The penny size of a nail indicates the length of the nail. the penny size d is given by the literal equation d=4n−2, where n is the length (in inches) of the nail. a. solve the equation for n. b. use the equation from part (a) to find the lengths of nails with the following penny sizes: 3, 6, and 10.

In this question ,it is given that

The penny size of a nail indicates the length of the nail. The penny size

d is given by the literal equation

where n is the length (in inches) of the nail.

In the first part we have to solve for n .

And for that firt we add 2 to both sides

Now we divide both sides by 4, that is

Part b.

When d=3

When d =6, we will get

When d =10, we will get

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)