Explain how you would graph the system of equations and why you would use that method.

t = 5c + 35,

t = 10c

See below  

Step-by-step explanation:

(1)  t = 5c + 35  

(2) t = 10c

(a) Create a table containing a few values of x and y

  t    5c + 35  10c  

  0        35          0

  2        45        20

  4        55        40

  6        65        60

  8        75        80

10         85      100

(b) Draw your axes

You should scale your axes so the graph covers most of the plot area.

The slopes of your lines are so steep that, without scaling, they will be quite steep, and it will be difficult to tell where they intersect.

The independent variable is c, so the c-axis is horizontal. The dependent variable is t, so it goes on the vertical axis.

Let the c-axis run from -2 to 12 and the t-axis from -20 to 120.

Divide the axes into convenient intervals for ease of reading (I chose units of 2 for the c-axis and 20 for the t-axis).

(2) Plot your points

Draw dots at the coordinates of each point.

(3) Draw the graphs

Draw straight lines through the points.

Extend the line in both directions to the edges of the plot area.

Your graph should look like the figure below.

With the scaled axes, it is easy to see that the two lines intersect at (7, 70).

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

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.