Answer:
Fourth degree polynomial (aka: quartic)
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Work Shown:
There isnt much work to show here because we can use the fundamental theorem of algebra. The fundamental theorem of algebra states that the number of roots is directly equal to the degree. So if we have 4 roots, then the degree is 4. This is assuming that there are no complex or imaginary roots.
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If you want to show more work, then you would effectively expand out the polynomial
(x-m)(x-n)(x-p)(x-q)
where
m = 4, n = 2, p = sqrt(2), q = -sqrt(2)
are the four roots in question
(x-m)(x-n)(x-p)(x-q)
(x-4)(x-2)(x-sqrt(2))(x-(-sqrt(2)))
(x-4)(x-2)(x-sqrt(2))(x+sqrt(2))
(x^2-6x+8)(x^2 - 2)
(x^2-2)(x^2-6x+8)
x^2(x^2-6x+8) - 2(x^2-6x+8)
x^4-6x^3+8x^2 - 2x^2 + 12x - 16
x^4 - 6x^3 + 6x^2 + 12x - 16
We end up with a 4th degree polynomial since the largest exponent is 4.
Answer:
X equals 6°.
Step-by-step explanation:
There is a geometry rule that states the outer angle of a triangle's interior angle is equivalent to the sum of the remaining two interior angles of the triangle. Following this rule, you can get that (6x + 8) + (5x + 8) = 82° ⇒ 11x + 16 = 82° ⇒ 11x = 66° ⇒ x = 6°.
Answer:
I. AC = 15 cm
II. h = 7.4 cm
Step-by-step explanation:
I. Determination of AC
AB = 9 cm
BC = 12 cm
AC =?
The length AC can be obtained by using pythagoras theory as illustrated below:
AC² = AB² + BC²
AC² = 9² + 12²
AC² = 81 + 144
AC² = 225
Take the square root of both side
AC = √225
AC = 15 cm
II. Determination of the height.
AB = 9 cm
AD = 5.1 cm
BD = h =?
The height of the triangle can be obtained by using pythagoras theory as illustrated below:
AB² = AD² + BD²
9² = 5.1² + h²
81 = 26.01 + h²
Collect like terms
h² = 81 – 26.01
h² = 54.99
Take the square root of
h = √54.99
h = 7.4 cm
The answer is
Exact form: -35/18
Decimal form:-1.94444444...
Mixed number form: -1 17/18
The dilation is 4. Everything is getting 3 times bigger.
