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astraxan [27]
3 years ago
9

describe two different ways that you could find the product 8 times 997 using mental math. Find the product and explain why your

methods work
Mathematics
1 answer:
Free_Kalibri [48]3 years ago
3 0

Answer:

First in your head multiply 8 by 7. this equals 56. now multiply 8 by 9 twice since there is two 9's. now you have two 72's. Add the 2's together from both 72's. now your numbers are 70, 70, 56 and 4. Add the four to your 5 which is now 96. split 96 between the 70's. not dividing just the two numbers. now you have 79, and 76. put together your numbers and your answer is 7976.

Step-by-step explanation:

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Step-by-step explanation:

8 0
2 years ago
Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points ​(4​,5​), ​(-6​,-6​), and ​(-14​,2​
Lilit [14]

Answer:

  (-2, -3)

Step-by-step explanation:

A careful graph shows the point (-2, -3) is at the intersection of the circles whose radii are the given distances from the receiving stations.

_____

The simultaneous equations for the circles can be solved algebraically.

The epicenter is 10 units from X, so lies on the circle ...

  (x -4)^2 +(y -5)^2 = 10^2

  x^2 -8x +16 +y^2 -10y +25 = 100

  x^2 +y^2 -8x -10y = 59

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The epicenter is 5 units from Y, so lies on the circle ...

  (x +6)^2 +(y +6)^2 = 5^2

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The epicenter is 13 units from Z, so lies on the circle ...

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Subtracting the second equation from each of the other two, we get ...

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  -20x -22y = 106 . . . . eq1 -eq2

  (x^2 +y^2 +28x -4y) -(x^2 +y^2 +12x +12y) = (-31) -(-47)

  16x -16y = 16 . . . . . . . .eq3 -eq2

These simultaneous linear equations can be solved a variety of ways. We might use substitution:

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  21y = -63 . . . . . . . . . . . . simplify, subtract 10

  y = -3

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The epicenter is located at (x, y) = (-2, -3).

8 0
3 years ago
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Step-by-step explanation:

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Step-by-step explanation:

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