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
Given that the two cone are similar, then
3/7 = x/5
7x = 15
x = 15/7
Answer:

Step-by-step explanation:

Find the sharing components:
<=> 
Apply the inverse of associative property:
<=> 
Identify two square components inside the parenthesis:
<=> 
Factorize:
<=> 
=> Option D is correct
Hope this helps!
:)
<em><u>The surface area of cylinder in standard form is:</u></em>

<em><u>Solution:</u></em>
Given that,
Radius of cylinder = 2x + 3 inches
Height of cylinder = 3 times radius = 3(2x + 3)
Height of cylinder = 6x + 9 inches
<em><u>The surface area of cylinder is given by formula:</u></em>

Where, "r" is the radius and "h" is the height of cylinder
<em><u>Substituting the given values we get,</u></em>

Thus the surface area of cylinder in standard form is found