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postnew [5]
3 years ago
9

What is a quartic polynomial function in standard form with zeros -2,4,4,and 3

Mathematics
1 answer:
Travka [436]3 years ago
6 0

We can simply multiply the roots together to find the original function.

(x + 2)(x - 4)(x - 4)(x - 3)

FOIL.

x^2 - 4x + 2x - 8(x - 4)(x - 3)

Combine like terms.

x^2 - 2x - 8(x - 4)(x - 3)

FOIL.

x^3 - 2x^2 - 8x - 4x^2 + 8x + 32(x - 3)

Combine like terms.

x^3 - 6x^2 + 32(x - 3)

FOIL.

x^4 - 6x^3 + 32x - 3x^3 + 18x^2 - 96

Combine like terms.

<h3>x^4 - 9x^3 + 18x^2 + 32x - 96 is the original function with the given roots.</h3>
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how many 5-digit even numbers can be formed with the digits 1,2,3,4,5, and 6 if repetition is allowed?​
Setler79 [48]

Given:

The given digits are 1,2,3,4,5, and 6.

To find:

The number of 5-digit even numbers that can be formed by using the given digits (if repetition is allowed).

Solution:

To form an even number, we need multiples of 2 at ones place.

In the given digits 2,4,6 are even number. So, the possible ways for the ones place is 3.

We have six given digits and repetition is allowed. So, the number of possible ways for each of the remaining four places is 6.

Total number of ways to form a 5 digit even number is:

Total=6\times 6\times 6\times 6\times 3

Total=3888

Therefore, total 3888 five-digit even numbers can be formed by using the given digits if repetition is allowed.

6 0
3 years ago
A semicircle is cut out of a rectangular paperboard 24in long and 18n wide, as shown below. What is the perimeter of the paperbo
svet-max [94.6K]

Answer:

Perimeter of the paperboard that remains after the semicircle is removed = 94.26 in

Step-by-step explanation:

Watch the attached figure of how the semi circle is cut out of the rectangular paperboard.

Length = 24 in

Width = 18 in

Radius of the semi circle = Half of the width of the paperboard = \frac{18}{2} = 9 in

1) Circumference of the semi circle = π*radius

= 3.14*9

= 28.26 in

2) Perimeter of the paperboard that remains after the semicircle is removed

= Top + Left + Bottom + Right Circumference of the semi circle

= 24 + 18 + 24 + 28.26

= 94.26 in


5 0
3 years ago
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