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Enrico spends $204 to buy packages of cleaning materials for an event

Enrico spends 204 dollars to buy packages of cleaning materials for an event. He buys T packages of towels. Each package is 4 dollars and contains 6 towels. He also buys S packages of soap; each package is 6 dollars and contains 10 bars of soap.

Enrico buys 20 packages of cleaning materials altogether.

Write a system of two equations to represent the packages of cleaning materials Enrico buys.

Find a polynomial function or equation that represents the perimeter of a rectangle

Find a polynomial function or equation that represents the perimeter of a rectangle that has a length of 2x - 3 and a width of x + 2.
Number: 

The perimeter of a rectangle is expressed by the formula P = 2L + 2W where P is the perimeter, L is the length and W is the width.

Given the length 2x - 3 and width x + 2, the perimeter then is:

P = 2L + 2W
P = 2(2x - 3) + 2(x + 2)
P = 4x - 6 + 2x + 4

Combining like terms and simplifying:

P = 4x + 2x - 6 + 4
P = 6x - 2

Therefore, the polynomial function or equation that represents the perimeter of a rectangle is:

P(x) = 6x - 2

When a plane flies with the wind it can travel 4200 miles in 6 hours.

When a plane flies with the wind it can travel 4200 miles in 6 hours. When the plane flies in the opposite direction, or against the wind, it takes 7 hours.

Find the speed or rate of the plane and the speed or rate of the wind.

Duration: 
expired

Suppose that in 2003 ,certain groups contributed $273 million to federal candidates

Suppose that in 2003, certain groups contributed USD273 million to federal candidates. In 2008, the figure rose to USD386.4 million. Assume that A(t) represent the amount of contributions, in millions, and t the number of years since 2000.

Find a liner function that models the data.

Duration: 
expired

The sum of three numbers is 134. If the third number is 4 times the first

Here is a number problem. If the sum of three numbers is 134, and the third number is 4 times the first, and the first number is 8 less than the second, what are the numbers? Please explain the answer.
Number: 

Assumptions:

x = the second number
x - 8 = the first number
4(x - 8) = third number

Given: Total is 134

first + second + third = 134
x - 8 + x + 4(x - 8) = 134

Simplifying gives:
x - 8 + x + 4x - 32 = 134

Adding like terms:
6x - 40  = 134
6x = 134 + 40
6x = 174
x = 29 => second number

First number =>  x - 8
29 - 8 = 21

Third number => 4(x - 8)
4(29 - 8) = 4(21) = 84

Therefore:
First number => 21
Second number => 29
Third number => 84
 
TOTAL = 21 + 29 + 84 = 134



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