The least common multiple of 5 and 12 is 60.
something noteworthy, the y-coordinate for each point is the same, 9⅛, that means is a horizontal line, over which the x-coordinates are at, so since it's a horizontal line, all we need to do is find, what's the distance between 
of course, let's firstly convert the mixed fraction to improper fraction and then check their difference.
![\bf \stackrel{mixed}{5\frac{7}{10}}\implies \cfrac{5\cdot 10+7}{10}\implies \stackrel{improper}{\cfrac{57}{10}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2}{5}-\left[-\cfrac{57}{10} \right]\implies \cfrac{2}{5}+\cfrac{57}{10}\implies \stackrel{\textit{using the LCD of 10}}{\cfrac{(2)2+(1)57}{10}}\implies \cfrac{4+57}{10}\implies \cfrac{61}{10}\implies 6\frac{1}{10}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B5%5Cfrac%7B7%7D%7B10%7D%7D%5Cimplies%20%5Ccfrac%7B5%5Ccdot%2010%2B7%7D%7B10%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B57%7D%7B10%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B2%7D%7B5%7D-%5Cleft%5B-%5Ccfrac%7B57%7D%7B10%7D%20%5Cright%5D%5Cimplies%20%5Ccfrac%7B2%7D%7B5%7D%2B%5Ccfrac%7B57%7D%7B10%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20LCD%20of%2010%7D%7D%7B%5Ccfrac%7B%282%292%2B%281%2957%7D%7B10%7D%7D%5Cimplies%20%5Ccfrac%7B4%2B57%7D%7B10%7D%5Cimplies%20%5Ccfrac%7B61%7D%7B10%7D%5Cimplies%206%5Cfrac%7B1%7D%7B10%7D)
Answer:
The ball will be at 100 feet at time x=0.5 sec and at time x=7.5 sec
Step-by-step explanation:
<u><em>The correct question is</em></u>
A ball is launched upward from a height 40 feet above ground level. the ball's height at t seconds is given by h(t)=-16t^2+128t+40 At what time(s) will the ball be at 100 feet?
we have

so
For h(t)=100 ft
substitute in the equation and solve for x


The formula to solve a quadratic equation of the form
is equal to
in this problem we have

so
substitute in the formula
therefore
The ball will be at 100 feet at time x=0.5 sec and at time x=7.5 sec