1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nydimaria [60]
3 years ago
13

Circle K is shown. Tangents S T and U T intersect at point T outside of the circle. A line is drawn from point T to point R on t

he opposite side of the circle. It goes through center point K. Lines are drawn from points S and U to center point K.
Line segment ST is congruent to which line segment?

Mathematics
2 answers:
alexgriva [62]3 years ago
5 0

The figure is missing so I attached a helping figure

Answer:

Line segment ST is congruent to line segment UT

Step-by-step explanation:

From the attached figure

∵ ST and UT are tangents to circle K at points S and U

∵ SK and UK are radii in the circle K

- The tangent is perpendicular to the radius at the point of tangent

∴ ST ⊥ KS ⇒ at point S

∴ m∠KST = 90°

∴ UT ⊥ KU ⇒ at point U

∴ m∠KUT = 90°

∴ m∠KST = m∠KUT

In the two triangles KST and KUT

∵ KS = KU ⇒ radii

∵ m∠KST = m∠KUT ⇒ proved

∵ KT is a common side in the two triangles

- That means the two triangles are congruent by HL postulate

    of congruence (hypotenuse and leg of right triangle)

∴ Δ KST ≅ KUT ⇒ HL postulate of congruence

- By using the result of congruence

∴ ST = UT

Line segment ST is congruent to line segment UT

sineoko [7]3 years ago
5 0

Answer:

c : UT

Step-by-step explanation:

test edg

You might be interested in
An urn contains 5 white and 10 black balls. A fair die is rolled and that number of balls is randomly chosen from the urn. What
galina1969 [7]

Answer:

Part A:

The probability that all of the balls selected are white:

P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\      P(A)=\frac{5}{66}=0.075757576

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516

Step-by-step explanation:

A is the event all balls are white.

D_i is the dice outcome.

Sine the die is fair:

P(D_i)=\frac{1}{6} for i∈{1,2,3,4,5,6}

In case of 10 black and 5 white balls:

P(A|D_1)=\frac{5_{C}_1}{15_{C}_1} =\frac{5}{15}=\frac{1}{3}

P(A|D_2)=\frac{5_{C}_2}{15_{C}_2} =\frac{10}{105}=\frac{2}{21}

P(A|D_3)=\frac{5_{C}_3}{15_{C}_3} =\frac{10}{455}=\frac{2}{91}

P(A|D_4)=\frac{5_{C}_4}{15_{C}_4} =\frac{5}{1365}=\frac{1}{273}

P(A|D_5)=\frac{5_{C}_5}{15_{C}_5} =\frac{1}{3003}=\frac{1}{3003}

P(A|D_6)=\frac{5_{C}_6}{15_{C}_6} =0

Part A:

The probability that all of the balls selected are white:

P(A)=\sum^6_{i=1} P(A|D_i)P(D_i)

P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\      P(A)=\frac{5}{66}=0.075757576

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

We have to find P(D_3|A)

The data required is calculated above:

P(D_3|A)=\frac{P(A|D_3)P(D_3)}{P(A)}\\ P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516

7 0
3 years ago
−9x (5x+4 ) +10 (x+3) can someone please solve his for me thank u step by step please i really need to find out how to do it
Ivahew [28]

Answer:

-45x^{2}-26x+30

Step-by-step explanation:

So first you let's divide this equation into three parts.

Part one -9x(5x+4)

  1. Step one: you have to distribute the -9x to the numbers in the parentheses. That would leave us with a -9x*5x = -45x^{2} and -9x*4 = -36x
  2. Step two: Put the answers together. That would leave us with -45x^{2}-36x.

Part two 10(x+3)

  1. Step one: you have to distribute the 10 to the numbers in the parentheses. That would leave us with a 10*x = 10x and 10*3 = 30
  2. Step two: Put the answers together. That would leave us with 10x+30

Part three solve

  1. Step one: combine and put together what you have solved for. That would leave us with a -45x^{2}-36x+ 10x+30
  2. Step two: combine like terms. The like terms here are -36x and 10x. When you combine them you would get -26x.
  3. Step three: Write the equation in standard form. Therefore the answer is -45x^{2}-26x+30.

Let me know if anything is confusing!

5 0
2 years ago
SOMEONE HELPFUL PLZ ANSWER!!!!!!!! WILL MARK BRAINLIEST!!!!!!!!!
Eva8 [605]

Answer:

a , c , b

Step-by-step explanation:

just input the numbers in a TI 84 calculator (if you don't have I would be happy to show you how to download the free online version.) And sort from greatest to least.

3 0
3 years ago
Read 2 more answers
Find the equation of the line that passes through points a and b :D
Nata [24]
The answer is y=2x-1



7 0
3 years ago
Read 2 more answers
Solve for x<br> 8x = -14
PSYCHO15rus [73]

Answer:

-7/4

Step-by-step explanation:

8x=-14

X=-14/8

X=-7/4

4 0
3 years ago
Read 2 more answers
Other questions:
  • Which is the best definition of a circle?
    12·1 answer
  • An airplane with an air speed of 165 mph is headed 210°. If the plane encounters a 15 mph wind from the west, find the ground sp
    13·1 answer
  • At 4 p.m., the temperature started to change drastically. Each hour, for three hours, the temperature decreased by 7°F. Which ex
    14·2 answers
  • Alex can make 14 bracelets in 5 minutes how many races did kiss you make in 1 hour ​
    13·1 answer
  • 6<br> TEL<br> X<br> -<br> 4<br> 2<br> 44<br> is it a function or not a function
    5·1 answer
  • 1.<br> 12 pizzas cost $20. What will 20 pizzas<br> costa
    13·2 answers
  • What connects the exterior angle at C with the sum of the angles at A and B​
    12·1 answer
  • Jeremy's password is the combination of letters and numbers shown below. He
    11·1 answer
  • Prove the following integration formula:
    12·2 answers
  • (4x^(4))^(2) without exponents
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!