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3 years ago

Angle measures and segment lengths. Algebra Find the value of each variable.

Mathematics

1 answer:

Katyanochek1 [597]3 years ago

6 0

(9)

x ° = 1/2 (130° - 30°) = 50°

(due to a theorem about intersecting secants/tangents)

(11) The labeled angle subtends a minor arc of meaure 120°, which means the larger arc has a measure of 360° - 120° = 240°. Then

x ° = 1/2 (240° - 120°) = 60°

(due to the same theorem)

(13) The labeling here is a bit confusing. I'm not sure what the 70° is referring to. It occurs to me that it might be info from a different exercise, so that y ° is the measure of the angle made by the tangent to the circle with a vertex of the pentagon, and x ° is the measure of each arc that passes over an edge of the pentagon.

Each arc makes up 1/5 of the circle's circumferece, so

x ° = 360°/5 = 72°

The pentagon is regular, so each of its interior angles have the same measure of 108°. (Why 108°? Each exterior angle measures 360°/5 = 72°, since the exterior angles sum to 360°. Interior and exterior angles are supplementary, so the interior angles measure 180° - 72° = 108° each.)

The angles formed by the tangent to the circle are supplementary, so that

y ° + 108° + y ° = 180°

2y ° = 72°

y ° = 36°

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From a radar station, the angle of elevation of an approaching airplane is 32.5 degree. The horizontal distance between the plan

denis23 [38]

Answer: 42.21 km

Step-by-step explanation:

We can solve this using trigonometry, since we have the following data:

$\theta=32.5\°$ is the the angle of elevation

$d=35.6 km$ is the horizontal distance between the plane and the radar station

$x$ is the hypotenuse of the right triangle formed between the radar station and the airplane

Now, the trigonometric function that will be used is cosine:

$cos\theta=\frac{d}{x}$ because $d$ is the adjacent side of the right triangle

$cos(32.5\°)=\frac{35.6 km}{x}$

Finding $x$ :

$x=\frac{35.6 km}{cos(32.5\°)}$

$x=42.21 km$

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4 years ago

Rodney bought a 50 pound bag of dog food. HIS dog ate 2/5 of the food in the first mon th and 2/10 of the food in the second mon

NeTakaya

Answer:

20 lbs

Step-by-step explanation:

2/5ths of the food would be 20 pounds because:

2/5 * 50 = 20

2/10ths of the food would be 10 pounds because:

2/10 * 50 = 10

If we add those two together, we would get the total amount that the dog ate, which would be 30 pounds. SInce the dog ate 30 pounds of food out of the 50 pounds, there would be 20 pounds left in the bag at the end of two months:

50- ( 20+ 10) = 20

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4 years ago

South Africa broke the world record for largest pizza in 1990. It weighed `26833` pounds

viva [34]

8,944 hope this helps

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3 years ago

The cost of 12 oranges and 7 coples is 55.36. Eight oranges and apples cost $3.68. Find the cost

victus00 [196]

Hello there i hope you are having a good day :) Your question : The cost of 12 oranges and 7 couples is 55.36. Eight oranges and apples cost $3.68. Find the cost of each : Firstly you would do oranges = O Apples = A. Then 12 oranges + 7 apples = 5.36 12o + 7A = 5.36 then you would take away from both sides so -12o Take away -12o = 7o = 5.36 - 12A now you would divide this by 7 so 7 cancels each out so you are left with 5.36/ 7 = 0.76 Then it would equal 0.76 - 12o/7 This would equal the amount of apples to be $0.76 each now for the oranges you would do the same that you work out for the apples.

Hopefully that help ya :)

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3 years ago

How many 100 make 3200?

Gelneren [198K]

32!

32 100s can go into the number 3200! Hope this helped!

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3 years ago