OLYMPICS The number of men and women participating in the Winter

A triangle ABC is inscribed in a circle, such that AB is a diameter. What are the measures of angles of this triangle if: measur

shutvik [7]

Answer:

The measures of angles of this Δ are 23° , 67° , 90°

Step-by-step explanation:

* Lets talk about some facts in the circle

- An inscribed angle is an angle made from points sitting on the

circle's circumference

- A central angle is the angle formed when the vertex is at the center

of the circle

- The measure of an arc of a circle is equal to the measure of the

central angle that intercepts the arc.

- The measure of an inscribed angle is equal to 1/2 the measure of

its intercepted arc

- An angle inscribed across a circle's diameter is always a right angle

- The triangle is inscribed in a circle if their vertices lie on the

circumference of the circle, and their angles will be inscribed

angles in the circle

* Now lets solve the problem

- Δ ABC is inscribed in a circle

∵ its side AB is a diameter of the circle

∵ Its vertex C is on the circle

∴ ∠C is inscribed and across the circle's diameter

∴ ∠C is a right angle

∴ m∠C = 90°

∵ The measure of arc BC = 134°

∵ ∠A is inscribed angle subtended by arc BC

∵ The measure of an inscribed angle is equal to 1/2 the measure

of its intercepted arc

∴ m∠A = 1/2 × 134° = 67°

∵ The sum of the measures of the interior angles of a triangle is 180°

∵ m∠A = 67°

∵ m∠C = 67°

∵ m∠A + m∠B + m∠C = 180°

∴ 67° + m∠B + 90° = 180°

∴ 157° + m∠B = 180° ⇒ subtract 157 from both sides

∴ m∠B = 23°

* The measures of angles of this Δ are 23° , 67° , 90°

4 0

2 years ago

A group of friends are going ice skating. The price of admission is $3.25. As a group, they spent $14 on refreshments. If they s

Helen [10]

Start with $30.25.
Subtract $14.00 to isolate the amount of money spent on admission.
30.25-14.00= 16.25. As a group $16.25 was spent on admission.
Admission is 3.25 per person. Divide 16.25 by 3.25.
16.25/3.25=5.
5 friends went ice skating.

4 0

2 years ago

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If the third term in an arithmetic sequence is 7 and the common difference is -5, what is the value of the fourth term?

pochemuha

The is Answer:

82

Explanation:

We observe that difference between first and second terms =12−5=7
Similarly difference between second and third terms =19−12=7

It shows that the given sequence of numbers is an arithmetic progression with common difference equal to 7.

We know that nth term of an AP whose first term is a1 and whose common difference is d is given by
an=a1+(n–1)d

To find the 12th term, insert given values in the general expression
a12=5+(12–1)7
a12=5+(11)7=5+77=82

4 0

2 years ago

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Dan enrolls in a basketball league for people over 40. He pays the following fees. --$25 for a team t-shirt --his share of the t

I am Lyosha [343]

I think that you should provide more details

5 0

2 years ago

Which sequences are arithmetic? Check all that apply.

Artyom0805 [142]

Answer:

Option C and E are correct.

The sequences which are arithmetic:

18, 5.5, -7, -19.5, -32,....

16, 32, 48, 64, 80

Step-by-step explanation:

Arithmetic sequence states that a sequence in which a common difference between each consecutive term is constant.

Common difference(d) = $a_{n+1}-a_n$ for every natural number n.

Option A:

-5, 5, -5, 5, -5, .....

5-(-5) = 5+5 = 10 ,

-5 -5 = -10 .....

Since, the common difference for the given sequence is not constant.

Option B:

96, 48, 24, 12, 6

48 -96 = -48

24-48 = -24 ....

Common difference for the given sequence is not constant.

Option C:

18, 5.5, -7, -19.5, -32,....

5.5-18 = -12.5

-7 -5.5 = -12.5 ....

∴Common difference for the sequence is constant.

Option D:

-1, -3, -9, -27, -81 ,....

-3 -(-1) = -3+1 = -2

-9-(-3) = -9+3 = -6 ....

∴Common difference for the sequence is not constant.

Option E:

16, 32, 48, 64, 80

32-16 = 16

48 - 32 = 16 and so on...

∴Common difference for the sequence is constant.

Therefore, the sequences which are arithmetic are:

18, 5.5, -7, -19.5, -32,....

16, 32, 48, 64, 80

4 0

2 years ago

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