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Daniel [21]
3 years ago
10

GEOMETRY QUESTION: PLEASE ANSWER FAST!

Mathematics
1 answer:
Scrat [10]3 years ago
4 0

Answer:

<A = 30

<B = 150

Step-by-step explanation:

  • cos<A =  AK / AB
  • AK = 4
  • AB = 8
  • Cos<A = 4/8
  • Cos<A = 1/2
  • A = Cos-1(0.5)
  • A = 30 degrees
  • Since BC and and AD are parallel, the interior angles of <A and <B  sre supplementary.
  • <A + <B = 180
  • 30 + <B = 180
  • <B = 180 - 30
  • <B = 150
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Answer:

The empty set \{ \}

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Roster method is simply listing explicitly all the elements in the set, one by one (writing them between two curly brackets, and separating them through commas).

We want then to list explicitly all the elements in the following set:

The set of natural numbers x that satisfy x+2=1.

So, first we have to figure out which numbers are in that set. The set is made ONLY of those natural numbers x, that when you add 2 to them, you get 1. Clearly no natural number has that property (since the only number that would give us 1 when adding 2 to it, is the number -1, which is NOT a natural number). So there aren't any numbers at all in that set. So if we were to list them, we'd just list nothing inside the set:

\{ \} (which is just the empty set)

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2 years ago
Perpendicular lines are two distinct coplanar lines that intersect to form what type of angle?
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Answer:

2 hours

Step-by-step explanation:

Given : The distance between New York City, NY, and Louisville, KY is 720 miles. One morning a train traveling 80 mph left from New York. Two hours later a slower train, traveling at 60 mph, left Louisville.

To find : How many hours will the slower train travel for before both trains will arrive at the same point?

Solution : Let the distance covered by NY is x

and  let the distance covered by KY is y

Total distance covered is  x+y=720   ........[1]

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Time taken = t+2

Formula is \text{Time}=\frac{\text{Distance}}{\text{Speed}}

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→ Louisville,

Distance traveled = y

Speed of the train = 60 mph

Time taken = t

Formula is \text{Time}=\frac{\text{Distance}}{\text{Speed}}

t=\frac{y}{60} .......[3]

Put the value of t from [3] into [2]

\frac{x}{80}- \frac{y}{60}=2  ......[4]

Now, we solve equation [1] and [4],

Put the value of y from [1] and put back in [4], y=720-x

\frac{x}{80}- \frac{y}{60}=2

\frac{x}{80}- \frac{720-x}{60}=2

\frac{60x-80(720-x)}{80\times60}=2

60x-57600+80x=9600

140x-57600=9600

140x=57600+9600=67200

x=\frac{67200}{140}=480

Put x=480 in [1]

x+y=720  

480+y=720  

y=240  

So, The distance covered by train from New York city is x=480 miles

The distance covered by train from Louisville is y=240 miles.

Now put value of y in [3] to get time,

t=\frac{y}{60}

t=\frac{240}{60}

t=4

So, The time taken by train from Louisville is 4 hr.

The time taken by train from New York city is t+2=4+2=6 hr.

→ 6-4=2 hours will the slower train travel for before both trains will arrive at the same point.




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Answer:

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