A gift bag shaped like a rectangular prism has a volume of 1152 cubic inches. The dimensions of the gift bag in terms of its wid
th are shown. The height is greater than the width.
What are the dimensions of the gift bag?
length: in.
width: in.
height: in.
What are the dimensions of the gift bag?
length: in.
width: in.
height: in.
1 answer:
Answer:
- Given below.
Step-by-step explanation:
Gift bag is shaped in a rectangular prism.
<em> rectangular volume: length * width * height</em>
( 2w + 4 ) ( w ) ( 18 - w ) = 1152
( 2w² + 4w ) ( 18 - w ) = 1152
-2w³+32w² +72w = 1152
-2w³+32w² +72w - 1152 = 0
w = 16 , -6 , 6
w = 16 , 6
- length = ( 2w + 4 ) = 36 inch , 16 inch
- width = ( w ) = 16 inch , 6 inch
- height = ( 18 - w ) = 2 inch , 12 inch
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Answer: 
Note: to write the domain in interval notation, you'd write [-4,5]
if you need the domain in set-builder notation, then you'd write
------------------------------------------------------------------------------
Explanation:
The domain is the set of possible x input values. Look at the left most point (-4,-1). The x coordinate here is x = -4. This is the smallest x value allowed. The largest x value allowed is x = 5 for similar reasons, but on the other side of the graph.
So that's how I got (x is between -4 and 5; inclusive of both endpoints)
Writing [-4,5] for interval notation tells us that we have an interval from -4 to 5 and we include both endpoints. The square brackets mean "include endpoint"
Writing is the set-builder notation way of expressing the domain. The 
portion means "x is a real number"
Note: to write the domain in interval notation, you'd write [-4,5]
if you need the domain in set-builder notation, then you'd write
------------------------------------------------------------------------------
Explanation:
The domain is the set of possible x input values. Look at the left most point (-4,-1). The x coordinate here is x = -4. This is the smallest x value allowed. The largest x value allowed is x = 5 for similar reasons, but on the other side of the graph.
So that's how I got
Writing [-4,5] for interval notation tells us that we have an interval from -4 to 5 and we include both endpoints. The square brackets mean "include endpoint"
Writing