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mr_godi [17]
3 years ago
10

If the sum of the legs of a right triangle is 49 inches and the hypotenuse is 41 inches, find the length of the other two sides

Mathematics
1 answer:
german3 years ago
4 0
The length of one leg is x inches.
The sum of the legs is 49 inches, so the length of the other leg is 49-x inches.
The length of the hypotenuse is 41 inches.

Use the Pythagorean theorem:
(\hbox{one leg})^2 + (\hbox{the other leg})^2=(\hbox{hypotenuse})^2 \\ x^2+(49-x)^2=41^2 \\
x^2+2401-98x+x^2=1681 \\
2x^2-98x+2401=1681 \ \ \ |-1681 \\
2x^2-98x+720=0 \\ \\
a=2 \\ b=-98 \\ c=720 \\ b^2-4ac=(-98)^2-4 \times 2 \times 720=9604-5760=3844 \\ \\
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-98) \pm \sqrt{3844}}{2 \times 2}=\frac{98 \pm 62}{4} \\
x=\frac{98-62}{4} \ \lor \ x=\frac{98+62}{4} \\
x=\frac{36}{4} \ \lor \ x=\frac{160}{4} \\
x=9 \ \lor \ x=40


49-x=49-9 \ \lor \ 49-x=49-40 \\
49-x=40 \ \lor \ 49-x=9

The lengths of the legs are 9 inches and 40 inches.
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Given:

The leading coefficient of a polynomial is 8.

Polynomial roots are 1 and 2.

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The 3rd root and the equation of the polynomial.

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y=a(x-c_1)(x-c_2)...(x-c_n)

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Polynomial roots are 1 and 2. So, (x-1) and (x-2) are the factors of the polynomial.

Let the third root of the polynomial by c, then (x-c) is a factor of the polynomial.

The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:

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The graph passes through the point (4,5). Putting x=4,y=5, we get

5=8(4-1)(4-2)(4-c)

5=8(3)(2)(4-c)

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\dfrac{5}{48}=4-c

c=4-\dfrac{5}{48}

c=\dfrac{192-5}{48}

c=\dfrac{187}{48}

Therefore, the 3rd root on the polynomial is \dfrac{187}{48}.

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2 years ago
Janine has 3 3/4 cup of flour. She uses 1/3 of the flour to make pancakes.How many cups of flour did she use?
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Step-by-step explanation:

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The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distribut
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Answer:

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Step-by-step explanation:

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Z = \frac{x-mean}{S.D} = \frac{280-320}{20} = -2

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<u><em>Step(iii):-</em></u>

The probability there will be between 280 and 360 column inches of classified advertisement

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                      = 2P(z≤2)

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