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Evgesh-ka [11]
3 years ago
9

A map has a scale of 1 in : 3 km. If the actual distance is 15 km, what is the distance on the map?

Mathematics
1 answer:
Black_prince [1.1K]3 years ago
4 0

Answer:

5 in.

Step-by-step explanation:

The ratio of map distance to real distance is 1 in : 3 km meaning that 1 inch on the map describes 15 km in real life.

15 km is 5 times 3 km, so the map distance is 5 times 1 in., or 5 in.

1 in. x 5 : 3 km x 5

This is a "school math" problem where things come out nicely!  Another way to look at this is with equivalent fractions.

\frac{\text{1 in}}{\text{5 km}} = \frac{\text{m}}{\text{15 km}}

"cross multiply"

5m = (15)(1)\\5m=15\\m=3 \text{ in.}

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Noah has a summer tree-trimming business. Based on experience, Noah knows that his profit, P, in dollars, can be modelled by = −
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Solving quadratic equations, it is found that he needs to charge:

1. He needs to charge $40 to break even.

2. He needs to charge $30 for a profit of $600.

<h3>What is a quadratic function?</h3>

A quadratic function is given according to the following rule:

y = ax^2 + bx + c

The solutions are:

  • x_1 = \frac{-b + \sqrt{\Delta}}{2a}
  • x_2 = \frac{-b - \sqrt{\Delta}}{2a}

In which:

\Delta = b^2 - 4ac

The profit equation in this problem is:

P(x) = -3x² + 150x - 1200.

He breaks even when P(x) = 0, hence:

-3x² + 150x - 1200 = 0.

The coefficients are a = -3, b = 150, c = -1200, hence:

  • \Delta = 150^2 - 4(-3)(-1200) = 8100
  • x_1 = \frac{-150 + \sqrt{8100}}{-6}
  • x_2 = \frac{-150 - \sqrt{8100}}{-6} = 40

He needs to charge $40 to break even.

For a profit of $600, we have that P(x) = 600, hence:

-3x² + 150x - 1200 = 600.

-3x² + 150x - 1800 = 0.

The coefficients are a = -3, b = 150, c = -1800, hence:

  • \Delta = 150^2 - 4(-3)(-1800) = 900
  • x_1 = \frac{-150 + \sqrt{900}}{-6}
  • x_2 = \frac{-150 - \sqrt{900}}{-6} = 30

He needs to charge $30 for a profit of $600.

More can be learned about quadratic equations at brainly.com/question/24737967

#SPJ1

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What is the equation of the line?
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Step-by-step explanation:

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