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3 years ago

Which is best estimate for the length of the short leg a if the hypotenuses c is about 10 cm 15 points!!

Mathematics

1 answer:

iVinArrow [24]3 years ago

3 0

Answer:

A)4

Step-by-step explanation:

Assuming all edges are integral values

The most basic right angles triangle with integral edges is

(3,4,5)

as it obeys pythogores theorem

which is

$a^{2}+ b^{2} =c^{2} \\\text{where c is the hypotenuse}\\\text{and a and b are the other side}$

$3^{2} +4^{2} =5^{2}$

Now, double each edge,it will still remain a right angled triangle since it will still obey pythogores theorem

so the edges are (4,6,10)

⇒4 cm is the short leg of a integral right triangle with hypotenuse 10 cm

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Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

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Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

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Read 2 more answers

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Answer:

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