(01.07 hc)
angle and becky each completed a separate proof to show that the measures of vertical angles akg and hkb are equal. who completed the proof incorrectly? explain.
angie's proof
statement
justification
1. segment gh intersects segment ab at k 1. given
2. m akg + gkb - 180°
2. definition of supplementary angles
m_gkb + m_hkb = 180°
3. m akg + m2 gkb gkb +mchkb 3. substitution property
4. m. akg - hkb
4. subtraction property
becky's proof
statement
justification
1. given
1. segment gh intersects segment abk
2. m akg + m gkb 180°
m_gkb + mchkb = 180°
3. m. akgmgkb gkb hkb
2. angle addition postulate
3. substitution property
4. m. akg = mchkb
4. subtraction property

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt