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victus00 [196]
3 years ago
11

A certain right triangle has area 30 in. squared . one leg of the triangle measures 1 in. less than the hypotenuse. let x repres

ent the length of the hypotenuse. ​a) express the length of the leg mentioned above in terms of x. give the domain of x. ​b) express the length of the other leg in terms of x. ​c) write an equation based on the information determined thus far. square both sides and then write the equation with one side as a polynomial with integer​ coefficients, in descending​ powers, and the other side equal to 0. divide out any common factors to find the most simplified form. ​d) solve the equation in part​ (c) graphically. find the lengths of the three sides of the triangle.

Mathematics
1 answer:
Brut [27]3 years ago
6 0
A) The length of the longer leg is x-1

b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).

c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0

d) There is one positive real root, at x=13. A graphical solution works well.

The three sides of the triangle are 5 in, 12 in, 13 in.


_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.

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Answer:

4 + y = 36

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NemiM [27]

1. Eyeballing the data, the best fit will be pretty close to a line between the leftmost point and the rightmost point.

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Solve: 2x+4y=20 and 2x-y=4
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docker41 [41]

Use the quadratic formula to find:

x

=

1

±

√

85

5

Explanation:

5

x

2

−

10

x

−

12

is of the form  

a

x

2

+

b

x

+

c

with  

a

=

5

,  

b

=

−

10

and  

c

=

−

12

This has discriminant  

Δ

given by the formula:

Δ

=

b

2

−

4

a

c

=

(

−

10

)

2

−

(

4

×

5

×

−

12

)

=

100

+

240

=

340

=

2

2

⋅

85

This is positive, but not a perfect square, so the quadratic equation has a pair of irrational roots, given by the quadratic formula:

x

=

−

b

±

√

b

2

−

4

a

c

2

a

=

−

b

±

√

Δ

2

a

=

10

±

√

340

10

=

10

±

2

√

85

10

=

1

±

√

85

5

5 0
3 years ago
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