What is the y-coordinate of the solution to the system of equations? 5x-y=25 4x+3y=1

The y-coordinate of the solution is thus -5.

Step-by-step explanation:

Rewrite 5x-y=25 4x+3y=1

in a column:

5x-y=25

4x+3y=1

If we want to find the y-coordinate of the solution, we need to eliminate x.  Solving the second equation for 4x yieds 4x = 1 - 3y, or

x = (1 - 3y)/4.

If this is inserted into 5x - y = 12, we get:

5(1 - 3y)/4 - y = 25, or (multiplying all terms by 4 to eliminate fractions):

5 - 15y - 4y = 100, or

-19y = 95, which yields y = -5

The y-coordinate of the solution is thus -5.

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.

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.