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NISA [10]
2 years ago
13

the hypotenuse of a triangle is one foot more than twice the length of the shorter legal. the longer leg is seven feet longer th

an the shorter leg. find the dimensions of the triangle
Mathematics
2 answers:
wolverine [178]2 years ago
6 0
8, 15, 17

You can do this by using the Pythagorean Theorem and setting the sides equal to

shorter leg = x
longer leg = x + 7
hypotenuse = 2x + 1

Then solve so that one side is equal to zero and use the quadratic formula.
Rus_ich [418]2 years ago
3 0

Answer:

<h2>The dimensions of the right triangle are 8, 15 and 17.</h2>

Step-by-step explanation:

First, we need to express the problem in equations. We will use the pythagorean theorem because we have a right triangle.

The longer side we're gonna call it l.

The shorter side will be s

The hypothenuse will be h

Now, the problem is giving us relations.

<h3>"The hypothenuse is one foot more than twice the length of the shorter leg"</h3>

This can be expressed like h=1+2s

<h3>"The longer leg is seven feet longer than the shorter leg"</h3>

This can be expressed like l=7+s

Now, applying the pythagorean theorem, we have:

h^{2}=s^{2}+l^{2}\\(1+2s)^{2}= s^{2}+(7+s)^{2}\\1+4s+4s^{2}= s^{2}+49+14s+s^{2}\\ 2s^{2}-10s-48=0\\s^{2}-5s-24=0\\(s-8)(s+3)=0\\s=8\\s=-3

From these values, we use the positive one, because it refers to length. Replacing this value in each expression, we find each element of the triangle:

h=1+2s=1+2(8)=17

l=7+s=15

Therefore, the dimensions of the right triangle are 8, 15 and 17.

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2 years ago
You are buying a house that cost 650,000 and you put down a down payment. you take out a loan for the remainder of the amount, o
gayaneshka [121]
<h3>Answers:</h3>

Monthly Payment = $4,702.68

Total Payments = $846,482.40

Interest = $261,482.40

Delete the dollar signs and/or commas if needed.

=====================================================

Explanation:

The down payment is 10% of the home's value

This means that the buyer pays $65,000 up front (since 0.10*650,000 = 65,000).

The remaining 650,000 - 65,000 = 585,000 dollars is loaned in the mortgage.

Or you could write it like this 95% of 650,000 = 0.95*650,000 = 585,000

-----------------

The monthly payment formula is

P = (L*i)/( 1-(1+i)^(-n) )

where,

  • P = monthly payment
  • L = amount loaned
  • i = interest rate per month in decimal form
  • n = number of months

In this case,

  • L = 585,000 dollars
  • i = 0.0525/12 = 0.004375 exactly
  • n = 15*12 = 180 months (equivalent to 15 years)

So,

P = (L*i)/( 1-(1+i)^(-n) )

P = (585000*0.004375)/( 1-(1+0.004375)^(-180) )

P = 4702.6846353538

P = 4702.68

The monthly payment is $4,702.68

-----------------

Let's now compute the total amount paid back (principal + interest)

If you pay 4,702.68 dollars per month over the course of 180 months, then you pay back a total of 4702.68*180 = 846,482.40

The total payments add up to 846,482.40 dollars.

-----------------

To compute the interest only, subtract the total payments from the amount loaned.

846,482.40 - 585,000 = 261,482.40 is the amount of interest only.

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Do 9/32. 32 is the total
8 0
3 years ago
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15PTS!!!! HELPPPP!!! Determine the length of fencing around an 80 m by 170 m rectangular playing field if fence is to be 25 m ou
marshall27 [118]
Perimeter=2L+2W, in this case L=80+2(25) and W=170+2(25) so

P=2(L+W)=2(80+50+170+50)

P=2(350)=700m
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3 years ago
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