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Zigmanuir [339]
2 years ago
7

What is the answer to this question? Write an expression in simplest form for the perimeter of a right triangle with leg lengths

of 3a to the third power and 4a to the third power.
Mathematics
1 answer:
blagie [28]2 years ago
7 0

Answer:

Step-by-step explanation:

Since the length of both legs of the right angle triangle are given, we would determine the hypotenuse, h by applying Pythagoras theorem which is expressed as

Hypotenuse² = one leg² + other leg²

Therefore,

h² = (3a)³ + (4a)³

h² = 27a³ + 64a³

h² = 91a³

Taking square root of both sides,

h = √91a³

The formula for determining the perimeter of a triangle is expressed as

Perimeter = a + b + c

a, b and c are the side length of the triangle. Therefore, the expression for the perimeter of the right angle triangle is

√91a³ + (3a)³ + (4a)³

= √91a³ + 91a³

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A certain forest covers an area of 2100 km². Suppose that each year this area decreases by 3.5%. What will the area be after 5 y
Blizzard [7]

Answer:

\large\boxed{\sf \ \ \ 1757 \ km^2 \ \ \  }

Step-by-step explanation:

Hello,

<em>I would recommend that you checked the answers I have already provided as this is the same method for all these questions, and maybe try to solve this one before you check the solution.</em>

<u>At the beginning the area is 2100</u>

<u>After one year</u> the area will be

   2100*(1-3.5%)=2100*0.965

<u>After n years</u> the area will be

   2100\cdot0.965^n

So after 5 years the area will be

   2100\cdot0.965^5=1757.34027...

So rounded to the nearest square kilometer is 1757

Hope this helps

8 0
3 years ago
Read 2 more answers
Viola has to relocate for her job. She finds a townhome with an option to rent or buy. The conditions of each are shown below. R
Zepler [3.9K]
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4 0
2 years ago
Jan jdjnznxwjzn help
Katyanochek1 [597]

Answer:

A.

Step-by-step explanation:

4 0
2 years ago
At a lake, there are 2 boat rental shops. Shop A charges $210 for a 4-hour rental, and shop B charges $246 for a 6-hour rental.
MrRissso [65]

Answer:

  Shop A is more expensive by $11.50 per hour

Step-by-step explanation:

I solved this three ways.

1) The difference in time for the two given charges is (6 -4) = 2 hours. The charge at Shop A for 2 hours is half the charge for 4 hours, so its equivalent rate for 6 hours is ...

  Shop A rate for 6 hours = rate for 4 hours + rate for 2 hours

  = $210 +105 = $315 . . . for 6 hours

This is way more than what Shop B charges for 6 hours.

__

2) The difference in the charges is $246 -$210 = $36 for 2 hours difference in time. This is way less than the equivalent charge from Shop A for 2 hours, so the rate from Shop A is definitely higher.

__

3) In order to answer the question, "how much more expensive?" we expect the rate difference will need to be expressed as a per-hour difference.* This means we have to figure the per-hour charge for each Shop and find the difference of them.

  Shop A = $210/(4 h) = $52.50 /h

  Shop B = $246/(6 h) = $41.00 /h

The rate from Shop A is higher by $52.50 -41.00 = $11.50 per hour.

_____

<em>Comments on How Much More</em>

* Using the first method, the rate difference is $315 -246 = $69 for 6 hours.

Using the second method, the rate difference is difficult to express exactly, but we can say the rate difference of $36 for 2 additional hours at Shop B is exceeded by the $105 expected charge for 2 additional hours at Shop A. That difference rate ($36/(2h)) isn't an actual charge anywhere, but represents a way to tell if the slope of one curve is more or less than the slope of the other.

If the rates were the same at the two shops, the charge at Shop B for 6 hours would be $315 as we figured in the first method, so the difference of $315 -210 = 105 would match exactly the increment at Shop A for 2 hours.

Personally, I see the second method as easiest to compute and most telling. However, to answer the question, "how much more expensive is it?", we needed to use one of the other methods.

5 0
2 years ago
Solve the system of equations for x andy shown using the substitution
Harlamova29_29 [7]

Answer:

(1,3)

Step-by-step explanation:

11x+3x=14

14x=14

x=1

y=3x

y=3(1)

y=3

4 0
3 years ago
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