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Lena [83]
3 years ago
6

Using Rigid motion, explain in detail, why triangle ABC must be congruent to triangle DEF

Mathematics
1 answer:
weeeeeb [17]3 years ago
7 0
Using rigid motion, both of these triangles will be congruent. The reason is because rigid motions include reflections, translations, and rotations.

None of these transformations will affect the size or shape of the figure, therefore keeping them congruent.
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I don’t understand this someone pls help me! (Question 10)
Likurg_2 [28]

Answer:

  a. f(n) = n(n+1)/2

  b. 351

  c. 19

  d. no; n would not be an integer for f(n) = 17.

Step-by-step explanation:

a. The terms are 1, 3, 6, 10, ...

Each term has the term number added to the previous term. That is, first differences are 3-1 = 2, 6-3 = 3, 10-6 = 4. These differences have a constant difference of 1.

When the 2nd differences are constant, a 2nd degree polynomial can describe the sequence. It is a little bit of trouble to find that polynomial.

For the polynomial ...

  f(n)=an^2+bn+c

We can substitute values for n and f(n) to get 3 equations in 3 unknowns:

  1=a\cdot1^2+b\cdot1+c\\\\3=a\cdot2^2+b\cdot2+c\\\\6=a\cdot3^2+b\cdot3+c

Solving these equations by your favorite method gives ...

  (a, b, c) = (1/2, 1/2, 0)

That is, the function representing the relationship is ...

  f(n) = n(n+1)/2 . . . . the function describing the relationship

__

b. f(26) = 26(27) = 13(27) = 351 . . . . the number of squares in term 26

__

c. The number of the term having 190 squares can be found by solving ...

  n(n +1)/2 = 190

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The 19th term will have 190 squares.

__

d. Terms 5 and 6 are 15 and 21.

17 is not the value of one of the terms in this sequence.

6 0
2 years ago
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