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)

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation:

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

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