8. workpad note: remember to show all of the steps you use to solve a problem. you can use the comments field to explain your work. your teacher will review each step of your response to ensure yiu recieve proper credit for your answer. at the half-time show, a marching band marched in formation. the lead drummer started at a point with coordinates (2,-5) and moved 3 steps up and 1 step right. a. write a rule to describe the translation. b. what were the coordinates of the drummer's final position?

a) (x, y) → (x + 1, y + 3)

              b) (2, -5) → (3, -2)

Step-by-step explanation:

the x-axis goes left and right, so 1 step to the right means you need to add 1 unit to the x-coordinate.

the y-axis goes up and down, so 3 steps up means you need to add 3 units to the y-coordinate.

Rule:

If original x-coordinate is x, then the new coordinate is x + 1 (x → x+1)

If original y-coordinate is y, then the new coordinate is y + 3 (y → y+3)

Final position:

If original x-coordinate is 2, then the new coordinate is 2 + 1 (2 → 3)

If original y-coordinate is -5, then the new coordinate is -5 + 3 (-5 → -2)

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

i suppose it should be (y=2x-5)

step-by-step explanation: