What is the value of the expression shown below? 7 + (10 - 4 )^2 divided 4 x (1/2)

43 / 2  = 21  1/2 = 21.5

Step-by-step explanation:

7+(10-4)^2/ 4 (12)        you can either multiply by  4(1/2)/4(12) or do the following

Subtract 4 from 10 to get 6.

7+6^2 / 4×(  1/2)  

Calculate 6 to the power of 2 and get 36.

7+36 / 4×(  1/2  )  

Add 7 and 36 to get 43.

43 / 4× 1/2  

 Multiply 4 and    1/2   ​ to get 2.

43 / 2  = 21  1/2 = 21.5

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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