a set is a collection of distinct, well-defined objects forming a group.

Let the number be x.

Then, according to the question:

x³ > 5x²

x³ - 5x² > 0

x²(x - 5) > 0

x² > 0 or x - 5 > 0

x > 0 or x > 5

This implies that

x ∈ (-∞, 0) ∪ (0, 5)

Hence, the correct answer is the third option, (-∞, 0) ∪ (0, 5).

Learn more about Set here:


Part a: if angle a and angle b are vertical angles, what is the value of X? part b: if angle a and angle b are supplementary angles, what is the measure of angle b?



a. x = 8

b. m<B = 140

Step-by-step explanation:


m<A = m<B

40 = 5x

x = 8


m<A + m<B = 180

m<B = 180 - m<A

m<B = 180 - 40

m<B = 140

1 poitWhat is the equation of the line in slope-intercept form of the line passing
through (1, 4) and (6, -1)? *
O y = x + 5
O y = -x + 5
y = x-5
O y = -x-5
Send me a copy of my responses.



Its y= -x+5

Step-by-step explanation:

see image

Assume you drop a rock from a cliff which is 5000 feet above the ground. The distance in feet, y, of the rock below the cliff at the time t seconds after it was dropped is given by the equationY=-1/2gt^2



Step-by-step explanation:

Given that height of cliff H = 5000 ft

You drop rock from cliff and the distance of rock below the cliff at time,t is given by:

y= -(1)/(2) gt^(2)

Q1. How far below the cliff is the rock 7 seconds after it dropped ?

Ans. Here, t=7 seconds

By using formula provide, g=32.18 ft{tex]s^(-2)

y=- \frac{1}{2} × 32.17 × (7)^{2}[/tex] = 788.165 ‬ft

Note: Negative sign shows the direction and 240.345 is magnitude

Therefore, Rock is 788.165‬ ft from Cliff

Q2. How far is the rock from the bottom 7 seconds after it dropped ?

By using formula provide,

Ans. After 7 seconds, Rock is 788.165‬ ft from Cliff

Therefore, Rock is 5000-788.165‬ = 4,211.835 ft from bottom

Q3. When will rock hit the bottom?

Ans. Height of cliff H= 5000 ft

Using formula provided, g=32.18 fts^(-2)

y = -(1)/(2) gt^(2)

-5000 = - (1)/(2) 32.18 × t^(2)

t^(2) = (5000×2)/(32.18)

t^(2) = 311.13876

t = 17.6s

Q4. The Velocity of the rock at impact?

Ans. Velocity is given as V= g×t

By using formula, We get

V= 32.14 × Total time to reach ground

V= 32.14 × 17.6 = 565.66 ft/s

Can someone help me on my last problem? #10


ok but what did i do wrong and if you never studied the subject how did you know i was wrong
Based on my small expertise in this subject,

the answer should be 1/(20)^22

the logic is the same as a coin flip
1st flip: call for heads, 1/2 chance
2nd: call for heads, (multiply by self) 1/2 x 1/2= 1/4 chance
3rd: heads, 1/4 x 1/2= 1/8
and so on...

HELP ASAP PLSS! The graph represents the relationship between the amount of money a babysitter makes, m, and the hours the baby sitter works, h. Which function can be used to determine the amount of money the babysitter makes, d, after h hours? d=17h+5 d = 5h + 7 d = 7h +5 d=15h+7



d = 7h +5

Step-by-step explanation

If you go to K-12 then this is the right answer I just took the quiz.


d = 7h +5