What is the slope of the line that goes through the points (-1,4) and (14,-2)? a. b. c. d.

The slope of the line that goes through the points (-1,4) and (14,-2) is -2/5

The formula for calculating the slope of a line is expressed as:

Given the coordinate point expressed as (-1,4) and (14,-2)

m = -2-4/14-(-1)

m = -6/14+1

m = -6/15

m = -2/5

Hence the slope of the line that goes through the points (-1,4) and (14,-2) is -2/5

Learn more on slopes here: link

-3/5

Step-by-step explanation:

Plot (in your mind or on paper):  starting point (-1, 4), ending point (14, -2).

As we move from start to end, x increases by 15 (this is the run) and y decreases by 6.  Thus, the slope of the line going through these two points is

m = rise / run = -6/15, which can be reduced to:

m = -3/5

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

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.