Verify that the vector X is a solution of the given homogeneous system. dx / dt = 3x − 3y
dy /dt = 3x − 7y;
X = (1 /3) e^−6t

Writing the system in the form X' = AX for some coefficient matrix A, one obtains the following:

X'= [ ] X

Atruck can be rented from company a $50 a day plus $0.60 per mile. company b charges $20 a day plus $0.80 per mile to rent the same truck. find the number of miles in a day at which the rental costs for company a and company b are the same

Leslie started last week with $1200 in her checking account. during the week, she wrote the checks below. trans typ./ check no. date description of transaction payment/ debit deposit/ credit (+) balance 1,200 00 324 10/6 miller's food market 45.87 45 87 groceries 1,154 13 325 10/7 cyber center computer outlet 218.59 218 59 monitor 935 54 326 10/9 sandy's beauty salon 30.00 30 00 haircut and styling 900 59 deposit 10/10 paycheck 621.33 621 33 1,621 92 evaluate leslie's check register. a. leslie did a good job. everything is correct. b. the final balance is wrong; she did not add everything correctly. c. leslie should have written debit instead of deposit for the transaction type. d. leslie switched the debit and credit columns.

Amoving truck rental costs a flat fee of $75 and $2 per mile driven. if you drive a moving truck for 10 miles, how much is the rental for the moving truck?