Sample Response: If you have SSA, then the third side determines the triangle. If it is too short to
intersect the other side, then it does not form a triangle.
The third side can also be just the right length to meet
the other side, making one triangle. Finally, the third
side might be long enough to intersect the other side at
two different points, creating two triangles.
What did you include in your response? Check all that
apply
When the third side of the triangle is too short to
intersect the other side, no triangles can be formed
o When the third side is just long enough to meet the
other side at one point, one triangle is formed.
When the third side is long enough to intersect the
other side at two points, two triangles are formed

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step-by-step explanation:

answer: rolling a number cube and flipping a coin.

step-by-step explanation:

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