5. To get to the library from his house, Robert biked 6 kilometers due east and then8 kilometers due south. On the way back, he cut across a field, taking the shortest
possible route home.
How far did Robert bike on the round-trip?
Home
6 km
8 km
Library

Answers

Answer 1

Answer:

Answer:

24 kilometers.

Step-by-step explanation:

The shortest path between two points is a straight segment that connects the two points.

Refer to the diagram attached. The 6-km segment and the 8-km segment are normal to each other. Together with the segment that joins the library and the house, the three segments now form a right triangle.

The two shorter segments are the two legs, and
The longer segment that joins the library and the house is the hypotenuse.

The length of the hypotenuse can be found with the Pythagorean Theorem.

$\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{Leg 1})^(2) + (\text{Leg 2})^(2)}\n&= \sqrt{6^(2) + 8^(2)}\n&= √(36 + 64) \n&= √(100)\n&= \rm 10\;km\end{aligned}$ .

The length of the round-trip will equal to the sum of the length of the three segments: $\rm 6\;km + 8\;km + 10\;km = 24\;km$ .

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Answers

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1. Anne wants to join five pieces of paper together. She plans to use 3 rectangular pieces of the same size and 2 square pieces of the same size. The length of each rectangular piece is 3 1/2 feet. The width of each rectangular piece, w, is the same as the length of each square piece. The expression below can be used to find the total surface area of the five pieces of paper. Anne decides that the width, w, of the rectangular pieces should be 2 feet. What is the total surface area, in square feet, of all five pieces of paper?

Answers

Answer and explanation:

Surface area of a rectangle = length * width

Surface area of a square = a² where a is length of a side

To find total surface area of the the five pieces of paper, we add up all the areas of all the shapes

Given that length of rectangle =3.5

And width = 2

Area of rectangle =3.5*2=7

Area of 3 rectangles given they are all equal = 7*3=21

Since width of rectangle equal to width of square and all sides of square are equal

Area of square = 2 *2 =4

Area of the two squares =4*2=8

Total surface area of the five plane shapes = 21+8= 29

Shannon wants to calculate her property tax. The market value of the property is $85,000. The assessment rate is 41%. The property tax rate is $46.30 per $1000 of assessed value. Show all work.

Answers

Given:
Market VAlue = 85,000
Assessed value = 41%
property tax rate is 46.30 per 1,000 of assessed value.

85,000 * 41% = 34,850
34,850 / 1000 = 34.85
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The property tax to be paid is $1,614.56

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Answers

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24.
220 miles = 10 gallons

$(220)/(550) ~=~ (10)/(x)$

cross multiply :

220x = 5500

Divide 220 from both sides

$(220x)/(220) ~=~ (5500)/(220)$

x = 25

Check :

$(220)/(550) ~=~ (10)/(25)$

0.4 = 0.4

My answer is correct. It's (D.) 25 gallons of gas :)

How do you write 72.5% as a fraction in simplest form

Answers

The 72.5% as a fraction in simplest form is (29/40)

What is the fundamental principle of multiplication?

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We have to write 72.5% as a fraction in simplest form.

So we put 72.5 over 100

That is (72.5/100)

Now multiply the top and the bottom by 10 to get rid of the decimal, giving;

725/1000

Then divide the top and bottom by like factors,

5 (145/200)

Then another 5,

29 over 40 (29/40)

Hence, the 72.5% as a fraction in simplest form is (29/40)

Learn more about multiplications;

brainly.com/question/14059007

#SPJ5

So you put 72.5 over 100 (72.5/100)
Then you multiply the top and the bottom by 10 to get rid of the decimal, giving you 725/1000
Then you divide the top and bottom by like factors, starting with 5 (145/200)
Then another 5, giving you 29 over 40 (29/40)

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