This breaks down into a system of equations. George will equal G, Sam will equal S and Alex will equal A. G=S+2 S=A+3 G+S+A=35 since S=A+3, we can substitute S for (A+3). If we plug that into the G=S+2, we get G=(A+3)+2. This simplifies to G=A+5.
our ultimate goal is to be able to substitute for two of their ages so we can solve the last equation for one age or variable. It would be easiest to solve for A.
so far we can substitute for two variables, S=A+3. and G=A+5
Next, we can plug this into the last equation and get 35=(A+3)+(A+5)+A
if we add like terms we get 35=3A+8. Next, we solve the equation by first subtracting 8 from each side. we then get 27=3A, then we divide each side by 3 to solve for A and get A=9.
Now we have one age, we need to find the other two. We can solve this by plugging A to the other two equations. if we do that we get S=(9)+3, or S=12. If we do it to the other equation we get G=(9)+5, or G=14
So your final answer would be George is 14, Sam is 12, and Alex is 9.
Answer:
Step-by-step explanation:
Area of the shaded region = Area of the square with side 25 ft - Area of the semicircle with radius (25/2) = 12.5 ft.
A /explanation bc I see no reason for the answer to have a - so I believe it’s A sorry if it’s wrong
first off, let's check what's the slope of that line through those two points anyway
now, let's take a peek of what is the slope of that equation then
![\bf y=\cfrac{(4+k)x-6}{5}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{(4+k)}{5}} x-\cfrac{6}{5}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{since both slopes are the same then}}{\cfrac{4+k}{5}=2\implies 4+k=10}\implies \blacktriangleright k=6 \blacktriangleleft](https://tex.z-dn.net/?f=%5Cbf%20y%3D%5Ccfrac%7B%284%2Bk%29x-6%7D%7B5%7D%5Cimplies%20y%3D%5Cstackrel%7B%5Cstackrel%7Bm%7D%7B%5Cdownarrow%20%7D%7D%7B%5Ccfrac%7B%284%2Bk%29%7D%7B5%7D%7D%20x-%5Ccfrac%7B6%7D%7B5%7D%5Cqquad%20%5Cimpliedby%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20slope-intercept~form%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y%3D%5Cunderset%7By-intercept%7D%7B%5Cstackrel%7Bslope%5Cqquad%20%7D%7B%5Cstackrel%7B%5Cdownarrow%20%7D%7Bm%7Dx%2B%5Cunderset%7B%5Cuparrow%20%7D%7Bb%7D%7D%7D%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsince%20both%20slopes%20are%20the%20same%20then%7D%7D%7B%5Ccfrac%7B4%2Bk%7D%7B5%7D%3D2%5Cimplies%204%2Bk%3D10%7D%5Cimplies%20%5Cblacktriangleright%20k%3D6%20%5Cblacktriangleleft)
