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olga55 [171]
3 years ago
11

Perry was going to sell all of his stamp collection to buy a video game. After selling half of them he changed his mind. He then

bought fifteen more. How many did he start with if he now has 34?
Mathematics
1 answer:
andrezito [222]3 years ago
4 0
The answer is 38, because if you take away the 15 he bought afterwards (34-15) you get 19, and then since he sold half his collection you would double that (19×2) and that's 38.
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Quadrilateral JKLM is graphed with vertices at J(-2,2), K(-1,-5), L(4,0), and M(3,7).
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Answer:

<u>Question (a)</u>

Midpoint of a line segment:

M=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)

Given:

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  • L = (4, 0)

\implies \textsf{midpoint of }JL=\left(\dfrac{-2+4}{2},\dfrac{2+0}{2}\right)=(1,1)

Given:

  • M = (3, 7)
  • K = (-1, -5)

\implies \textsf{midpoint of }MK=\left(\dfrac{3-1}{2},\dfrac{7-5}{2}\right)=(1, 1)

<u>Question (b)</u>

Find slopes (gradients) of JL and MK then compare.  If the product of the slopes of JL and MK equal -1, then JL and MK are perpendicular.

\textsf{slope }m=\dfrac{y_2-y_1}{x_2-x_1}

Given:

  • J = (-2, 2)
  • L = (4, 0)

\implies \textsf{slope of }JL=\dfrac{0-2}{4+2}=-\dfrac13

Given:

  • M = (3, 7)
  • K = (-1, -5)

\implies \textsf{slope of }MK=\dfrac{-5-7}{-1-3}=3

\textsf{slope of }JL \times \textsf{slope of }MK=-\dfrac13 \times3=-1

Hence segments JL and MK are perpendicular

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