Equation if the line for the graph is
y = -2x+1
Answer:
Step-by-step explanation:
This is good! The length of the metal is 20 inches longer than the width. But we fold up 4-inch flaps on each side, so the height of the box is 4 inches, and the length and width will each decrease by 8 inches (4 inches on each side). Since the length and width decrease by the same amount, the length will still be 20 inches longer than the width. So the equations would be:
l = w + 20
vol = l x w x h = 1716 in3
1716 = (w + 20)(w)(4)
1716 = 4w2 + 80w
4w2 + 80w - 1716 = 0
4(w2 + 20w - 429) = 0
4(w + 33)(w - 13) = 0
w + 33 = 0, so w = -33
w - 13 = 0, so w = 13
Since the width can't be negative, the width of the box is 13 and the length is 33 (13 + 20).
But remember, the length and width of the piece of metal are each 8 inches longer than the box, so it was 41 inches by 21 inches.
So for this question (for finding x and y) you will want to use elimination. To do this you will need to bring the x and y to the same side (I put them on the left):
-3/2x+y=6
x+y=0
Now subtract the y on the bottom from the top to isolate x:
3/2x=6
Now the easiest way to bring over the 3/2 to isolate the x fully is to convert it to decimal (1.5) and divide it by 6 (because when multiplication on one side of problem the only way to bring it over is to divide):
x=6/1.5
which simplifies to:
x=4
Hope this helps!
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