Matthew bought 4 new compact discs at $16.99 each and a carrying case for $35.89. he paid 8 1/4% sales tax on his purchases. if matthew paid $112.42 total, determine if he paid the correct amount.

a. matthew paid $0.15 too little for his purchases.

b. matthew paid $0.16 too much for his purchases.

c. matthew paid $0.05 too much for his purchases.

d. matthew paid the correct amount for his purchases.

D. Matthew paid the correct amount for his purchases.

Step-by-step explanation:

($16.99 x 4) + $35.89 = $103.85 --cost of purchases

8.25% of $103.85 = $8.57 --sales tax

$103.85 + $8.57 = $112.42 --total cost

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3