Which is a solution to (x - 2)(x + 10) = 13?
o x= 3
o x = 8
o x = 10
o x= 11

x = 3.

Step-by-step explanation:

(x - 2)(x + 10) = 13

x^2 + 8x - 20 = 13

x^2 + 8x - 33 = 0

( x +11)(x - 3) = 0

x = 3, -11.

x = - 11, x = 3

Step-by-step explanation:

Given

(x - 2)(x + 10) = 13 ← expand the left side using FOIL

x² + 8x - 20 = 13 ( subtract 13 from both sides )

x² + 8x - 33 = 0 ← in standard form

Consider the factors of the constant term (- 33) which sum to give the coefficient of the x- term (+ 8)

The factors are + 11 and - 3, since

11 × - 3 = - 33 and 11 - 3 = + 8, thus

(x + 11)(x - 3) = 0

Equate each factor to zero and solve for x

x + 11 = 0 ⇒ x = - 11

x - 3 = 0 ⇒ x = 3

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.