Answer:
A. 2·x² + 16·x + 32 ≥ 254
Step-by-step explanation:
The given dimensional relationship between the dimensions of the photo in the center of the cake and the dimensions of the cake are
The width of the cake = The width of the photo at the center of the cake, x + 4 inches
The length of the cake = 2 × The width of the cake
The area of the cake Wanda is working on ≥ 254 in.²
Where 'x' represents the width of the photo (at the center of the cake), let 'W' represent the width of the cake, let 'L' represent the length of the cake, we get;
W = x + 4
L = 2 × W
Area of the cake, A = W × L ≥ 254
∴ A = (x + 4) × 2 × (x + 4) = 2·x² + 16·x + 32 ≥ 254
The inequality representing the solution is therefore;
2·x² + 16·x + 32 ≥ 254
edit; found the wrong thing lol
Working out the expression 7(3ˣ) is first to calculate the value of 3ˣ then multiply the answer to 7.
For example, let x = 2
Then 7(3ˣ) = 7(3²) = 7 × 9 = 63
With the same value of x = 2, calculating 21ˣ = 21² = 441, which isn't the same answer with the expression 7(3ˣ)
Complete question:
Rich is comparing the cost of maintaining his car with the depreciation value of the car.
The value starts at $20,000 and decreases by 15% each year. The maintanance cost is $500 the first year and increases by 28% per year.
When will the maintenance cost and the value be the same.
Answer:
9 years
Step-by-step explanation:
Depreciation is modeled by an exponential function :
A = p(1 - r)^t [decrease, '-']
A = 20,000(1 - 0.15)^t
A = 20000(0.85)^t - - - (1)
Maintainace cost :
A = p(1 + r)^t ; [increase, '+']
A = 500(1 + 0.28)^t
A = 500(1.28)^t - - - (2)
Equating (1) and 2
20000(0.85)^t = 500(1.28)^t
1.28^t / 0.85^t = 20000/500
(1.28 / 0.85)^t = 40
Take log of both sides
Log (1.28 / 0.85)^t = log 40
t * 0.1777910 = 1.6020599
t = 1.6020599 / 0.1777910
t = 9.01
t = 9 years
