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andriy [413]
3 years ago
14

HELP ASAP!! A truck starts from a warehouse, which is 8 miles south and 3 miles west of the town center. The truck travels 3 mil

es north, makes a right turn, and then travels for 4 miles. What is the truck’s final position? What single translation vector moves the truck from its starting position to its final position?

Mathematics
1 answer:
butalik [34]3 years ago
6 0

The answer, I think, is (1, -5);(4,3).

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Regular hexagon ABCDEF has vertices at A(4, 4!3), B(8, 4!3), C(10, 2!3), D(8, 0), E(4, 0) and F(2, 2!3).
marissa [1.9K]

Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:

A=\frac{3\sqrt{3}}{2} a^2

Where A is the area of the regular hexagon

a is the side length of the regular hexagon

Also, it's Perimeter is given by:

P=6a

Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.

A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.

Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.

Let us now find the distance between the points D and E using the distance formula which is as:

d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

Where d is the distance.

(x_1,y_1) and (x_2,y_2) are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance d)

Applying the above formula we get:

d=\sqrt{(8-4)^2+(0-0)^2} =\sqrt{4^2}=4

\therefore d=4

We know that this distance is the side length of the given regular hexagon.

\therefore d=a=4

Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:

a_{small}=4-\frac{40}{100}\times 4=2.4

Thus, the area of the smaller hexagon will be:

A_{small}=\frac{3\sqrt{3}}{2} a_{small}^2=\frac{3\sqrt{3}}{2} (2.4)^2\approx14.96 unit squared

and the new smaller perimeter will be:

P_{small}=6a_{small}=6\times 2.4=14.4 unit

Which are the required answers.

5 0
3 years ago
pls help me with this question. just one! thank you so much to whoever decides to it will make my day a lot ❤️❤️
Yuliya22 [10]

Answer:

2 385/3913

i think..

Step-by-step explanation:

6 0
2 years ago
Which of the following figures could represent the cross section of a rectangular pyramid? Select all that apply.
Rama09 [41]

Answer:

Options C and E

Step-by-step explanation:

Option A. Circle

We can't get a cross section in the form of a circle.

Option B. Cube

We can't get a cross section in the form of a cube.

Option C. Rectangle

When we slice a rectangular pyramid parallel to the base but not through the vertex, we get a Rectangle.

Option D. Square

We can not get a square by slicing a rectangular pyramid.

Option E. Triangle

By slicing a rectangular pyramid perpendicular to the base and passing through the vertex we can get the cross section in the form of  triangle.

Options C and E will be the answer.

4 0
3 years ago
The two toy store owners agree to specialize and to trade 30 puzzles for 10 puppets. The terms of trade are still 3 puzzles for
likoan [24]

Based on the exchange rate, at the end of the trade, Lewis will have 31 puppets and 2 puzzles left over while Geppeto will have 158 puzzles and 4 puppets left over.

<h3>What is the exchange rate of puzzles for puppets?</h3>

The exchange rate of puzzles for puppets is 3 to 1.

Geppeto has 20 puppets to exchange for puzzles.

Lewis has 50 puzzles to exchange for puppets.

Number of times Lewis can exchange puzzles for puppets = 50/3 = 16 times.

Lewis will get 16 puppets in exchange for 48 puzzles.

Therefore;

Lewis will have 16 + 25 puppets = 31 puppets and 2 puzzles left over

Geppeto will have 48 + 100 puzzles = 158 puzzles and 4 puppets left over.

in conclusion, the exchange rate determines the how many puzzles and puppets will each one have after they complete their trade.

Learn more about exchange rate at: brainly.com/question/2202418

#SPJ1

7 0
2 years ago
Help plz it’s my final grade besties
Furkat [3]

a)

blank table values:

1, 2, 4, 8, 16, 32, 64

(2,4) and (6,64)

b)

y = 1 * 2^{x}

2^{20} = 1048576

5 0
3 years ago
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