Answer:
Part one: The function rule for the area of the rectangle is A(x) = 3x² - 2x
Part two: The area of the rectangle is 8 feet² when its width is 2 feet
Step-by-step explanation:
Assume that the width of the rectangle is x
∵ The width of the rectangle = x feet
∵ The length of the rectangle is 2 ft less than three times its width
→ That means multiply the width by 3, then subtract 2 from the product
∴ The length of the rectangle = 3(x) - 2
∴ The length of the rectangle = (3x - 2) feet
∵ The area of the rectangle = length × width
∴ A(x) = (3x - 2) × x
→ Multiply each term in the bracket by x
∵ A(x) = x(3x) - x(2)
∴ A(x) = 3x² - 2x
∴ The function rule for the area of the rectangle is A(x) = 3x² - 2x
∵ The rectangle has a width of 2 ft
∵ The width = x
∴ x = 2
→ Substitute x by 2 in A(x)
∵ A(2) = 3(2)² - 2(2)
∴ A(2) = 3(4) - 4
∴ A(2) = 12 - 4
∴ A(2) = 8
∴ The area of the rectangle is 8 feet² when its width is 2 feet
Answer:
The factorised term is:

Step-by-step explanation:
We are asked to factor the algebraic expression given as:

Now we will take out the variable which is common among all the terms and write the remaining expression in parantheses.
As
is common among all the terms hence we write this term out of the parantheses and the remaining term inside it as to obtain then simplified expression as:

Answer:
The answer to this question can be defined as follows:
In part (i), the answer is "option d".
In part (ii), the answer is "option 2".
Step-by-step explanation:
Given:
Part (a)

Solve the above equation:

Given:
Part (b)

Solve the above equation:
factor of 

apply limit value:

Recall your d = rt, distance = rate * time.
keeping in mind that, the distance upstream as well as downstream is the same, 90 miles, let's say the boat has a speed rate of "b", thus when the boat was going upstream, it really wasn't going "b" fast, it was going "b - 8", because the 8mph speed of the current is subtracting from it. Likewise, when the boat was going downstream, it wasn't going "b" fast either, because the current was adding to it, since it was going with the current, then it was really going "b + 8" fast.
now, let's notice the trip took a total of 6 hours, thus, if the trip downstream took say "t" hours, then the trip upstream took the slack from 6 and "t", that is, it took "6 - t" hours.


since the rate of speed wouldn't be a negative unit, then is not -2.