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2 years ago

9

When a certain polynomial is divide by binomial x-3, the result is 4x-5+6/x-3. What is the polynomial

1 answer:

Dmitry_Shevchenko [17]2 years ago

7 0

$\frac{p(x)}{x-3} = 4x-5 + \frac{6}{x-3}$

The polynomial p(x) can be found by multiplying 'x-3' to every term
$p(x) = (4x-5)(x-3) + 6$

Now distribute and you have your answer.
$p(x) = 4x^2 -12x-5x+15 +6 \\ \\ p(x) = 4x^2 -17x+21$

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Oksanka [162]

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<h3>What is a function?</h3>

A function is an expression or rule that explains the relationship between a dependent and independent variable.

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1 year ago

Nadia is investigating rotations about the center of regular polygons that carry the regular polygon onto itself. She claims tha

GalinKa [24]

Answer:

$\theta_1 \ n\ \theta_2 = 120, 240$

Step-by-step explanation:

The question is incomplete, as the angles of rotation are not stated.

However, I will list the angles less than 360 degrees that will carry the hexagon and the nonagon onto itself

We have:

$Nonagon = 9\ sides$

$Hexagon = 6\ sides$

Divide 360 degrees by the number of sides in each angle, then find the multiples.

<u>Nonagon</u>

$\theta = \frac{360}{9} =40$

List the multiples of 40

$\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320$

<u>Hexagon</u>

$\theta = \frac{360}{6} =60$

List the multiples of 60

$\theta_2 = 60, 120, 180, 240, 300$

List out the common angles

$\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320$

$\theta_2 = 60, 120, 180, 240, 300$

$\theta_1 \ n\ \theta_2 = 120, 240$

This means that, only a rotation of $120, 240$ will lift both shapes onto themselves, when applied to both shapes.

The other angles will only work on one of the shapes, but not both at the same time.

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