Graph the solution to this system of inequalities in the coordinate plane. 3y > 2x + 12
2x + y < -5

Plotting the inequalities using geogebra online graphing calculator. The graph is attached

Inequalities is an expression used to show the non equal comparison of numbers and variables.

Given the system of inequalities:

3y > 2x + 12

3y - 2x > 12   (1)

2x + y < -5    (2)

Plotting the inequalities using geogebra online graphing calculator. The graph is attached

Find out more on inequalities at: link

Step-by-step explanation:

3y > 2x + 12

This inequality will be represented by the a dotted line and solution area for the inequality will be shaded area (In red) above the dotted line.

2x + y ≤ -5

y ≤ -2x - 5

This inequality will be represented by a solid line and solution area will be the shaded area (in blue) below the solid line.

Therefore, common area of both will be the solution area for the system of inequalities.

x -

median = 1.25

range = 12-14.5

interquartile = q12-q14.5

y -

median = 1

range = 15-17

interquartile = q15-q17

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.