Richard is building a rectangular backyard from 360 feet of fencing. the fencing must cover three sides of the backyard (the fourth side is bordered by richard's house). what is the maximum area of this backyard?

  16200 ft²

Step-by-step explanation:

The maximum area is obtained when half the fence is parallel to the house, and the other half is used for the ends of the rectangle. The resulting area will be 180 ft long by 90 ft wide, or ...

  (180 ft)(90 ft) = 16200 ft²

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Let x represent the length of the fence parallel to the house. Then the ends of the rectangular backyard will have length (360-x)/2, and the total area will be ...

  A = x(360 -x)/2

This describes a parabola opening downward with zeros at x=0 and x=360. The vertex is halfway between the zeros, at x = 180. This is the value of x that gives the maximum area.

attachment?

step-by-step explanation:

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!