The greatest common factor is 32
You need to use a ratio of height (H) to shadow length (L) to solve the first problem. It's basically a use of similar triangles, with two perpendicular sides, and with the shadow making the same angle with the vertical.
6 ft = 72 ins, so that rH/L = 72/16 = 9/2 for the player.
So the bleachers are 9/2 x 6 ft = 27 ft.
For the second problem, 9 ft = 108 in, so that the ratio of the actual linear dimensions to the plan's linear dimensions are 9ft/(1/2in) = 2 x 108 = 216.
So the stage will have dimensions 216 times larger than 1.75" by 3".
That would be 31ft 6ins x 54ft.
Live long and prosper.
Answer:
![\left[\begin{array}{cccc}-12&-13&13&|15\\7&-10&-3&|11\\7&14&5&\:\:\:|-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-12%26-13%2613%26%7C15%5C%5C7%26-10%26-3%26%7C11%5C%5C7%2614%265%26%5C%3A%5C%3A%5C%3A%7C-5%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The system of equations is;
-12x-13y +13z =15
7x-10y-3z = 11
7x+14y +5z = -5
The coefficient matrix is ![\left[\begin{array}{ccc}-12&-13&13\\7&-10&-3\\7&14&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-12%26-13%2613%5C%5C7%26-10%26-3%5C%5C7%2614%265%5Cend%7Barray%7D%5Cright%5D)
The constant matrix is ![\left[\begin{array}{c}15\\11\\-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D15%5C%5C11%5C%5C-5%5Cend%7Barray%7D%5Cright%5D)
The augmented matrix is
Let T be total of money earned and W= number of windows washed
T=4W
