Algebra- Linear Functions?

Question

Task: By the Book

Question # 1:

After experimenting with the different weights of paper, you discover that 100 sheets of paper averages 1.25 cm thick. 

A) What is the unit rate for sheets of paper per centimeter? Explain how you know.

B) Based on the request, determine if the variables in the relationship are proportional. Explain how you know.

C) Complete the table for manuscripts from 0 to 500 in 50 page intervals; use the variable "t" for thickness in cm and the variable "p" for the total pages.


Question # 2: 
Rachel take care of homes during the summer while their owners are away on vacation. She charges $8, plus $2.50 a day.

A) Create chart that shows the charges when the owners are away for up to 5 days. C dollars, to the number of days, n,

B) Write an equation that relates the charge, that the owners are away.

C) What will the charge be when the owners are away for 14 days? Show the math to prove your answer.

D) How many days were the owners away when the charge was $33?

Question # 3:
Shirley has $540 in her bank account, She withdraws $35 each week to cover her expenses.

A)Write an equation that relates the amount of money in her account, "d" dollars, after "n" weeks.

B) Determine the amount of money in Shirley's account after 8 weeks.

C) What will Shirley have in her account at the close of one full year?

Ben · Accepted Answer

A) Set a proportion to find the unit rate of sheets per paper:

1.25 cm / 100 sheets = 1 cm/ x sheets

x = 1 * 100 / 1.25 = 80 sheets

B) based on the fact that we can find a constant rate of sheets of paper per thickness, you know that the number of sheets is proportional to the weight.  That is, we can always say that if you have x sheets of thickness y, then
x/y = 80 sheets / 1 cm

C)
take the numbers 0, 50, 100, ..., 500 and divide by 80 to find the thickness in cm of each number of pages.

2
B) 
C = $8 + $2.50*n

C)
8 + 14 * $2.50 = $8 + $35 = $43

$33 = 8 + $2.50*n
$25 = $2.50 * n
n = $25/$2.50 = 10

3
A)
d = $540 - $35*n

B)
d = $540 - $35*8 = ?

C)
d = $540 - $35*52 = ?
the answer to the above is negative, which means that at some point, she ran out of money (since you can't have a negative amount in your bank account).  If she ran out of money, she has no money ($0) left.

rhum · Answer

Open question instruct me yet another » college Algebra linear function HEELLPPPP? ok so homework difficulty I also have a table with right here factors--- (-3, -a million.sixty 5) (6, -a million.2) (15, -0.seventy 5) (24, -0.3) and that i'd desire to take those factors and write a linear function in the type f(x)=mx+b the place m is the slope and b is the y-intercept. So I calculated slope to be equivalent between all 4 factors and it got here out to be valuable 0.05. i'm having hassle calculating the y-intercept??? the thank you to try this?? I did graph it and located a coarse estimate of y-intercept to be aproximately -a million.5. Is that the thank you to define out?? Is -a million.5 the appropriate answer?? 4 minutes in the past - 4 days left to respond to.

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Algebra- Linear Functions?

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