Question

What’s the answer for 1,3??

Answer 1

Part 1)
`\$227.25`

Part 2)

a) The graph in the attached figure

b) The cost of each extra line is $5.25

c) The cost of one line the same as the cost of four lines

Part 3)
`\$611`

Explanation:

Part 1)

Let

x ----> the number of lines in the ad

y ----> the cost to run the ad for one week

we know that

The total cost to place a 6-line ad for one week is equal to sum the cost for one line ($42) plus the cost of 5 additional extra line ($6.75 per extra line)

so

The linear equation that represent this situation is

`y=42+6.75(x-1)`

For x=6 lines

substitute

`y=42+6.75(6-1)`

`y=\$75.75` ----> this is the cost for one week

To find out the cost for three weeks multiply by 3

`\$75.75(3)=\$227.25`

Part 2) we have

`C(x)=35.50` when x≤ 4

`C(x)=35.50+5.25(x-4)` when x>4

where

x is the number of lines in the ad

C(x) the cost of a classified ad

Part a) Graph the function

we know that

In the interval [0,4] the graph is a horizontal line (constant) C(x)=35.50

In the interval (4,∞) the graph is the linear equation C(x)=35.50+5.25(x-4)

using a graphing tool

The graph in the attached figure

Part b) Find out the cost of each extra line

we have

`C(x)=35.50+5.25(x-4)`

For x=5

`C(x)=35.50+5.25(5-4)`

`C(x)=35.50+5.25(1)`

so

The cost of each extra line is $5.25

Part c) Is the cost of one line the same as the cost of four lines?

we know that

`C(x)=35.50` when x≤ 4

so

For one line x=1

For four lines x=4

Both values belong to the interval [0,4]

therefore

The cost of one line the same as the cost of four lines

Part 3) we know that

To find out the amount of sales tax multiply the total amount by the percentage of sales tax

Remember that

`6.5\%=6.5/100=0.065`

so

`\$9,400(0.065)=\$611`