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tatyana61 [14]
3 years ago
15

A rectangle has a length of (3.2a + 0.18b)centimeters.The width is half the length. Sasha writes the expression (12.8a + 0.72b)

to represent the perimeter of the rectangle in centimeters. Is Sasha’s reasoning correct? Explain.
Mathematics
1 answer:
jeka943 years ago
8 0
The width is half the length, so is
  width = (1/2)*length
  width = (1/2)*(<span>3.2a + 0.18b) cm
  width = (1.6a +0.09b) cm

The perimeter of the rectangle is twice the sum of length and width.
  perimeter = 2*(length + width)
  perimeter = 2*((3.2a +0.18b) cm + (1.6a +0.09b) cm)
  perimeter = 2*(4.8a +0.27b) cm)
  perimeter = (9.6a +0.54b) cm

Sasha did not get this answer, so apparently ...
  her reasoning was not correct.</span>
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Answer:

1. 4x^{3} + 26x² + 4x - 48

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3. x^{5} + 7x^{3} - 4x + 2x^{4} + 14x² - 8

4. 2x^{7} + x^{6} - 28x^{5} + 3x + 12

Step-by-step explanation:

To multiply polynomials, simply distribute whatever's outside the largest set of parenthesis, then combine like terms.

1) Distribute the parenthesis (x + 6):

x(4x² + 2x - 8)  +  6(4x² + 2x - 8)

4x^{3} + 2x² -8x  +  6(4x² + 2x -8)

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Combine like terms:

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2) Distribute the parenthesis (x - 8):

x(2x² - 7x + 4)  +  (-8)(2x² - 7x + 4)

2x^{3} - 7x² + 4x  +  (-8)(2x² - 7x + 4)

2x^{3} - 7x² + 4x  +  -16x² + 56x - 32

Combine like terms:

2x^{3} - 23x² + 60x - 32

3) Distribute the parenthesis (x + 2):

x(x^{4} + 7x² - 4)  +  2(x^{4} + 7x² - 4)

x^{5} + 7x^{3} - 4x  +  2(x^{4} + 7x² - 4)

x^{5} + 7x^{3} - 4x + 2x^{4} + 14x² - 8

No like terms to combine, so:

x^{5} + 7x^{3} - 4x + 2x^{4} + 14x² - 8

4) Distribute the parenthesis (x + 4):

x(2x^{6} - 7x^{5} + 3)  +  4(2x^{6} - 7x^{5} + 3)

2x^{7} - 7x^{6} + 3x  +  4(2x^{6} - 7x^{5} + 3)

2x^{7} - 7x^{6} + 3x + 8  x^{6} - 28x^{5} + 12

Combine like terms:

2x^{7} + x^{6} - 28x^{5} + 3x + 12

hope this helps!

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