9514 1404 393
Answer:
(x1, x2) = (3, -4)
Step-by-step explanation:
As with any 2-step linear equation, subtract the constant, then multiply by the inverse of the coefficient of the variable.
![\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]+\left[\begin{array}{c}1\\2\end{array}\right]=\left[\begin{array}{c}2\\-3\end{array}\right]\\\\\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}1\\-5\end{array}\right]\\\\\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{5}\left[\begin{array}{cc}5&-2\\-5&3\end{array}\right]\left[\begin{array}{c}1\\-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%262%5C%5C5%265%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C2%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%262%5C%5C5%265%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C-5%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cdfrac%7B1%7D%7B5%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26-2%5C%5C-5%263%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C-5%5Cend%7Barray%7D%5Cright%5D)
Performing the multiplication of the matrix by the vector gives the solution.
x = ((5)(1) +(-2)(-5))/5 = 15/5 = 3
y = ((-5)(1) +(3)(-5))/5 = -20/5 = -4
Using your variables, x1, x2, the solution is ...
(x1, x2) = (3, -4)
Answer:
y=6.2 and x=0.4 or (0.4,6.2)
Step-by-step explanation:
Since both expressions are equal to y, we can set them equal to each other and solve for x:
3x+5=8x+3
5=5x+3
2=5x
2/5=x
0.4=x
Now to solve y:
y=8(2/5)+3
y=16/5+3
y=3.2+3
y=6.2
Check answers:
6.2=3(0.4)+5
6.2=1.2+5
6.2=6.2
6.2=8(0.4)+3
6.2=3.2+3
6.2=6.2
Answers work, so y=6.2 and x=0.4 or (0.4,6.2) as an ordered pair
The distance traveled in 1 roation is assumed to be the circumferece
c=2pir
in 13 rotations
13 times 2pir=26pir=distance traveled for 13 revolutions
r=13
d=26pi13
d=338pi
using 3.14 for pi
d=1061.32 inches
Answer:
4 gallons
Step-by-step explanation:
80/5 will give you 16 so for each gallon the car can move 16 milles
so 64/16 = 4 so he will need 4 gallons of gas in order make the trip
