Ineed !

which statement is true of x2 + 8x – 6?

(x – 2) is a factor of the polynomial.
(x + 2) is a factor of the polynomial.
(x – 4) is a factor of the polynomial.
the polynomial is prime.

The correct option is

The polynomial is prime.

Step-by-step explanation:

we have to select the true statement for the equation

As, we know if is a positive perfect square integer, then the trinomial can be factored over the rational numbers. Otherwise, we cannot factor over the rational numbers,

so the trinomial is considered to be prime.

Equation:

a=1, b=8 and c=-6

which is not a perfect square integer.

Hence, the above trinomial can not be factored into lowe degree.

⇒ Given polynomial is prime.

hence, option 4 is correct.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

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