Suppose that the functions f and g are defined for all real numbers x as follows.
1 answer:
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<u>Answer-</u>
Set of constraints to model the problem are,
<u>Solution-</u>
<em>x = the number of lawns weeded by Gwen,</em>
<em>y = the number of dogs walked by Fabio.</em>
1.
As, Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,
They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.
The equation for this is,
2.
The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means
y must be less than or equal to 2x.
The equation for this is,
3.
Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.
The equation for this is,
Given dimensions of a rectangular garden are:
length = 2(x+6) feet
width = 3.5x feet
using the distributive property on length we get, length = 2x+12
Perimeter of a rectangle is 2(length+width)
So, P = 2(2x+12+3.5x)
Solving it we get,
P = 2(5.5x +12) ..............adding like terms
P = .............multiplying and adding
P = 11x+24
So, perimeter is 11x+24 feet. This value of fencing will be needed.