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s2008m [1.1K]
2 years ago
11

I need help! This pattern repeats every 4 terms. The pattern is square, hexagon, trapezoid, triangle. What is the shape in the 7

th term of this pattern?
Mathematics
1 answer:
alina1380 [7]2 years ago
6 0
<h3>Answer:  Trapezoid</h3>

==========================================================

Explanation:

There are two ways to do this problem.

Method 1 involves listing out the terms until we reach the seventh one.

  1. square
  2. hexagon
  3. trapezoid
  4. triangle
  5. square
  6. hexagon
  7. trapezoid
  8. triangle

We see that the trapezoid is term 7.

-------------

Method 2 is faster and the one I recommend.

Since the pattern repeats every 4 items, this means we divide by 4 and look at the remainder. Ignore the quotient entirely.

7/4 = 1 remainder 3

The remainder 3 means that the answer is found in term 3, which is the trapezoid.

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<h3>Answer: 1</h3>

where x is nonzero

=======================================================

Explanation:

We'll use two rules here

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------------------------------

The portion [ x^(a-b) ]^(a+b) would turn into x^[ (a-b)(a+b) ] after using the first rule shown above. That turns into x^(a^2 - b^2) after using the difference of squares rule.

Similarly, the second portion turns into x^(b^2-c^2) and the third part becomes x^(c^2-a^2)

-------------------------------

After applying rule 1 to each of the three pieces, we will have 3 bases of x with the exponents of (a^2-b^2),  (b^2-c^2) and (c^2-a^2)

Add up those exponents (using rule 2 above) and we get

(a^2-b^2)+(b^2-c^2)+(c^2-a^2)

a^2-b^2+b^2-c^2+c^2-a^2

(a^2-a^2) + (-b^2+b^2) + (-c^2+c^2)

0a^2 + 0b^2 + 0c^2

0+0+0

0

All three exponents add to 0. As long as x is nonzero, then x^0 = 1

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From the attached figure we can see that two sides and one angle is given

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\frac{sin A}{a} = \frac{Sin B}{b}  = \frac{Sin C}{c}

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\frac{sin Q}{q} = \frac{Sin R}{r}  = \frac{Sin S}{s}

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