Problem 37
<h3>Answer: B. 4 & 1/4 gallons</h3>
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Work Shown:
The 3/4 and 1/2 add up to (3/4)+(1/2) = (3/4)+(2/4) = 5/4 = 1&1/4
The whole part 1 is then added to the other whole parts 1 and 2 to get 1+2+1 = 4
Overall, the grand total is 4 & 1/4
An alternative way is to convert each mixed number to a decimal to get 1&1/2 = 1+1/2 = 1+0.5 = 1.5 and 2&3/4 = 2+3/4 = 2+0.75 = 2.75
Add up those decimals 1.5+2.75 = 4.25
then convert that result to a mixed number: 4.25 = 4+0.25 = 4+1/4 = 4&1/4
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Problem 38
<h3>Answer: C. Cubic feet</h3>
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The units for volume follow the template "Cubic _____" where you'll write "feet", "inches", "centimeters" or whatever unit you are using in the blank.
Some other examples:
* cubic miles
* cubic meters
* cubic yards
Answer:
What picture?
Step-by-step explanation:
-3x^2 + 2y^2 = 10
2y^2 = 10 + 3x^2
y^2 = 5 + 3/2x^2
distance between two points is given by
d = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((x - 4)^2 + (y - 0)^2) = sqrt((x - 4)^2 + y^2) = sqrt((x - 4)^2 + 5 + 3/2x^2)
For d to be minimum (closest), dd/dx = 0
(2(x - 4) + 3x)/2sqrt((x - 4)^2 + 5 + 3/2x^2) = 0
2(x - 4) + 3x = 0
2x - 8 + 3x = 0
5x = 8
x = 8/5 = 1.6
y^2 = 5 + 3/2(1.6)^2 = 5 + 3/2(2.56) = 221/25
y = sqrt(221/25) = 2.97
Therefore, the required point is (1.6, 2.97)
The next score is 90 because 85+91+92+92=360/4= 90 average.