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Anna35 [415]
3 years ago
15

Joshua is 1.45 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 31.65 meters. He stands 26.2 meters away

from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter .

Mathematics
1 answer:
Lena [83]3 years ago
6 0

Answer:

The height of the tree=8.42 m

Step-by-step explanation:

We are given that

Height of Joshua, h=1.45 m

Length of tree's shadow, L=31.65 m

Distance between tree and Joshua=26.2 m

We have to find the height of the tree.

BC=26.2 m

BD=31.65m

CD=BD-BC

CD=31.65-26.2=5.45 m

EC=1.45 m

All right triangles are similar .When two triangles are similar then the ratio of their corresponding sides are equal.

\triangle ABD\sim \triangle ECD

\frac{AB}{EC}=\frac{BD}{CD}

Substitute the values

\frac{AB}{1.45}=\frac{31.65}{5.45}

AB=\frac{31.65\times 1.45}{5.45}

AB=8.42m

Hence, the height of the tree=8.42 m

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Answer: The equations are

6x - 6y = 9

4x + 4y = 9

Step-by-step explanation:

Let x represent the speed of the row boat in still water.

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Dana can travel 9 miles in her rowboat in 6 hours against the current. This means that the total speed at which she travelled is

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Distance = speed × time

Distance travelled against the current is expressed as

9 = 6(x - y)

6x - 6y = 9

With the current, it takes 4 hours to row the same distance. This means that the total speed at which she travelled is

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Distance travelled with the current is expressed as

9 = 4(x + y)

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7 0
3 years ago
A landscape business charges $50 to deliver rocks. The cost of the rocks are $27 per cubic yard. write and solve a linear equati
Nuetrik [128]
<h2>Answer: 27x + 50 = y, $266</h2>

Step-by-step explanation:

First, let's form a linear equation that will help us find out how much that will cost.

Let's set x = the cubic yards of rocks delivered and y = total cost.

First, we know that the business charges 27 dollars for every x that you buy. That can be shown with a multiplication expression:

27x

Next, we know that the business charges a fixed fee of $50 for their services. This fee would be <em>added on</em> to the amount that they charge for the rocks that you buy.

<h2>27x + 50 = y</h2>

That's our linear expression! Next, we need to find out the <em>total cost</em>, y, when you need 8 cubic yards of rocks delivered, x.

To solve this, we need to substitute values for at least one of our variables.

Since 8 describes the cubic yards of rocks delivered, we can substitute 8 for x.

But we don't know y, the total cost- that's what we're solving for! In other words, we're solving for y.

Let's just substitute in what we know:

27(8) + 50 = y.

216 + 50 = y

<h2>y = 266</h2>

So, we know that it would cost $266 dollars to have 8 cubic yards of rocks delivered to a site.

By the way, you can also graph your linear equation to find the corresponding y-value to 8 as another way to solve your problem.

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3 years ago
Claire is putting up a fence around her rectangular garden. The length is four less than double the width. The perimeter is 22 f
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Answer:

The dimensions are 6 by 5 feet.

Length = 6 feet.

Width = 5 feet.

Step-by-step explanation:

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Perimeter of a rectangle = 2L + 2W

Translating the word problem into an algebraic equation, we have;

L = 2W - 4 ........equation 1

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Substituting the value of "L" into equation 2, we have;

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solutions are : (-1,3) and (3,5)

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gulaghasi [49]

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