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Darya [45]
3 years ago
7

The coordinate bridge shows the cost of different numbers of bookmarks how many sense do for bookmarks cost.

Mathematics
1 answer:
pogonyaev3 years ago
7 0

Answer:

54 cents

Step-by-step explanation:

The cost of bookmarks relating to the number of bookmarks is given by the graph shown. Therefore:

From the graph, we can determine the relationship between the cost of bookmarks and the number of bookmarks by using two points. The equation of a line passing through points (x_1,y_1)\ and\ (x_2,y_2) is:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\

From the graph, y represents the cost of bookmarks in cents and x represent the number of bookmarks. we can see that it passes through the point (2, 30) and (7, 90). Hence:

y-30=\frac{90-30}{7-2}(x-2)\\\\y-30=12(x-2) \\\\y-30=12x-24\\\\y=12x+6

The cost of 4 bookmarks (x = 4):

y = 12(4) + 6

y = 54 cents

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0.444 = 444/1000 = 222/500 = 111/250

0.444 is the same as 111/250, a fraction of integers, so 0.444 is rational.
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You use 6 gallons of water on 20 plants in your garden. At that rate, how much water will it take to water 30 plants?
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Read 2 more answers
The base of a prism has n sides. Find the numbers of faces, edges, and
Harman [31]

Answers:

  • faces = n+2
  • edges = 3n
  • vertices = 2n

===========================================================

Explanation:

Think of a hexagonal room with n = 6 walls, i.e. the floor is a hexagon with n = 6 sides. The floor and ceiling are parallel to each other, and congruent hexagons. That's 2 faces so far. Then we have another 6 faces to account for the walls. This gives 2+6 = 8 faces of a hexagonal prism.

In more general terms, a prism with a base of n sides will have 2 parallel and congruent base faces, and n walls or lateral faces. This gives n+2 total faces.

------------------------

Let's go back to the hexagonal prism. The floor has 6 sides to it, and so does the ceiling. We have 6+6 = 12 edges so far. Then we have another 6 edges where each of the rectangular walls meet up. That gives 12+6 = 18 edges total of this hexagonal prism room.

For any more general case, each base has n sides. That gives 2n sides so far for just the bases. Then add on another n for the lateral edges and we get 3n total edges.

--------------------------

Once again lets revisit the room with the hexagonal floor and ceiling. The floor has 6 vertices and the ceiling has the same vertex count. Therefore, this prism has 6+6 = 12 vertices.

For the general case, each base has n vertices. There are 2 such identical bases giving 2n vertices total.

---------------------------

One way to check the answer:

We could use Euler's Polyhedron Formula which is

F+V-E = 2

where,

  • F = number of faces
  • V = number of vertices
  • E = number of edges

For the hexagonal prism we found

  • F = 8
  • V = 12
  • E = 18

Then notice how

F+V-E = 2

8+12-18 = 2

20-18 = 2

2 = 2

This confirms the formula works for a hexagonal prism.

Now let's check it for the more general case

We found earlier that,

  • F = n+2
  • V = 2n
  • E = 3n

So,

F+V-E = 2

n+2+2n-3n = 2

3n-3n+2 = 2

0n+2 = 2

0+2 = 2

2 = 2

This helps confirm the answer for any prism with the base of n sides.

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