Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line −3x+5y=−15 ?

The answer to your question is below

Step-by-step explanation:

Data

Two lines are parallel if their slopes are the same.

Two lines are perpendicular if their slopes are reciprocal.

If there is no relation between the slopes of two lines they are neither parallel nor perpendicular.

Process

1.- Find the slope of the line given

                         -3x + 5y = -15

                          5y = 3x - 15

                          y = x - 3

Slope =

2.- Find the slopes of the other lines

a) 5x + 3y = 15

  3y = -5x + 15

  y = - + 5

slope = -            This line is perpendicular to the line  given

                                                         because the slopes are reciprocal.

b)   3x + 5y = 15

     5y = -3x + 15

     y = - x + 15    This line is neither parallel nor

    slope  = -                                  perpendicular

c)     -3x + 5y = 15

       5y = 3x + 15

       y = x + 15

 slope =             This line is parallel to the line given

d)   3x + 5y = 15

     5y = -3x + 15

     y = + 3

     slope =        This line is neither parallel nor perpendicular to the line given

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m

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.