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2 years ago

The angle of depression from a balloon on a 75ft string to a person on the ground is 36°. How high is the balloon?

Mathematics

1 answer:

Rainbow [258]2 years ago

5 0

Answer:

Step-by-step explanation:

sin36=h/75

h=75sin36

h=44.08ft

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50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle

aalyn [17]

Answer:

$EF=4\sqrt{3}$

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

$A_{\text{rect}}=8(6)=48\text{ cm}^2$

The area of the triangle is 1/4 of this. Therefore:

$\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2$

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

$\displaystyle 12=\frac{1}{2}(DE)(DF)$

Since DE = DF:

$24=DF^2$

Thus:

$DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE$

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

$(DE)^2+(DF)^2=(EF)^2$

Therefore:

$(2\sqrt6)^2+(2\sqrt6)^2=EF^2$

Square:

$24+24=EF^2$

Add:

$EF^2=48$

And finally, we can take the square root of both sides:

$EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}$

6 0

2 years ago

Read 2 more answers

Answer the question in the image below

umka21 [38]

Answer:

B. m $\geq 2\frac{1}{2}$

Step-by-step explanation:

$m\geq \frac{5}{2}$

6 0

2 years ago

At the movies, tickets for a night show cost $9, and tickets for a day show cost $6.75. What percent is the discount you get for

Nadya [2.5K]

I think it is 3.25%. That is what I had got when I had did my math

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2 years ago

Which graph shows y=x^2+3x-4

Ivahew [28]

Answer:

Third graph in the photo

Step-by-step explanation:

x^2+3x-4 can be factored as (x+4)(x-1). When y=0, x must be -4 or 1 to satisfy the equations, and thus the roots of the graph are at x=-4 and x=1. When x=0, y=(4)(-1)=-4. The only graph that satisfies both of these requirements is the third/last one.

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1 year ago

Graph and label each figure and it’s image under the given translation. Give the coordinates of the image.

lutik1710 [3]

Answer:

See below ~

Step-by-step explanation:

Question 3 : (x, y - 5)

K' = (-3, 2 - 5) = (-3, -3)
L' = (1, 4 - 5) = (1, -1)
M' = (-1, 0 - 5) = (-1, -5)
N' = (-5, -2 - 5) = (-5, -7)

Question 4 : (x + 4, y + 1)

D' = (-4 + 4, 3 + 1) = (0, 4)
E' = (0 + 4, 2 + 1) = (4, 3)
F' = (-2 + 4, -6 + 1) = (2, -5)
G' = (-6 + 4, -5 + 1) = (-2, -4)

5 0

1 year ago