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svetoff [14.1K]
3 years ago
14

Triangles Unit Test part 1 A length of rope is stretched between the top edge of a building and a stake in the ground. The head

of the stake is at ground level. The rope also touches a tree that is growing halfway between the stake and the building. If the tree is 16 feet tall, how tall is the building?

Mathematics
1 answer:
musickatia [10]3 years ago
5 0

Answer:

The building is 32 feet tall.

Step-by-step explanation:

Consider the figure drawn below representing the given scenario.

AB represents the height of building, BC is the distance between the stake and building, C represents the stake at ground level, and DE represents the height of the tree growing halfway between building and stake.

Since the tree is growing halfway between B and C, therefore, the point E divides the line segment BC into 2 equal parts.

Therefore, BE = EC or E is the midpoint of BC.

Also, from the figure, it is clear that both tree and building are vertical to the ground. So, DE || AB.

Now, from converse of mid-segment theorem, if a line passes through the midpoint of one side of a triangle and also parallel to the third side, then the line also passes through the midpoint of the second side and half the length of the third side (parallel side)

So,

DE=\frac{1}{2}\times AB\\\\16=\frac{AB}{2}\\\\AB=16\times 2=32\ ft

Therefore, the building is 32 feet tall.

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Five times the sum of the digits of a two-digit number is 13 less than the original number. If you reverse the digits in the two
mafiozo [28]

Answer:

The difference of the original two-digit number and the number with reversed digits is 18.

Step-by-step explanation:

Since it's a two digit number, let x represent the tens digit and let y represent the units digit.

Thus, the original two digit number is;

10x + y.

The reverse two digit number is;

10y + x.

We are told that five times the sum of the digits of the two-digit number is 13 less than the original number.

Thus;

5(x + y) = (10x + y) - 13

Multiplying out the bracket gives;

5x + 5y = 10x + y - 13

Rearranging gives;

10x - 5x + y - 5y = 13

5x - 4y = 13 - - - - (3)

Also,we are told that, four times the sum of its two digits is 21 less than the reversed two-digit number. Thus;

4(x + y) = (10y + x) - 21 - - - (4)

Simplifying gives;

4x + 4y = 10y + x - 21

>> 10y - 4y - 4x + x = 21

>> 6y - 3x = 21 - - - (4)

Solving eq(3) and (4) simultaneously gives;

x = 5 and y = 3

Thus,

Original number = 53

Reversed number = 35

Difference between original and reversed number = 53 - 35 = 18

6 0
3 years ago
Plz help me plz I need answer and explanation plz
pentagon [3]

9514 1404 393

Answer:

  A = {put, the, cake, in, basket}

  B = {is, the, cake, in, basket}

  C = {no, the, cake, in, basket}

  D = { }

Step-by-step explanation:

A = (A -B) ∪ (A∩B) ∪ (A∩C}

A = {put} ∪ {the, cake, in, basket} ∪ {the, cake, in, basket}

A = {put, the, cake, in, basket}

__

B = (B -A) ∪ (B -C) ∪ (B∩A) ∪ (B∩C)

B = {is} ∪ {is} ∪ {the, cake, in, basket} ∪ {the, cake, in, basket}

B = {is, the, cake, in, basket}

__

C = (C -B) ∪ (C∩A) ∪ (C∩B)

C = {no} ∪ {the, cake, in, basket} ∪ {the, cake, in, basket}

C = {no, the, cake, in, basket}

__

D = { } . . . . not defined anywhere

8 0
3 years ago
You have cards with the letters A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P. Event U is choosing the cards A, B, C
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Answer:

If you are asking how many events use P: 1 event is using the letter P (event W)

Step-by-step explanation:

Why event U cannot be using P: This event is only using the letters A, B, C, and D.

Why event V cannot be using P: This event is only using vowels (A, E, I, O, U)

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Meldrick had $28 in his savings account. On Monday, he deposited his earnings from mowing lawns on the weekend. He earned the sa
IceJOKER [234]

Answer:

70 - 28 = 42

42/100 X 40 = 16.8

42 - 16.8 = 25.20

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2 years ago
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