Write the prime factorization of 48. use exponents when appropriate and order the factors from least to greatest
1 answer:
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Answer:
Explanation:
The complete question is:
<em>A hole the size of a photograph is cut from a red piece of paper to use in a picture frame.</em>
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<em>On a coordinate plane, 2 squares are shown. The photograph has points (-3, -2), (- 2, 2), (2, 1), and (1, -3). The red paper has points (- 4, 4), (4, 4), (4, -4), and (-4, -4).</em>
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<em>What is the area of the piece of red paper after the hole for the photograph has been cut?</em>
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<h2><em>Solution</em></h2><em />
The area of the piece of redpaper after the hole has been cut is equal to the area of the big square less the area of the small rectangle.
<u>1. Area of the big rectangle</u>
Vertices:
- <em>(- 4, 4) </em>
- <em>(4, 4)</em>
- <em>(4, -4)</em>
- <em>(-4, -4)</em>
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The side length is the distance between two consecutive vertices:
The two points (-4,4) and (4,4) has the same y-coordinate, thus the length is just the absolute value of the difference of the x-coordinates:
The area of this square is
<u>2. Area of the small square</u>
Vertices:
- <em>(-3, -2)</em>
- <em>(- 2, 2) </em>
- <em>(2, 1)</em>
- <em>(1, -3)</em>
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To find the side length use the distance formula for two consecutive points, for instance (2,1) and (-2,2):
The area is:
<u>3. Area of the piece of red paper after the holw for the photograph has been cut:</u>
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Find the difference:
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The nth term of an arithmetic sequence is found from:
Plugging in the given values, we get for the 13th term:
-58=14+12d
12d =-58 - 14 = -72
d = -6
So, the 32nd term is:
Plugging in the given values, we get for the 13th term:
-58=14+12d
12d =-58 - 14 = -72
d = -6
So, the 32nd term is: