Which algebraic equation is represented by the diagram?

a. 2(a+b)=2a+2b
b. a2+b2=a2+2ab+b2
c. a(a+2b)=a2+2ab
d. b(a+b)=ba+b2

The figure represents the area of the rectangle.

Step-by-step explanation:

Area of the rectangle  = l X b

where 'l' is the length of the rectangle and

'b' is the breadth.

Here the length of the rectangle = a + b + b

⇒ l = a + 2b

Also breadth, b = a

∴ The area would be l X b = a(a + 2b) = a² + 2ab

OPTION C is the answer.

2 apples

step-by-step explanation:

taking away equals subtraction. 6-4=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