The legs of a right triangle have lengths of 4 and 5 units. what is the length of the hypotenuse

1 answer:

3 0

This question can be solved using the Pythagorean theorem. $a^2 + b^2 = c^2$ where a and b are the legs of the triangle and c is the hypotenuse.

$4^2 + 5^2 = c^2$
$16 + 25 = c^2$
$41 = c^2$
$\sqrt{41} = c$
So, c is approximately 6.403.

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Based on the polynomial remainder theorem, what is the value of the function when x=−6 ?

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EXPLANATION

The given function is
$f(x) = {x}^{4} + 8 {x}^{3} + 10 {x}^{2} - 7x + 40$

According to the remainder theorem,

$f( - 6) = R$
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$f(x)$

is divided by
$x + 6$

We therefore substitute the value of x and evaluate to obtain,

$f( - 6) = { (- 6)}^{4} + 8 {( - 6)}^{3} + 10 { (- 6)}^{2} - 7( - 6)+ 40$

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This will evaluate to,

$f( - 6) = 10$

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is
$10$

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$10$
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$f(x) = {x}^{4} + 8 {x}^{3} + 10 {x}^{2} - 7x + 40$
is divided by
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