He would walk 2.125 miles or 2 1/8 miles in one hour
Answer: b, d
Step-by-step explanation:
Corresponding angles are formed when two parallel straight lines are cut by a transversal
![\angle b=62^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20b%3D62%5E%7B%5Ccirc%7D)
In the figure,
are alternate angle
![\therefore \angle d=62^{\circ}](https://tex.z-dn.net/?f=%5Ctherefore%20%5Cangle%20d%3D62%5E%7B%5Ccirc%7D)
To solve this problem you must apply the proccedure shown below:
1. Clear the radius from the formula for the circumference of a circle and substitute values, as following:
![C=2\pi r\\ r=C/2\pi \\ r=37.699in/2\pi \\ r=5.99in](https://tex.z-dn.net/?f=%20C%3D2%5Cpi%20r%5C%5C%20r%3DC%2F2%5Cpi%20%5C%5C%20r%3D37.699in%2F2%5Cpi%20%5C%5C%20r%3D5.99in%20)
2. Substitute the radius calculated into the formula for calculate the surface area of the sphere:
![SA=4\pi r^{2} \\ SA=4\pi(5.99in^{2})\\ SA=450.88in^{2}](https://tex.z-dn.net/?f=%20SA%3D4%5Cpi%20r%5E%7B2%7D%20%5C%5C%20SA%3D4%5Cpi%285.99in%5E%7B2%7D%29%5C%5C%20SA%3D450.88in%5E%7B2%7D%20%20)
The answer is: ![450.88in^{2}](https://tex.z-dn.net/?f=%20450.88in%5E%7B2%7D%20%20)
Answer: Cost of a tray of club sandwiches is $49 and Cost of a tray of vegetarian sandwiches is $70.
Step-by-step explanation:
Since we have given that
![\begin{bmatrix} 7&10 \\ 0& 1\end{bmatrix}\begin{bmatrix}c \\ v\end{bmatrix}=\begin{bmatrix}149 \\ 10\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%207%2610%20%5C%5C%200%26%201%5Cend%7Bbmatrix%7D%5Cbegin%7Bbmatrix%7Dc%20%5C%5C%20v%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7D149%20%5C%5C%2010%5Cend%7Bbmatrix%7D)
since we know the formula for "System of linear of equation of matrix"
i.e.
![AX=B\\\\Here,\\\\A=\begin{bmatrix} 7&10 \\ 0& 1\end{bmatrix}\\\\X=\begin{bmatrix}c \\ v\end{bmatrix}\\\\B=\begin{bmatrix}149 \\ 10\end{bmatrix}](https://tex.z-dn.net/?f=AX%3DB%5C%5C%5C%5CHere%2C%5C%5C%5C%5CA%3D%5Cbegin%7Bbmatrix%7D%207%2610%20%5C%5C%200%26%201%5Cend%7Bbmatrix%7D%5C%5C%5C%5CX%3D%5Cbegin%7Bbmatrix%7Dc%20%5C%5C%20v%5Cend%7Bbmatrix%7D%5C%5C%5C%5CB%3D%5Cbegin%7Bbmatrix%7D149%20%5C%5C%2010%5Cend%7Bbmatrix%7D)
Now, we will solve it :
![\begin{bmatrix}c \\\\ v\end{bmatrix}=\begin{bmatrix} 7&10 \\\\ 0& 1\end{bmatrix}^{-1}\begin{bmatrix}149 \\\\10\end{bmatrix}\\\\\begin{bmatrix}c \\\\ v\end{bmatrix}=\frac{1}{\det \begin{pmatrix}7&10\\ 0&1\end{pmatrix}}\begin{pmatrix}1&-10\\ -0&7\end{pmatrix}\begin{bmatrix}149 \\\\10\end{bmatrix}=\frac{1}{7}\begin{pmatrix}1&-10\\ -0&7\end{pmatrix}\begin{bmatrix}149 \\\\10\end{bmatrix}=\begin{bmatrix} 1&-10 \\\\ 0& 7\end{bmatrix}\begin{bmatrix}149 \\\\10\end{bmatrix}\\\\\begin{bmatrix}c \\\\v\end{bmatrix}=\begin{bmatrix}149-100\\\\70\end{bmatrix}\\\\\begin{bmatrix}c \\\\v\end{bmatrix}=\begin{bmatrix}49\\\\70\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dc%20%5C%5C%5C%5C%20v%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7D%207%2610%20%5C%5C%5C%5C%200%26%201%5Cend%7Bbmatrix%7D%5E%7B-1%7D%5Cbegin%7Bbmatrix%7D149%20%5C%5C%5C%5C10%5Cend%7Bbmatrix%7D%5C%5C%5C%5C%5Cbegin%7Bbmatrix%7Dc%20%5C%5C%5C%5C%20v%5Cend%7Bbmatrix%7D%3D%5Cfrac%7B1%7D%7B%5Cdet%20%5Cbegin%7Bpmatrix%7D7%2610%5C%5C%200%261%5Cend%7Bpmatrix%7D%7D%5Cbegin%7Bpmatrix%7D1%26-10%5C%5C%20-0%267%5Cend%7Bpmatrix%7D%5Cbegin%7Bbmatrix%7D149%20%5C%5C%5C%5C10%5Cend%7Bbmatrix%7D%3D%5Cfrac%7B1%7D%7B7%7D%5Cbegin%7Bpmatrix%7D1%26-10%5C%5C%20-0%267%5Cend%7Bpmatrix%7D%5Cbegin%7Bbmatrix%7D149%20%5C%5C%5C%5C10%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7D%201%26-10%20%5C%5C%5C%5C%200%26%207%5Cend%7Bbmatrix%7D%5Cbegin%7Bbmatrix%7D149%20%5C%5C%5C%5C10%5Cend%7Bbmatrix%7D%5C%5C%5C%5C%5Cbegin%7Bbmatrix%7Dc%20%5C%5C%5C%5Cv%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7D149-100%5C%5C%5C%5C70%5Cend%7Bbmatrix%7D%5C%5C%5C%5C%5Cbegin%7Bbmatrix%7Dc%20%5C%5C%5C%5Cv%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7D49%5C%5C%5C%5C70%5Cend%7Bbmatrix%7D)
Hence Cost of a tray of club sandwiches is $49 and Cost of a tray of vegetarian sandwiches is $70.
3.45
5.48
1.07
+1.50
----------
11.50