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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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Answer:

y = 4x - 12

Step-by-step explanation:

The equation of a line in slope- intercept form is

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m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = E(4, 4) and (x₂, y₂ ) = F(2, - 4)

m = \frac{-4-4}{2-4} = \frac{-8}{-2} = 4 , then

y = 4x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 4), then

4 = 16 + c ⇒ c = 4 - 16 = - 12

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3 years ago
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Paisley is going to invest $28,000 and leave it in an account for 14 years. Assuming the interest is compounded monthly, what in
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divide 74000 by 28000, and cancel out 28000.

1.00580=1+r/12

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The following proof shows an equivalent system of equations created from another system of equations. Fill in the missing reason
Nookie1986 [14]

Answer:

<h2>A.Multiplication Property of Equality</h2>

Step-by-step explanation:

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Find the sum of 5m + 3n + p, -5p + 3n, and 2n - m
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<span>5m + 3n + p -5p + 3n + 2n - m
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Write and solve a system of equations to determine how many tickets were sold before and at the music festival. PLEASE HELPPP
strojnjashka [21]

b = number of tickets sold before

a = number of tickets sold after

cost of a ticket = number of tickets times cost per ticket

before cost = 39.95b

after cost = 54.95a

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39.95b + 54.95a = 925000

total number tickets = 20000

b + a = 20000

we have

39.95b + 54.95a = 925000

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a = 8400

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minus 8400 both sides

b = 11600

11,600 tickets sold before

8400 tickets sold after

3 0
3 years ago
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