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e-lub [12.9K]
3 years ago
13

Tanya wants to find the height of the tree. She walks away from the base of the tree so the tip of her shadow coincides with the

tip of the tree's shadow at point C. BE is two and a half times EC. Tanya is 5 feet, 3 inches tall. How tall is the tree in feet?

Mathematics
1 answer:
shtirl [24]3 years ago
4 0
Refer to the diagram attached.

TRIANGLE ABC
The height of the tree is the segment AB. The shadow of the tree is BC.

TRIANGLE DEC
Tanya's height is 5 feet 3 inches (since there are 12 inches in one foot that is (5)(12)+3 = 63 inches).
Tanya's shadow is EC

Since both triangles are right triangles (the both have a right angle) and they share the angle at C, they are similar triangles. That means that their corresponding angles are congruent and their corresponding sides are in proportion.

We can set up the following proportion:
(tree height / tree shadow) = (Tanya's height / Tanya's shadow)

BE is 2.5 times EC. This means that BE is (2.5)(EC). It also means that BC = 2.5EC + EC = 3.5EC

The shadow of the tree is 3.5 times Tanya's shadow. That means that the height of the tree must be 3.5 times Tanya's height.

The height of the tree is (3.5)(63) = 220.5 inches. If we divide this by 12 we get 18.375 which means 18 feet and some inches.  (18)(12)=216 and the tree is 220.5. That means the tree is 18 feet and 4.5 inches.

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Kiran is spending $12 on games and rides at another carnival, where a game
Alinara [238K]

Answer:

0.25x + y = 12

Step-by-step explanation:

Given

Kiran is spending $12 on games

it means that he can spend total of $12 on rides and games

number of games is represented by x

cost of 1 game = $0.25

cost of x games = $0.25*x = $0.25x

number of rides is represented by y

cost of 1 rides = $1

cost of x rides = $1*y = $y

Total cost for x games and y rides =cost of x games  + cost of y rides

Total cost for x games and y rides =  $0.25x + $y

given that Kiran is spending $12 on games

Total cost for x games and y rides will be $12

thus,

$12 = $0.25x + $y

removing dollar sign for equation formation

0.25x + y = 12

given above is the equation to represent the relationship between the dollar

amount Kiran is spending and the number of games, x, and the number of

rides, y.

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3 years ago
How do i quit branily
Andre45 [30]

Answer:

look it up

Step-by-step explanation:

5 0
3 years ago
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What project did mary jackson work on at naca soon after she was hired?.
saw5 [17]
The project Mary Jackson worked on at nasa soon after she was hired was landing astronauts on the moon and how to return them safely back to earth.
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Find the fifth term of the binomial expansion.<br> (x2+y5) ^8
OlgaM077 [116]

Answer:

The fifth term of the binomial expansion

T_{5} = 70 x^{8} y^{20}

Step-by-step explanation:

<u><em>Step:1</em></u>

Given that the binomial expansion

     ( x² + y⁵ )⁸

we know that

T_{r+1} = n_{C_{r} } a^{r} x^{n-r} ...(i)

<u><em>Step:2</em></u>

put r = 4  

T_{4+1} = 8_{c_{4} } (x^{2} )^{4} (y^{5} )^{8-4}

T_{5} = 70 x^{8} y^{20}

<u><em>Final answer:</em></u>-

The fifth term of the binomial expansion

T_{5} = 70 x^{8} y^{20}

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3 years ago
A rectangle is reduced by a scale factor of One-fourth.
Dvinal [7]

The ratio of the area of the smaller rectangle to the area of the larger rectangle is 1:16

Area of a rectangle

The formula for calculating the area of a rectangle is expressed as:

A = length * width

For the large triangle

Area = 16 * 12

Area of large triangle = 192 square units

For the smaller rectangle

Area = 4 * 3

Area. of small rectangle = 12 square units

Ratio = 12/192 = 1:16

Hence the ratio of the area of the smaller rectangle to the area of the larger rectangle is 1:16

Learn more on area of rectangle here: brainly.com/question/25292087

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2 years ago
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