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Novosadov [1.4K]
3 years ago
12

What is the circumference of the following circle?

Mathematics
2 answers:
Sholpan [36]3 years ago
4 0

Answer:

Answer Is A

Step-by-step explanation:

Annette [7]3 years ago
3 0
The formula for a circumference of a circle is 2πr

2 × π × 25 = 157

so your answer is A 157in.

I hope I've helped!
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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
Use the Fundamental Counting Principle to find the total number of possible outcomes.
krok68 [10]

Answer:

gfhcfgjcfgjdfgjvhjvhkftfhcyjftyjvjftykftyvgjcgjfyfg gjvvgvggvgvhjvhvg

Step-by-step explanation:

vgjkcgyjvghj vhjvjvhvhjvhjvghjghjvghjvhjhvgghvghvhvhvhvhjvghjvghjvh .jvghvghj gj vjvhjvhjv .v .hvhjvhjvhvb vh vv bhjvb f  

4 0
3 years ago
Please Help!! If answer, please answer them all, thank you!!
Sergio [31]

9514 1404 393

Answer:

  (b) angle FOA

  (c) angle EOA

  (d) angle AOH

Step-by-step explanation:

(b) The rays of vertical angles are opposites that form intersecting lines.

The opposite of ray OG is OF. The opposite of ray OB is OA, so the vertical angle to GOB is angle FOA.

__

(c) The opposite of ray OB is OA, so the supplement to angle EOB is angle EOA.

__

(d) Similarly, the supplement to angle BOH is angle AOH.

_____

<em>Comment on supplementary angles</em>

Angles that form a linear pair are supplementary. Angles do not have to form a linear pair to be supplementary. They merely have to have a sum of 180°. Here, the supplementary angles of interest do form a linear pair, so finding the other angle of the pair means only finding the other point that names the line being formed by the pair.

8 0
2 years ago
provide a counterexample (specific values of a,b, etc. which make the statement false) for each of the following statements. Ass
ivolga24 [154]

Answer:

1. a=3, b = 2, c = 1.

2. a=2, b=3, c=4, d=6.

3. a = 9, b = 3.

Step-by-step explanation:

1.  3 | 21   is a counterexample  because 3 does not divide into  2 or 1.

2. 23 | 46 is a counterexample because 2 does not divide into 3.

3. 9 | 3^2 is a counterexample because 9 does not divide into 3.

8 0
2 years ago
Write the number 0.5 in the form a/b using integers to show that it is a rational number
LekaFEV [45]
0.5 = \frac{5}{10} =  \frac{1}{2}
5 0
2 years ago
Read 2 more answers
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