Please help me
you just need to form quadratic equations

The value of x is 6

Step-by-step explanation:

The formula of the area of the rectangle is A = l × w, where

In the rectangle ABCD

∵ AB = 2x cm

∴ l = 2x

∵ AD = x cm

∴ w = x

→ Use the formula of the area above to find its area

∵ A = 2x × x

∴ A = 2x²

∵ The area of the shaded region = 50 cm²

→ When the shaded region removed, then the remaining area is the

   unshaded region

∵ The area of unshaded region = 22 cm²

∵ The area the ABCD = area the shaded region + area unshaded region

∴ A = 50 + 22

∴ A = 72 cm²

→ Equate the two right side of A

∵ 2x² = 72

→ Divide both sides by 2

∴ x² = 36

→ Take √  for both sides

∴ x = 6

∴ The value of x is 6

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.

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