Suppose you invest $750.00 in a fund earning 6% simple discount. a certain time later you withdraw the investment (principal and interest) and invest it in another fund earning 3.5% compound interest for two years. how much total time (including the two years earning compound interest) will be required for the original $750.00 to accumulate to $1,000.00? (two decimal places)

4.08 + 2 = 6.08 years

Step-by-step explanation:

we know that

Simple Interest(S.I.) = (P × R × T) ÷ 100

where, P = Principal = 750

R = Rate = 6%

T = unknown

⇒ S.I. = (750 × 6 × t)÷ 100

⇒ S.I. = 45t

Also, Amount = S.I + Principal

⇒ Amount = 750 + 45t

Now Formula for Compound Interest is:

where A = Amount

=1000

P = Principle

r = rate

t = total number of year

Here, P = 750 + 45t, r = 3.5% , and t = 2.

Putting all these values in above formula:

⇒

⇒ t = 4.08

Hence, total time required will be 2 + 4.08 = 6.08 years.

(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