1. COST Mr. Rivera wants to purchase a riding lawn

mower, which is on sale for 15% off the marked price.

The store charges sales tax 6.5% on all sales. Write a

function p(x) that represents the price after a 15%

discount. Write a function t(x) that represents the total

cost with sales tax. Write a composition of functions that

represents the total cost of a riding lawn mower on sale.

How much will Mr. Rivera pay for a riding lawn mower

that has a marked price of $3000?

Mr. Rivera would pay $2715.75 for a riding lawn mower  that has a marked price of $3000

Let x represent the marked price. Let P(x) represent the price after a 15% discount and T(x) represents the total  cost with sales tax.

P(x) = x - 15% of x

P(x) = 0.85x

T(x) = P(x) + tax = P(x) + 6.5% of P(x)

T(x) = 0.85x + 0.05525x

T(x) = 0.90525x

For a marked price of $3000:

T(3000) = 0.90525(3000) = $2715.75

Mr. Rivera would pay $2715.75 for a riding lawn mower  that has a marked price of $3000

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p(x) = 0.85x

t(x) = 1.065x

(t o p)(x) = 0.9x

$2700

Step-by-step explanation:

If the marked price is $x, then the function p(x) that gives the price of the riding lawn mower after 15% discount will be

where x is the marked price.

Now, the function that gives the total cost with sales tax will be given by

where x is the discounted price.

Therefore, the composite function that gives the total cost of the riding lawn mower on sale is given by

(t o p)(x) = 1.065(0.85x) = 0.9x ............ (1)

where x is the marked price.

If the marked price x = $3000, then Mr. Rivera has to pay for the riding lawn mower, from equation (1),

(t o p)(3000) = 0.9 × 3000 = 2700 dollars. (Answer)

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.