Which graph represents the following system of inequalities? y < -3x+5 y < x+2 y < -1

The graph was plotted and is attached below.

Inequality is the unequal comparison of numbers or expressions.

Given the inequalities: y < -3x+5, y < x+2, y < -1

Graphing the above inequalities using the geogebra online graphing calculator.

The graph is attached below.

Find out more at: link

The attached graph represents the system

Step-by-step explanation:

Let us describe the graph of each line

In y < -3x + 5

∵ The sign of inequality without =

∴ The line represents it must be dashed

The slope-intercept form of the inequality is y < m x + b, where m is the slope and b is the y-intercept

∵ y < -3x + 5

∴ m = -3 and b = 5

∴ The direction of the line is to the left and intersect the y-axis at (0, 5)

∴ y < -3x + 5 represented by the green line

∵ The sign of inequality is <, then the shading is under the green line

In y < x + 2

∵ The sign of inequality without =

∴ The line represents it must be dashed

∴ m = 1 and b = 2

∴ The direction of the line is to the right and intersect the y-axis at (0, 2)

∴ y < x + 2 represented by the blue line

∵ The sign of inequality is <, then the shading is under the blue line

In y < -1

∵ The sign of inequality without =

∴ The line represents it must be dashed

∴ m = 0 and b = -1

∴ The line is horizontal and intersects the y-axis at (0, -1)

∴ y < -1 represented by the red line

∵ The sign of inequality is <, then the shading is under the red line

∵ The shading of the three inequalities is under the lines

∴ The solutions of the system of inequalities lie in the common

   shaded part under the three lines

∴ The attached graph represents the system

a) justify

step-by-step explanation:

justifying is just part of everyday life. justify kind of means proof so i think the answer is a) justify.

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.