Which system of equations is represented by this table of values?

can you explain as well but like you don't have to but try.

  see below

Step-by-step explanation:

As is often the case with multiple choice questions involving linear equations, a suitable solution strategy is to eliminate the choices that don't make any sense.

Here, you're given all of the answer choices in slope-intercept form. You are also given a line for x=0 in the table, so the table values on that line give the intercepts of the functions.

f1 has a "y-intercept" of -2, eliminating the upper right and lower left answer choices.

When x increases by 1, from 0 to 1, f1(x) increases by 2, from -2 to 0. So, the coefficient of x in the equation for f1(x) will be 2, matching the upper left answer choice.

You can try other table values in those equations to check that they work. It is usually sufficient to check one other value (since you already know the equations work for x=0). x=1 is often a convenient value to use.

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In slope-intercept form, the equation for a line is ...

  y = mx + b

where m is the slope and b is the intercept. The intercept is the value of y when x=0.

The slope is the amount of increase of y when x increases by 1.

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.