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Dennis_Churaev [7]
3 years ago
14

Billy has x marbles. Write an expression for the number of marbles the following have… a) Charlie has 5 more than Billy b) Danny

has 8 fewer than Billy c) Eric has three times as many as Billy
Mathematics
1 answer:
tankabanditka [31]3 years ago
8 0

Answer:

  1. Charlie: 5 + x
  2. Danny: x - 8
  3. Eric: x × 3

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A triangle is rotated around N to give the primed version.


A. Same shape and size -- TRUE.  Rotation doesn't change shape or size.

B. Corresponding points are equidistant to N.  That's TRUE, each point is rotated around N to get its corresponding point, which will be the same distance from N.

C. DN=D'N.  TRUE, just an example of corresponding points.

D. Corresponding side lengths unequal, FALSE.  Rotation doesn't change lengths.



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3 years ago
In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD=√2 cm.
Zielflug [23.3K]

Given that triangle ABC is right angle triangle. CD is altitude such that AD=BC

ABC is a right angle triangle so apply Pythogorean theorem

AC^{2} + BC^{2} = AB^{2}

AC^{2} + AD^{2} = AB^{2}      (Given that AD = BC)

AC^{2} + AD^{2} = 3^{2}      (Given that AB=3)

AC^{2} + AD^{2} = 9 ...(i)

ADC is a right angle triangle so apply Pythogorean theorem

AD^{2} + CD^{2} = AC^{2}

AD^{2}+(\sqrt{2})^2= AC^{2}

AD^{2}+2= AC^{2}

AD^{2}=AC^{2} -2 ...(ii)


Plug value (ii) into (i)

AC^{2} + AC^{2}-2 = 9

2AC^{2} -2=9

2AC^{2} =11

AC^{2} =\frac{11}{2}

AC=\sqrt{\frac{11}{2} }


Hence final answer is AC=\sqrt{\frac{11}{2} }

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Answer:

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I hope that this helps! :)

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