Question 70028: 1. A parking lot has a perimeter of 600 ft. the width is 30 ft less than the length. find the dimensions of the parking lot.
2. Solve and write in interval notation for the solution set
-5 <_ 2x + 1 < 7
Answer by tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! 1. Use the formula for a perimeter:
Perimeter = 2(Length + Width)
P=2(L+w)
P=600
L=L
w=L-30
.
P=2(L+w)
600=(2(L+(L-30)) [plug-in the values]
600=2(2L-30) [simplify]
600/2=2(2L -30)/2
300=2L-30
300+30=2L-30+30
330=2L
330/2=2L/2
165=L
.
Since the Width = Length -30,
Than, Width = 165-30=135
.
Check by plugging-in all of the values back into the original formula:
P=2(L+w)
600=2(165+135)
600=2(300)
600=600 [checks out]
.
.
2. Solve and write in interval notation for the solution set
-5 <_ 2x + 1 < 7[isolate the x variable]
-5-1 <_ 2x + 1-1 < 7-1
-6 <_ 2x < 6
-6/2 <_ 2x/2 < 6/2
-3 <_ x < 3
.
[-3, 3)
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