The table shows several units of mass. Unit of mass kilogram hectogram dekagram decigram centigram milligram microgram nanogram
10-6
10-9
10-3
102
101
10-2
103
10-1
Mass
(in grams)
a. How many times larger is the kilogram than the nanogram? Write your answer using only positive exponents.
The solution is
b. How many times smaller is a milligram than a hectogram? Write your answer using only positive exponents.
The solution is
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Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.

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