Rewrite x2 − 8x + 13 = 0 in the form (x − a)2 = b, where a and b are integers, to determine the a and b values. a = 4 and b = 3
2 answers:
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Answer: max capacity is 1625 gallons.
Diagram is shown below.
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Explanation:
We'll draw two horizontal number lines to help make a comparison or connection between percentages and tank capacity.
For the top number line, make 5 sections with the labels: 0%, 20%, 40%, 60%, 100%. The reason I'm picking 5 is because 40% = 40/100 = 2/5. So having 40% capacity means we're 2/5 full. That denominator 5 tells us how to subdivide each number line.
The bottom number line will also have 5 sections. We only know one label for this bottom portion right now. That label is 650. Place this directly under the "40%". This visually is one way to represent that 650 gallons is 40% filled. See the diagram below.
Cut the 650 in half to get 325. This corresponds to 40% cut in half to get 20%. Therefore, 325 will go under the 20%. Being 20% full means we have 325 gallons of water.
To figure out the 60% portion, we will multiply 325 by 3. This is because 3*20% = 60%, so 3*325 = 975. We'll write "975 gallons" under the "60%"
Then we have 1300 gallons under the 80% since 4*325 = 1300. Note how 4*20% = 80%, so that's where the '4' multiplier comes from.
Finally, we multiply 325 by 5 to get 1625 and that represents the full tank's capacity. Technically we could have just jumped to this directly without having to find the 60% or 80% capacity values, but it's good practice I think.
Again the diagram is shown below. The answer we're after is at the very bottom right corner. It's under the 100% to indicate the tank is completely full, or has reached max capacity.
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Here's a way to find the answer without a double number line. This method involves setting up a proportion.
(40% full)/(650 gallons) = (100% full)/(x gallons)
40/650 = 100/x
40x = 650*100
40x = 65000
x = 65000/40
x = 1625
We confirm that the tank's max capacity is 1625 gallons.
