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Paladinen [302]
3 years ago
6

What are the coordinates of the midpoint of the segment whose endpoints are A (-1, -2) and B (6, 12)

Mathematics
1 answer:
Klio2033 [76]3 years ago
5 0

<u>Answer:</u>

Mid point = (\frac{5}{2} ,5)

<u>Step-by-step explanation:</u>

We are given the coordinates of the end points of a line segment AB and we are to find the coordinates of its mid point.

The coordinates of the end points are: A (-1, -2) and B (6, 12).

We know the formula of the mid point:

Mid point = (\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )

So putting in the given values to find the mid point of line segment AB:

Mid point = (\frac{-1+6}{2} ,\frac{-2+12}{2} ) = (\frac{5}{2} ,5)

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1. Dorothy bought a teddy bear and sold it at a 20% profit to Kim. Kim bought a suit costing $100 and dressed the teddy bear up
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1. Dorothy paid $200 for the teddy bear

2. y is more than x by 33\frac{1}{3} %

Step-by-step explanation:

1. The given is:

  • Dorothy bought a teddy bear and sold it at a 20% profit to Kim
  • Kim bought a suit costing $100 and dressed the teddy bear up in the suit
  • Kim then sold the teddy bear in the suit to Karen for $442
  • Kim made a profit of 30%

We need to find how much Dorothy paid for the teddy bear

Assume that Dorothy bought a teddy bear for $x

∵ Dorothy bought a teddy bear for $x

∵ She sold it at a profit 20% to Kim

By using the ratio method

→  Buying price    :    Profit    :    Selling price

→  100%                 :   20%       :    120% ⇒ (100% + 20%)

→  x                         :                 :    ?

By using cross multiplication  

∴ 100% × Selling price = x × 120%

- Divide both sides by 100%

∴ Selling price = 1.2x

∴ Dorothy sold the teddy bear for $1.2x to Kim

∵ Kim bought a suit costing $100 and dressed the teddy bear

  up in the suit

∴ The cost of the teddy bear = 1.2x + 100

∵ Kim sold the teddy bear in the suit to Karen for $442

∵ Kim made a profit of 30%

By using the ratio method

→  Cost price    :    Profit    :    Selling price

→  100%             :   30%      :    130% ⇒ (100% + 30%)

→  1.2x + 100     :                 :    442

By using cross multiplication  

∴ (1.2x + 100) × 130% =  100% × 422

- Divide both sides by 130%

∴ 1.2x + 100 = 340

- Subtract 100 from both sides

∴ 1.2x = 240

- Divide both sides by 1.2

∴ x = 200

∴ Dorothy bought the teddy bear for $200

Dorothy paid $200 for the teddy bear

2. The given is:

  • x is less than y by 25%
  • Then y is more than x by how many percent

Assume that y is 100%

∵ y = 100%

∵ x is less than y by 25%

∴ x = 100% - 25%

∴ x = 75%

- The percentage of increasing of y = \frac{y-x}{x} × 100%

∵ The percentage of increasing of y = \frac{100-75}{75} × 100%

∴ The percentage of increasing of y = \frac{25}{75} × 100%

∴ The percentage of increasing of y = \frac{1}{3} × 100%

∴ The percentage of increasing of y = 33\frac{1}{3} %

y is more than x by 33\frac{1}{3} %

Learn more:

You can learn more about the ratio in brainly.com/question/4713715

#LearnwithBrainly

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