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elena-14-01-66 [18.8K]
3 years ago
14

A pet store currently has a total of 45 cats and dogs. There are 7 more cats than dogs. Find the number of cats and dogs in the

store. Write and solve a system of equations that represents the situation. Interpret the solution
Mathematics
1 answer:
Evgesh-ka [11]3 years ago
7 0
The dog is 19, cat is 26
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  • It is the last graph: solid line, shaded area over the line x = 2 - x/2

Explanation:

1) <u>Set the algebraigic expression that represents the combinations of sofa and pillow orders:</u>

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  • Number of pillows: 2y (given, since they come in pairs)
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<u>2) Predict the graph of the inequality x + 2y ≥ 4</u>

  • The border line is the equation x + 2y = 4
  • You can choose two points to draw a line
  • Choose the axis-intercepst:

        x = 0 ⇒ 2y = 4 ⇒ y =4/2 ⇒ y = 2 ⇒ point (0,2)

        y = 0 ⇒ x = 4 ⇒ point (4,0)

        Then the lines goes through (0,2) and (4,0) ... [the four graphs meet this]

  • The shading area is above the line because when you solve for y you get y ≥   2 - x/2, and the line is included because the "equal to" part of the symbol (≥ means greater than or equal to).

  •  To state that the line is included the graph uses a continous line instead of a dotted one.

<u>3) Conclusion:</u>

That means that the correct graph is the last one: solid line, shaded area over the line y = 2 - x/2.

Note: a more detailed graph would include the fact that the items cannot be negative, i.e. x ≥ 0 and y ≥ 0, which would result in that the shaded area would be on the first quadrant.

   

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