On average one tank holds 108 gallons because 432.4 divided by 4 is 108.1. One half full tank would hold about 54 gallons (54.05 to be exact) because half of 108.1 gallons (a full tank) is 54.05 gallons.
1. Find the H.C.F. of 4x2y3 and 6xy2z.
Solution:
The H.C.F. of numerical coefficients = The H.C.F. of 4 and 6.
Since, 4 = 2 × 2 = 22 and 6 = 2 × 3 = 21 × 31
Therefore, the H.C.F. of 4 and 6 is 2
24.67 rounded to one significant figure would be 25.
Change in April's weight is -7
<em><u>Solution:</u></em>
Let the initial weight be "x"
April lost 5 pounds in her first week of college
First week = lost 5 pounds
Therefore, x - 5
Over the next three weeks she lost 3 pounds, gained 2 pounds, and then lost 1 pound
<em><u>Next three week:</u></em>
Lost 3 pound
Gained 2 pound
Lost 1 pound
<em><u>Therefore, weight after 4 weeks is given as:</u></em>
x - 5 - 3 + 2 - 1 = x -7
After 4 week, the weight is x - 7
<em><u>The change in April weight is given as:</u></em>
Weight after 4 week - initial weight = x - 7 - x = -7
Thus change in April's weight is -7 (Negative sign represents loss in weight )
-3x/4 + 9/4 = (1/2)^x + 1
-3x/4 - 2^-x = -5/4
(Using log rules)
㏑|-3x/4| - ㏑|2^-x| = ㏑|-5/4|
㏑|3x/4| - x㏑|2| = ㏑|5/4|
e^㏑|3x/4| - e^㏑|2|x = e^㏑|5/4|
|3x/4| - 2x = 5/4
|3x| - 8x = 5
|3x-8x| = 5
|-5x| = 5
|5x| = 5
x=1, -1
