Rufus collected 100 pounds of aluminum cans to recycle. he plans to collect and additional 25 pounds each week. write the equation for the total pounds, p, of aluminum cans after w weeks. what does the slope and y-intercet represent? how long will it take rufus to collect 400 pounds of aluminum cans?

The equation for the total pounds P, of aluminum cans that can be collected after W weeks is P = 100 + 25W

Therefore, the equation for the total pounds,P, of aluminum cans that can be collected after W weeks will be:

= 100 + (25 × W)

P = 100 + 25W

The number of weeks that'll be taken to collect 400 pounds of aluminum cans will be:

P = 100 + 25W

400 = 100 + 25W

Collect like terms

25W = 400 - 100

25W = 300

W = 300/25

W = 12.

Therefore, Rufus will take 12 weeks to collect 400 pounds of aluminum cans.

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Slope represents that the weight of can increased by 25 pounds each week. Y-intercept represents initial weight of cans, i.e., 100 pounds.

The time taken by Rufus to collect 400 pounds of aluminum cans is 12 weeks.

Step-by-step explanation:

It is given that Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect and additional 25 pounds each week.

It means initial weight of cans = 100 pounds

Additional weight of cans = 25 pounds each week

Let W be the number of week.

The equation for the total pounds P of aluminum cans after W weeks is

          .... (1)

The slope intercept form of a line is

             .... (2)

where, m is slope and b is y-intercept.

From (1) and (2) we get

It means slope and y-intercept are 25 and 100 respectively.

Slope represents that the weight of can increased by 25 pounds each week. Y-intercept represents initial weight of cans, i.e., 100 pounds.

We need to find the time taken by Rufus to collect 400 pounds of aluminum cans.

Substitute P =400 in equation (1).

Subtract 100 from both sides.

Divide both sides by 25.

Therefore, the time taken by Rufus to collect 400 pounds of aluminum cans is 12 weeks.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total